jsPrelude.js

/* eslint-disable max-lines-per-function */
/* eslint-disable no-undef */
/* eslint-disable strict */
/* eslint-disable no-unused-vars */

// Endo :: (a -> a) -> Endo a
const Endo = f =>
    // An endofunction lifted into an Endo object.
    // A wrapper around an (a -> a) function, used as
    // the monoid of endomorphisms under composition.
    ({
        type: "Endo",
        appEndo: f
    });

// Just :: a -> Maybe a
const Just = x => ({
    type: "Maybe",
    Just: x
});

// Left :: a -> Either a b
const Left = x => ({
    type: "Either",
    Left: x
});

// Node :: a -> [Tree a] -> Tree a
const Node = v =>
    // Constructor for a Tree node which connects a
    // value of some kind to a list of zero or
    // more child trees.
    xs => ({
        type: "Node",
        root: v,
        nest: xs || []
    });

// Nothing :: Maybe a
const Nothing = () => ({
    type: "Maybe",
    Nothing: true
});

// Ratio :: Integral a => a -> a -> Ratio a
const Ratio = a => b => {
    const go = (x, y) =>
        0 !== y
            ? (() => {
                const d = gcd(x)(y);

                return {
                    type: "Ratio",
                    // numerator
                    "n": Math.trunc(x / d),
                    // denominator
                    "d": Math.trunc(y / d)
                };
            })()
            : undefined;

    return go(a * signum(b), abs(b));
};

// Right :: b -> Either a b
const Right = x => ({
    type: "Either",
    Right: x
});

// Tuple (,) :: a -> b -> (a, b)
const Tuple = a =>
    // A pair of values, possibly of
    // different types.
    b => ({
        type: "Tuple",
        "0": a,
        "1": b,
        length: 2,
        *[Symbol.iterator]() {
            for (const k in this) {
                if (!isNaN(k)) {
                    yield this[k];
                }
            }
        }
    });

// Tuple3 (,,) :: a -> b -> c -> (a, b, c)
const Tuple3 = a => b => c => ({
    type: "Tuple3",
    "0": a,
    "1": b,
    "2": c,
    length: 3,
    *[Symbol.iterator]() {
        for (const k in this) {
            if (!isNaN(k)) {
                yield this[k];
            }
        }
    }
});

// TupleN :: a -> b ...  -> (a, b ... )
const TupleN = (...args) => {
    // A Tuple of an arbitrary number of items.
    const n = args.length;

    return {
        ...args.reduce(
            (a, x, i) => ({
                ...a,
                [i]: x
            }),
            {
                type: 2 !== n
                    ? `Tuple${n}`
                    : "Tuple",
                length: n,
                *[Symbol.iterator]() {
                    for (const k in this) {
                        if (!isNaN(k)) {
                            yield this[k];
                        }
                    }
                }
            })
    };
};

// ZipList :: a -> {getZipList :: [a]}
const ZipList = x => ({
    // Constructor for an applicative ZipList
    type: "ZipList",
    getZipList: x
});

// abs :: Num -> Num
const abs = x =>
    // Absolute value of a given number
    // without the sign.
    0 > x
        ? -x
        : x;

// add (+) :: Num a => a -> a -> a
const add = a =>
    // Curried addition.
    b => a + b;

// adjust :: (a -> a) -> Key ->
// Dict Key a -> Dict Key a
const adjust = f =>
    // The orginal dictionary, unmodified, if k is
    // not an existing key.
    // Otherwise, a new copy in which the existing
    // value of k is updated by application of f.
    k => dict => k in dict
        ? {
            ...dict,
            [k]: f(dict[k])
        }
        : dict;

// all :: (a -> Bool) -> [a] -> Bool
const all = p =>
    // True if p(x) holds for every x in xs.
    xs => [...xs].every(p);

// allSame :: [a] -> Bool
const allSame = xs =>
    // True if xs has less than 2 items, or every item
    // in the tail of the list is identical to the head.
    2 > xs.length || (() => {
        const [h, ...t] = xs;

        return t.every(x => h === x);
    })();

// allTree :: (a -> Bool) -> Tree a -> Bool
const allTree = p =>
    // True if p holds for all nodes of the
    // tree to which allTree(p) is applied.
    foldTree(
        x => xs => p(x) && xs.every(Boolean)
    );

// and :: [Bool] -> Bool
const and = xs =>
    // True unless any value in xs is false.
    [...xs].every(Boolean);

// any :: (a -> Bool) -> [a] -> Bool
const any = p =>
    // True if p(x) holds for at least
    // one item in xs.
    xs => [...xs].some(p);

// anyTree :: (a -> Bool) -> Tree a -> Bool
const anyTree = p =>
    // True if p holds for any node of the
    // tree to which anyTree(p) is applied.
    foldTree(
        x => xs =>
            p(x) || xs.some(Boolean)
    );

// ap (<*>) :: Monad m => m (a -> b) -> m a -> m b
const ap = mf =>
    // Applies wrapped functions to wrapped values,
    // for example applying a list of functions to a list
    // of values or applying:
    // Just(f) to Just(x),  Right(f) to Right(x),
    // f(x) to g(x) etc.
    mx => ({
        "Either": () => apLR,
        "Maybe": () => apMay,
        "Node": () => apTree,
        "Tuple": () => apTuple,
        "List": () => apList,
        "(a -> b)": () => apFn
    })[typeName(mx) || "List"]()(mf)(mx);

// apFn :: (a -> b -> c) -> (a -> b) -> (a -> c)
const apFn = f =>
    // Applicative instance for functions.
    // f(x) applied to g(x).
    g => x => f(x)(
        g(x)
    );

// apLR (<*>) :: Either e (a -> b) -> Either e a -> Either e b
const apLR = flr =>
    // Either a Left value, or the application of a
    // function in Either to a value in Either.
    liftA2LR(x => x)(flr);

// apList (<*>) :: [(a -> b)] -> [a] -> [b]
const apList = fs =>
    // The sequential application of each of a list
    // of functions to each of a list of values.
    // apList([x => 2 * x, x => 20 + x])([1, 2, 3])
    //     -> [2, 4, 6, 21, 22, 23]
    xs => fs.flatMap(f => xs.map(f));

// apMay (<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b
const apMay = mf =>
    // Just an application of Maybe a function to
    // to Maybe a value, or Nothing.
    liftA2May(x => x)(mf);

// apTree (<*>) :: Tree (a -> b) -> Tree a -> Tree b
const apTree = tf =>
    // A new tree derived by applying each of a tree
    // of functions to each node value in another tree.
    liftA2Tree(
        x => x
    )(tf);

// apTuple (<*>) :: Monoid m => (m, (a -> b)) -> (m, a) -> (m, b)
const apTuple = ab =>
    // A tuple obtained by applying the function in the second
    // value of ab to the second value in an existing tuple,
    // and concatenating the first values of each tuple.
    liftA2Tuple(x => x)(ab);

// apZL (<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b
// The application of a function in one ZipList
// to each value in another ZipList.
const apZL = zf =>
    liftA2ZL(x => x)(zf);

// apZip :: [(a -> b)] -> [a] -> [b]
const apZip = fs =>
    // Zip applicative.
    // Each function in fs applied to the value
    // in the corresponding position in xs.
    xs => fs.slice(
        0, Math.min(fs.length, xs.length)
    )
        .map((f, i) => f(xs[i]));

// appEndo :: Endo a -> (a -> a)
const appEndo = endo =>
    // Accessor for the function in an Endo type.
    endo.appEndo;

// append (<>) :: [a] -> [a] -> [a]
const append = xs =>
    // Two lists joined into one.
    ys => xs.concat(ys);

// appendGen (++) :: Gen [a] -> Gen [a] -> Gen [a]
const appendGen = xs =>
    // A new generator composed from the
    // concatenation of two existing generators.
    function *(ys) {
        for (const vs of [xs, ys]) {
            let nxt = vs.next();

            while (!nxt.done) {
                yield nxt.value;
                nxt = vs.next();
            }
        }
    };

// apply ($) :: (a -> b) -> a -> b
const apply = f =>
    // Application operator.
    x => f(x);

// applyN :: Int -> (a -> a) -> a -> a
const applyN = n =>
    // The value of n applications of f to x.
    // (Church numeral n)
    f => x => Array.from({
        length: n
    }, () => f)
    .reduce((a, g) => g(a), x);

// approxRatio :: Real -> Real -> Ratio
const approxRatio = epsilon =>
    n => {
        const
            c = gcdApprox(
                Boolean(epsilon)
                    ? epsilon
                    : (1 / 10000)
            )(1, n);

        return Ratio(
            Math.floor(n / c)
        )(
            Math.floor(1 / c)
        );
    };

// argvLength :: Function -> Int
const argvLength = f =>
    // The number of arguments defined for the given function.
    f.length;

// assocs :: Map k a -> [(k, a)]
const assocs = m =>
    // A list of (key, value) tuples derived from
    // the given dictionary.
    Object.entries(m).map(
        ([k, v]) => Tuple(k)(v)
    );

// biList :: (a, a) -> [a]
const biList = ab =>
    // A list of two items derived from a tuple.
    [...ab];

// bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)
const bimap = f =>
    // Tuple instance of bimap.
    // A tuple of the application of f and g to the
    // first and second values respectively.
    g => tpl => Tuple(f(tpl[0]))(
        g(tpl[1])
    );

// bimapLR :: (a -> b) -> (c -> d) -> ֵEither ֵֵa c -> Either b d
const bimapLR = f =>
    // Instance of bimap for Either values.
    // Either the application of f to a Left value,
    // or the application of g to a Right value.
    g => lr => lr.Left
        ? Left(f(lr.Left))
        : Right(g(lr.Right));

// bimapN :: (a -> b) -> (c -> d) -> TupleN -> TupleN
const bimapN = f =>
    // An n-tuple instance of bimap.
    // An n-tuple of unchanged dimension in which
    // the final value is an application of g
    // and the penultimate value is an application of f.
    g => nTuple => {
        const n = nTuple.length;

        return 1 < n
            ? TupleN(
                ...Array.from(nTuple).slice(0, n - 2),
                f(nTuple[n - 2]), g(nTuple[n - 1])
            )
            : null;
    };

// bind (>>=) :: Monad m => m a -> (a -> m b) -> m b
const bind = m =>
    // Two computations sequentially composed,
    // with any value produced by the first
    // passed as an argument to the second.
    mf => Array.isArray(m)
        ? bindList(m)(mf)
        : ({
            "Either": () => bindLR,
            "Maybe": () => bindMay,
            "Tuple": () => bindTuple,
            "function": () => bindFn
        })[m.type || typeof m]()(m)(mf);

// bindFn (>>=) :: (a -> b) -> (b -> a -> c) -> a -> c
const bindFn = f =>
    // Binary operator applied over f x and x.
    op => x => op(f(x))(x);

// bindLR (>>=) :: Either a ->
// (a -> Either b) -> Either b
const bindLR = lr =>
    // Bind operator for the Either option type.
    // If lr has a Left value then lr unchanged,
    // otherwise the function mf applied to the
    // Right value in lr.
    mf => "Left" in lr
        ? lr
        : mf(lr.Right);

// bindList (>>=) :: [a] -> (a -> [b]) -> [b]
const bindList = xs =>
    // The bind operator for Arrays.
    mf => [...xs].flatMap(mf);

// bindMay (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b
const bindMay = mb =>
    // Nothing if mb is Nothing, or the application of the
    // (a -> Maybe b) function mf to the contents of mb.
    mf => mb.Nothing
        ? mb
        : mf(mb.Just);

// bindTuple (>>=) :: Monoid a => (a, a) -> (a -> (a, b)) -> (a, b)
const bindTuple = ([a, b]) =>
    // The bind operator for Tuples
    f => first(mappend(a))(
        f(b)
    );

// bool :: a -> a -> Bool -> a
const bool = f =>
    // t if p(x) else f.
    t => p => p ? t : f;

// both :: (a -> b) -> (a, a) -> (b, b)
const both = f =>
    // A tuple obtained by separately
    // applying f to each of the two
    // values in the given tuple.
    ([a, b]) => Tuple(
        f(a)
    )(
        f(b)
    );

// breakOn :: Eq a => [a] -> [a] -> ([a], [a])
// breakOn :: String -> String -> ([Char], [Char])
const breakOn = needle =>
    // A tuple of the prefix before the first match
    // and the whole remainder (including the match).
    haystack => {
        const ns = [...needle];

        const go = hs =>
            isPrefixOf(ns)(hs)
                ? Tuple([])(hs)
                : 0 === hs.length
                    ? Tuple([])([])
                    : first(
                        v => [hs[0]].concat(v)
                    )(
                        go(hs.slice(1))
                    );

        return go([...haystack]);
    };

// breakOnAll :: String -> String -> [(String, String)]
const breakOnAll = needle =>
    // Tuples breaking the string at
    // all non-overlapping instances
    // of the needle in the haystack.
    haystack => Boolean(needle)
        ? haystack.split(needle)
        .reduce((a, _, i, xs) =>
            0 < i
                ? a.concat([
                    Tuple(
                        xs.slice(0, i).join(needle)
                    )(
                        needle + xs.slice(i)
                        .join(needle)
                    )
                ])
                : a, [])
        : null;

// breakOnMay :: String -> String -> Maybe (String, String)
const breakOnMay = needle =>
    // Maybe (prefix before match, match + rest)
    haystack => Boolean(needle)
        ? (() => {
            const xs = haystack.split(needle);

            return Just(Boolean(xs.length)
                ? Tuple(
                    xs[0]
                )(
                    haystack.slice(xs[0].length)
                )
                : Tuple(haystack)(""));
        })()
        : Nothing();

// break_ :: (a -> Bool) -> [a] -> ([a], [a])
const break_ = p =>
    // The longest prefix of xs in which
    // all values return false for p,
    // tupled with the rest.
    xs => {
        const i = xs.findIndex(p);

        return -1 !== i
            ? Tuple(xs.slice(0, i))(
                xs.slice(i)
            )
            : Tuple(xs)([]);
    };

// bulleted :: String -> String -> String
const bulleted = strTab =>
    // A copy of s in which each line is
    // preceded by a whitespace indent,
    // followed by a hyphen and space.
    s => s.split(/[\n\r]+/u).map(
        x => "" !== x
            ? `${strTab}- ${x}`
            : x
    )
    .join("\n");

// cartesianProduct :: [a] -> [b] -> [[a, b]]
const cartesianProduct = xs =>
    // Every tuple in the cartesian product
    // of xs and ys.
    ys => [...xs].flatMap(
        x => [...ys].flatMap(
            y => [Tuple(x)(y)]
        )
    );

// caseOf :: [(a -> Bool, b)] -> b -> a ->  b
const caseOf = pvs =>
    // List of (Predicate, value) tuples ->
    // Default value -> Value to test -> Output value
    otherwise => x => {
        const mb = pvs.reduce(
            (a, pv) => a.Nothing
                ? pv[0](x)
                    ? Just(pv[1])
                    : a
                : a,
            Nothing()
        );

        return mb.Nothing
            ? otherwise
            : mb.Just;
    };

// catMaybes :: [Maybe a] -> [a]
const catMaybes = mbs =>
    mbs.flatMap(
        m => m.Nothing
            ? []
            : [m.Just]
    );

// ceiling :: Num -> Int
const ceiling = x => {
    // The least integer not less than x.
    const
        nr = properFraction(x),
        n = nr[0];

    return 0 < nr[1]
        ? 1 + n
        : n;
};

// center :: Int -> Char -> String -> String
const center = n =>
    // Size of space -> filler Char ->
    // String -> Centered String
    c => s => {
        const gap = n - s.length;

        return 0 < gap
            ? (() => {
                const
                    margin = c.repeat(Math.floor(gap / 2)),
                    dust = c.repeat(gap % 2);

                return `${margin}${s}${margin}${dust}`;
            })()
            : s;
    };

// chars :: String -> [Char]
const chars = s =>
    [...s];

// chop :: ([a] -> (b, [a])) -> [a] -> [b]
const chop = f =>
    // A segmentation of xs by tail recursion with a
    // function which returns a (prefix, residue) tuple.
    xs => {
        const go = ys =>
            0 < ys.length
                ? (() => {
                    const [b, bs] = f(ys);

                    return [b].concat(go(bs));
                })()
                : [];

        return go([...xs]);
    };

// chr :: Int -> Char
const chr = x =>
    // The character at unix code-point x.
    String.fromCodePoint(x);

// chunksOf :: Int -> [a] -> [[a]]
const chunksOf = n => {
    // xs split into sublists of length n.
    // The last sublist will be short if n
    // does not evenly divide the length of xs .
    const go = xs => {
        const chunk = xs.slice(0, n);

        return 0 < chunk.length
            ? [chunk, ...go(xs.slice(n))]
            : [];
    };

    return go;
};

// combinations :: Int -> [a] -> [[a]]
const combinations = n =>
    // All combinations, without repetition,
    // of n items drawn from xs.
    xs => {
        const go = (m, ys) =>
            1 > m
                ? [[]]
                : 0 === ys.length
                    ? []
                    : (
                        (h, rest) => [
                            ...go(m - 1, rest)
                            .map(t => [h, ...t]),
                            ...go(m, rest)
                        ]
                    )(
                        ys[0], ys.slice(1)
                    );

        return (go)(n, xs);
    };

// combine (</>) :: FilePath -> FilePath -> FilePath
const combine = fp =>
    // The concatenation of two filePath segments,
    // without omission or duplication of "/".
    fp1 => Boolean(fp) && Boolean(fp1)
        ? "/" === fp1.slice(0, 1)
            ? fp1
            : "/" === fp.slice(-1)
                ? fp + fp1
                : `${fp}/${fp1}`
        : (fp + fp1);

// compare :: a -> a -> Ordering
const compare = a =>
    b => a < b
        ? -1
        : a > b
            ? 1
            : 0;

// compareList :: [a] -> [a] -> Ordering
const compareList = xs =>
    // 0 if two lists are identical.
    // -1 if xs is empty, or has a lower leftward value.
    // 1 if ys is empty, or has a lower leftward value.
    ys => compare(0 === xs.length)(0 === ys.length) || (
        compare(xs[0])(ys[0]) || (
            compareList(xs.slice(1))(ys.slice(1))
        )
    );

// comparing :: Ord a => (b -> a) -> b -> b -> Ordering
const comparing = f =>
    // The ordering of f(x) and f(y) as a value
    // drawn from {-1, 0, 1}, representing {LT, EQ, GT}.
    x => y => {
        const
            a = f(x),
            b = f(y);

        return a < b
            ? -1
            : a > b
                ? 1
                : 0;
    };

// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
    // A function defined by the right-to-left
    // composition of all the functions in fs.
    fs.reduce(
        (f, g) => x => f(g(x)),
        x => x
    );

// composeList :: [(a -> a)] -> (a -> a)
const composeList = fs =>
    fs.reduce(
        (f, g) => x => f(g(x)),
        x => x
    );

// composeListR :: [(a -> a)] -> (a -> a)
const composeListR = fs =>
    x => fs.reduce((a, f) => f(a), x);

// composeR (>>>) :: (a -> b) -> (b -> c) -> a -> c
const composeR = f =>
    g => x => f(g(x));

// concat :: [[a]] -> [a]
const concat = xs =>
    // The concatenation of all the lists
    // in a list of lists.
    xs.flat(1);

// concatGen :: Gen [[a]] -> Gen [a]
const concatGen = gen =>
    // A flattened stream of generator values;
    (function* (g) {
        let m = g.next();

        while (!m.done) {
            const xs = lazyList(m.value);
            let x = xs.next();

            while (!x.done) {
                yield x.value;
                x = xs.next();
            }
            m = g.next();
        }
    }(gen));

// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = f =>
    // Concatenated results of a map of f over xs.
    // f is any function which returns a list value.
    // Any empty lists returned are filtered out by
    // the concatenation.
    xs => xs.flatMap(f);

// concats :: [String] -> String
const concats = xs =>
    xs.join("");

// cons :: a -> [a] -> [a]
const cons = x =>
    // A list constructed from the item x,
    // followed by the existing list xs.
    xs => Array.isArray(xs)
        ? [x].concat(xs)
        : "GeneratorFunction" !== (
            xs.constructor.constructor.name
        )
            ? x + xs
            : (function *() {
                yield x;
                let nxt = xs.next();

                while (!nxt.done) {
                    yield nxt.value;
                    nxt = xs.next();
                }
            }());

// constant :: a -> b -> a
const constant = k =>
    () => k;

// curry :: ((a, b) -> c) -> a -> b -> c
const curry = f =>
    a => b => 1 < f.length
        ? f(a, b)
        : f(Tuple(a)(b));

// curryN :: Curry a b => a -> b
const curryN = f =>
    // A curried function derived from a
    // function over a tuple of any order.
    (...args) => {
        const
            go = xs => f.length <= xs.length
                ? f(...xs)
                : (...ys) => go(xs.concat(ys));

        return go(args);
    };

// cycle :: [a] -> Generator [a]
const cycle = function* (xs) {
    // An infinite repetition of xs,
    // from which a prefix of arbitrary
    // length may be drawn.
    const n = xs.length;
    let i = 0;

    while (true) {
        yield xs[i];
        i = (1 + i) % n;
    }
};

// decodedPath :: Percent Encoded String -> FilePath
const decodedPath = decodeURI;

// degrees :: Float x => Radians x -> Degrees x
const degrees = r =>
    (180 / Math.PI) * r;

// delete :: Eq a => a -> [a] -> [a]
const delete_ = x =>
    // xs with first instance of x (if any) removed.
    xs => {
        const i = xs.findIndex(v => x === v);

        return -1 === i
            ? xs.slice(0)
            : xs.slice(0, i).concat(
                xs.slice(1 + i)
            );
    };

// deleteAt :: Int -> [a] -> [a]
const deleteAt = i =>
    // A copy of xs without any element at i, 
    // if i is a valid index.
    xs => xs.slice(0, i).concat(
        xs.slice(1 + i)
    );

// deleteBy :: (a -> a -> Bool) -> a -> [a] -> [a]
const deleteBy = fEq =>
    // A copy of the given list excluding the first
    // item which matches x in terms of the supplied
    // fEq equality operator.
    x => xs => {
        const i = xs.findIndex(fEq(x));

        return -1 === i
            ? xs.slice(0)
            : xs.slice(0, i).concat(
                xs.slice(1 + i)
            );
    };

// deleteFirst :: a -> [a] -> [a]
const deleteFirst = x => {
    const go = xs => 0 < xs.length
        ? x === xs[0]
            ? xs.slice(1)
            : [...xs[0], ...go(xs.slice(1))]
        : [];

    return go;
};

// deleteFirstsBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
const deleteFirstsBy = fEq =>
    // The first list purged of the first instance of
    // each predicate-matching element in the second list.
    xs => targets => {
        const d = deleteBy(fEq);

        return targets.reduce(
            (a, t) => d(t)(a),
            xs
        );
    };

// deleteKey :: String -> Dict -> Dict
const deleteKey = k =>
    // A new dictionary, without the key k.
    dict => {
        const d = { ...dict };

        return (delete d[k], d);
    };

// dictFromList :: [(k, v)] -> Dict
const dictFromList = kvs =>
    Object.fromEntries(kvs);

// difference :: Eq a => [a] -> [a] -> [a]
const difference = xs =>
    ys => {
        const s = new Set(ys);

        return xs.filter(x => !s.has(x));
    };

// differenceGen :: Gen [a] -> Gen [a] -> Gen [a]
const differenceGen = ga =>
    function *(gb) {
        // All values of generator stream ga except any
        // already seen in generator stream gb.
        const
            stream = zipGen(ga)(gb),
            sb = new Set([]);

        let xy = take(1)(stream);

        while (Boolean(xy.length)) {
            const [x, y] = Array.from(xy[0]);

            sb.add(y);
            if (!sb.has(x)) {
                yield x;
            }
            xy = take(1)(stream);
        }
    };

// digitToInt :: Char -> Int
const digitToInt = c => {
    const
        ord = x => x.codePointAt(0),
        oc = ord(c);

    return 48 > oc || 102 < oc
        ? null
        : (() => {
            const
                dec = oc - ord("0"),
                hexu = oc - ord("A"),
                hexl = oc - ord("a");

            return 9 >= dec
                ? dec
                : 0 <= hexu && 5 >= hexu
                    ? 10 + hexu
                    : 0 <= hexl && 5 >= hexl
                        ? 10 + hexl
                        : null;
        })();
};

// div :: Int -> Int -> Int
const div = x =>
    y => Math.floor(x / y);

// divMod :: Int -> Int -> (Int, Int)
const divMod = n => d => {
    // Integer division, truncated toward negative infinity,
    // and integer modulus such that:
    // (x `div` y)*y + (x `mod` y) == x
    const [q, r] = [Math.trunc(n / d), n % d];

    return signum(n) === signum(-d)
        ? Tuple(q - 1)(r + d)
        : Tuple(q)(r);
};

// dot (.) :: (b -> c) -> (a -> b) -> a -> c
const dot = f =>
    // The composition of two functions.
    g => x => f(g(x));

// draw :: Tree String -> [String]
const draw = node => {
    // shifted :: String -> String -> [String] -> [String]
    const shifted = (first, other, xs) =>
        xs.map((x, i) =>
            (0 < i ? other : first) + x
        );

    // drawSubTrees :: [Tree String] -> [String]
    const drawSubTrees = xs => {
        const n = xs.length;

        return 0 < n
            ? ["│"].concat(
                1 < n
                    ? shifted("├─ ", "│  ", draw(xs[0]))
                        .concat(
                            drawSubTrees(xs.slice(1))
                        )
                    : shifted("└─ ", "   ", draw(xs[0]))
            )
            : [];
    };

    return node.root.split("\n").concat(
        drawSubTrees(node.nest)
    );
};

// drawForest :: [Tree String] -> String
const drawForest = trees =>
    trees.map(drawTree).join("\n");

// drawTree :: Tree String -> String
const drawTree = tree =>
    draw(tree).join("\n");

// drawTree2 :: Bool -> Bool -> Tree String -> String
// eslint-disable-next-line max-lines-per-function
const drawTree2 = blnCompact => blnPruned => tree => {
    // Tree design and algorithm inspired by the Haskell snippet at:
    // https://doisinkidney.com/snippets/drawing-trees.html
    const
    // Lefts, Middle, Rights
        lmrFromStrings = xs => {
            const [ls, rs] = Array.from(splitAt(
                Math.floor(xs.length / 2)
            )(xs));

            return TupleN(ls, rs[0], rs.slice(1));
        },
        stringsFromLMR = lmr =>
            Array.from(lmr).reduce((a, x) => a.concat(x), []),
        fghOverLMR = (f, g, h) => lmr => {
            const [ls, m, rs] = Array.from(lmr);

            return TupleN(ls.map(f), g(m), rs.map(h));
        };

    // eslint-disable-next-line max-lines-per-function
    const lmrBuild = (f, w) => wsTree => {
        const
            leftPad = n => s => " ".repeat(n) + s,
            xs = wsTree.nest,
            lng = xs.length,
            [nChars, x] = Array.from(wsTree.root);

        // ------------------ LEAF NODE ------------------
        return 0 === lng
            ? TupleN([], "─".repeat(w - nChars) + x, [])

        // --------- NODE WITH SINGLE CHILD ----------
            : 1 === lng
                ? (() => {
                    const indented = leftPad(1 + w);

                    return fghOverLMR(
                        indented,
                        z => `${"─".repeat(w - nChars)}${x}-${z}`,
                        indented
                    )(f(xs[0]));

                // ----------- NODE WITH CHILDREN ------------
                })()
                : (() => {
                    const
                        cFix = y => ys => y + ys,
                        treeFix = (l, m, r) => compose(
                            stringsFromLMR,
                            fghOverLMR(cFix(l), cFix(m), cFix(r))
                        ),
                        _x = "─".repeat(w - nChars) + x,
                        indented = leftPad(w),
                        lmrs = xs.map(f);

                    return fghOverLMR(
                        indented,
                        s => _x + ({
                            "┌": "┬",
                            "├": "┼",
                            "│": "┤",
                            "└": "┴"
                        })[s[0]] + s.slice(1),
                        indented
                    )(lmrFromStrings(
                        intercalate(
                            blnCompact
                                ? []
                                : ["│"]
                        )(
                            [treeFix(" ", "┌", "│")(lmrs[0])]
                            .concat(init(lmrs.slice(1)).map(
                                treeFix("│", "├", "│")
                            ))
                            .concat([treeFix("│", "└", " ")(
                                lmrs[lmrs.length - 1]
                            )])
                        )
                    ));
                })();
    };

    const
        measuredTree = fmapTree(
            v => {
                const s = ` ${v} `;

                return Tuple(s.length)(s);
            })(tree),
        levelWidths = levels(measuredTree)
        .reduce(
            (a, level) => a.concat(maximum(level.map(fst))),
            []
        ),
        treeLines = stringsFromLMR(
            levelWidths.reduceRight(
                lmrBuild, x => x
            )(measuredTree)
        );

    return unlines(
        blnPruned
            ? treeLines.filter(
                s => s.split("")
                .some(c => !" │".includes(c))
            )
            : treeLines
    );
};

// drop :: Int -> [a] -> [a]
// drop :: Int -> Generator [a] -> Generator [a]
// drop :: Int -> String -> String
const drop = n =>
    xs => Infinity > length(xs)
        ? xs.slice(n)
        : (take(n)(xs), xs);

// dropAround :: (a -> Bool) -> [a] -> [a]
// dropAround :: (Char -> Bool) -> String -> String
const dropAround = p =>
    xs => dropWhile(p)(
        dropWhileEnd(p)(xs)
    );

// dropFileName :: FilePath -> FilePath
const dropFileName = fp =>
    "" !== fp
        ? (() => {
            const
                xs = (fp.split("/"))
                .slice(0, -1);

            return Boolean(xs.length)
                ? `${xs.join("/")}/`
                : "./";
        })()
        : "./";

// dropLength :: [a] -> [b] -> [b]
const dropLength = xs =>
    ys => {
        const go = (x, y) =>
            0 < x.length
                ? 0 < y.length
                    ? go(x.slice(1), y.slice(1))
                    : []
                : y;

        return go(xs, ys);
    };

// dropLengthMaybe :: [a] -> [b] -> Maybe [b]
const dropLengthMaybe = xs =>
    ys => {
        const go = (x, y) =>
            Boolean(x.length) ? (
                Boolean(y.length) ? (
                    go(x.slice(1), y.slice(1))
                ) : Nothing()
            ) : Just(y);

        return go(xs, ys);
    };

// dropWhile :: (a -> Bool) -> [a] -> [a]
const dropWhile = p =>
    // The suffix remaining after takeWhile p xs.
    xs => {
        const i = xs.findIndex(x => !p(x));

        return -1 !== i
            ? xs.slice(i)
            : [];
    };

// dropWhileEnd :: (a -> Bool) -> [a] -> [a]
const dropWhileEnd = p =>
    // xs without the largest suffix in which p holds
    // for every element.
    xs => xs.slice(
        0, 1 + xs.findLastIndex(
            x => !p(x)
        )
    );

// dropWhileGen :: (a -> Bool) -> Gen [a] -> [a]
const dropWhileGen = p =>
    xs => {
        let
            nxt = xs.next(),
            v = nxt.value;

        while (!nxt.done && p(v)) {
            nxt = xs.next();
            v = nxt.value;
        }

        return cons(v)(xs);
    };

// either :: (a -> c) -> (b -> c) -> Either a b -> c
const either = fl =>
    // Application of the function fl to the
    // contents of any Left value in e, or
    // the application of fr to its Right value.
    fr => e => "Left" in e
        ? fl(e.Left)
        : fr(e.Right);

// elem :: Eq a => a -> [a] -> Bool
const elem = x =>
    // True if xs contains an instance of x.
    xs => {
        const t = xs.constructor.name;

        return "Array" !== t
            ? xs["Set" !== t
                ? "includes"
                : "has"](x)
            : xs.some(eq(x));
    };

// elemAtMay :: Int -> Dict -> Maybe (String, a)
// elemAtMay :: Int -> [a] -> Maybe a
const elemAtMay = i =>
    // Just the item at the indexed position in an array,
    // or in the lexically sorted key-values of a dict,
    // or Nothing, if the index is out of range.
    obj => {
        const
            vs = Array.isArray(obj)
                ? obj
                : Object.entries(obj).sort(
                    (a, b) => b[0].localeCompare(a[0])
                );

        return (0 <= i) && (i < vs.length)
            ? Just(vs[i])
            : Nothing();
    };

// elemIndex :: Eq a => a -> [a] -> Maybe Int
const elemIndex = x =>
    // Just the index of x in xs, if it is found,
    // or Nothing, if xs does not contain x.
    xs => {
        const i = xs.indexOf(x);

        return -1 === i
            ? Nothing()
            : Just(i);
    };

// elemIndices :: Eq a => a -> [a] -> [Int]
const elemIndices = x =>
    // The indices at which x occurs in xs.
    xs => [...xs].flatMap(
        (y, i) => y === x
            ? [i]
            : []
    );

// elemTree :: a -> Tree a -> Bool
const elemTree = x =>
    // True if the root of any node in the tree
    // has the value x.
    tree => {
        const go = t =>
            x === t.root || t.nest.some(go);

        return go(tree);
    };

// elems :: Map k a -> [a]
// elems :: Set a -> [a]
const elems = x =>
    "Set" !== x.constructor.name
        ? Object.values(x)
        : Array.from(x.values());

// encodedPath :: FilePath -> Percent Encoded String
const encodedPath = encodeURI;

// enumFrom :: Enum a => a -> [a]
const enumFrom = function* (x) {
    // A non-finite succession of enumerable
    // values, starting with the value x.
    let v = x;

    while (true) {
        yield v;
        v = succ(v);
    }
};

// enumFromPairs :: String -> [(String, Int)] -> Dict
const enumFromPairs = enumName =>
    kvs => {
        const
            iMax = kvs[kvs.length - 1][1],
            iMin = kvs[0][1];

        return kvs.reduce(
            (a, kv) => ({
                ...a,
                [kv[0]]: {
                    "type": "enum",
                    "name": enumName,
                    "key": kv[0],
                    "max": iMax,
                    "min": iMin,
                    "value": kv[1]
                },
                [kv[1]]: kv[0]
            }), {}
        );
    };

// enumFromThen :: Int -> Int -> Gen [Int]
const enumFromThen = x =>
    // A non-finite stream of integers,
    // starting with x and y, and continuing
    // with the same interval.
    function* (y) {
        const d = y - x;
        let v = y + d;

        yield x;
        yield y;
        while (true) {
            yield v;
            v = d + v;
        }
    };

// enumFromThenTo :: Int -> Int -> Int -> [Int]
const enumFromThenTo = m =>
    // Integer values enumerated from m to n
    // with a step defined by (nxt - m).
    nxt => n => {
        const d = nxt - m;

        return Array.from({
            length: (Math.floor(n - nxt) / d) + 2
        }, (_, i) => m + (d * i));
    };

// enumFromThenToChar :: Char -> Char -> Char -> [Char]
const enumFromThenToChar = x1 =>
    x2 => y => {
        const
            [i1, i2, iY] = [x1, x2, y].map(
                x => x.codePointAt(0)
            ),
            d = i2 - i1;

        return Array.from({
            length: (Math.floor(iY - i2) / d) + 2
        },
        (_, i) => String.fromCodePoint(
            i1 + (d * i)
        ));
    };

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
    // Enumeration of the integers from m to n.
    n => Array.from(
        {length: 1 + n - m},
        (_, i) => m + i
    );

// enumFromToChar :: Char -> Char -> [Char]
const enumFromToChar = m => n => {
    const
        [intM, intN] = [m, n].map(
            x => x.codePointAt(0)
        );

    return Array.from({
        length: Math.floor(intN - intM) + 1
    }, (_, i) => String.fromCodePoint(intM + i));
};

// enumFromTo_ :: Enum a => a -> a -> [a]
const enumFromTo_ = m => n => {
    const
        [x, y] = [m, n].map(fromEnum),
        b = x + (
            isNaN(m)
                ? 0
                : m - x
        );

    return Array.from({
        length: 1 + (y - x)
    }, (_, i) => toEnum(m)(b + i));
};

// eq (==) :: Eq a => a -> a -> Bool
const eq = a =>
    // True when a and b are equivalent in the terms
    // defined below for their shared data type.
    b => {
        const t = typeof a;

        return t === typeof b && (
            "object" !== t
                ? "function" !== t
                    ? a === b
                    : a.toString() === b.toString()
                : (() => {
                    const kvs = Object.entries(a);

                    return kvs.length !== Object.keys(b).length
                        ? false
                        : kvs.every(([k, v]) => eq(v)(b[k]));
                })()
        );
    };

// eqDate :: Date -> Date -> Bool
const eqDate = dte =>
    // True if the date parts of two date-time objects
    // (ignoring the time parts) are the same.
    dte1 => {
        const dayOnly = dateTime =>
            new Date(dateTime).setUTCHours(0, 0, 0, 0);

        return dayOnly(dte) === dayOnly(dte1);
    };

// eqDateTime :: Int -> Date -> Date -> Bool
const eqDateTime = n =>
    // Equivalence of two JS Date values
    // at a granularity of n minutes.
    // e.g.
    //  Same minute: eqDateTime(1)(a)(b)
    //    Same hour: eqDateTime(60)(a)(b)
    on(a => b => a === b)(
        flip(div)(6E4 * n)
    );

// eqSet :: Set a -> Set a -> Bool
const eqSet = a =>
    // True if the two sets have
    // the same size and members.
    b => a.size === b.size && (
        Array.from(a).every(x => b.has(x))
    );

// evalJSLR :: String -> Either String a
const evalJSLR = s => {
    try {
        // eslint-disable-next-line no-eval
        return Right(eval(`(${s})`));
    } catch (e) {
        return Left(e.message);
    }
};

// evalJSMay :: String -> Maybe a
const evalJSMay = s => {
    try {
        // eslint-disable-next-line no-eval
        return Just(eval(`(${s})`));
    } catch (e) {
        return Nothing();
    }
};

// even :: Int -> Bool
const even = n =>
    // True if 2 is a factor of n.
    0 === n % 2;

// exp :: Float -> Float
const exp = Math.exp;

// fTable :: String -> (a -> String) ->
// (b -> String) -> (a -> b) -> [a] -> String
const fTable = s =>
    // Heading -> x display function ->
    //           fx display function ->
    //    f -> values -> tabular string
    xShow => fxShow => f => xs => {
        const
            ys = xs.map(xShow),
            w = Math.max(...ys.map(y => [...y].length)),
            table = zipWith(
                a => b => `${a.padStart(w, " ")} -> ${b}`
            )(ys)(
                xs.map(x => fxShow(f(x)))
            ).join("\n");

        return `${s}\n${table}`;
    };

// fType :: (a -> f b) -> f
const fType = g => {
    const s = g.toString();

    return s.includes("Right")
        ? Right
        : s.includes("Left")
            ? Left
            : s.includes("Nothing")
                ? Just
                : s.includes("Node")
                    ? flip(Node)([])
                    : x => [x];
};

// fanArrow (&&&) ::
// (a -> b) -> (a -> c) -> (a -> (b, c))
const fanArrow = f =>
    // A combined function, given f and g,
    // from x to a tuple of (f(x), g(x))
    // ((,) . f <*> g)
    g => x => Tuple(f(x))(
        g(x)
    );

// filePathTree :: filePath -> [Tree String] -> Tree FilePath
const filePathTree = fpAnchor =>
    trees => {
        const go = fp => tree => {
            const path = `${fp}/${tree.root.text}`;

            return Node(path)(
                tree.nest.map(go(path))
            );
        };

        return Node(fpAnchor)(
            trees.map(go(fpAnchor))
        );
    };

// filter :: (a -> Bool) -> [a] -> [a]
const filter = p =>
    // The elements of xs which match
    // the predicate p.
    xs => [...xs].filter(p);

// filterGen :: (a -> Bool) -> Gen [a] -> Gen [a]
const filterGen = p =>
    // A stream of values which are drawn
    // from a generator, and satisfy p.
    xs => {
        const go = function* () {
            let x = xs.next();

            while (!x.done) {
                const v = x.value;

                if (p(v)) {
                    yield v;
                }
                x = xs.next();
            }
        };

        return go(xs);
    };

// filterTree (a -> Bool) -> Tree a -> [a]
const filterTree = p =>
    // List of all values in the tree
    // which match the predicate p.
    foldTree(x => xs =>
        p(x)
            ? [x, ...xs.flat()]
            : xs.flat()
    );

// filteredForest :: (a -> Bool) -> [Tree a] -> [Tree a]
const filteredForest = p =>
    // A forest of trees which all subtrees match the predicate.
    trees => {
        const go = t => {
            const v = root(t);

            return p(v)
                ? [
                    Node(v)(
                        nest(t).flatMap(go)
                    )
                ]
                : [];
        };

        return trees.flatMap(go);
    };

// filteredSubTrees :: (Tree a -> Bool) -> Tree a -> [Tree a]
const filteredSubTrees = p => {
    // SubTrees (within the given tree) which match p.
    const go = tree => (
        p(root(tree))
            ? [tree]
            : []
    )
        .concat(nest(tree).flatMap(go));

    return go;
};

// find :: (a -> Bool) -> [a] -> Maybe a
const find = p =>
    // Just the first element in xs which
    // matches the predicate p, or
    // Nothing if no match is found.
    xs => "GeneratorFunction" !== (
        xs.constructor.constructor.name
    )
        ? (() => {
            const i = xs.findIndex(p);

            return -1 !== i
                ? Just(xs[i])
                : Nothing();
        })()
        : findGen(p)(xs);

// findGen :: (a -> Bool) -> Gen [a] -> Maybe a
const findGen = p =>
    // Just the first match for the predicate p
    // in the generator stream xs, or Nothing
    // if no match is found.
    xs => {
        const
            mb = until(
                ([nxt]) => nxt.done || p(nxt.value)
            )(
                ([, b]) => Tuple(b.next())(
                    b
                )
            )(
                Tuple(xs.next())(xs)
            )[0];

        return mb.done
            ? Nothing()
            : Just(mb.value);
    };

// findIndex :: (a -> Bool) -> [a] -> Maybe Int
const findIndex = p =>
    //  Just the index of the first element in
    //  xs for which p(x) is true, or
    //  Nothing if there is no such element.
    xs => {
        const i = [...xs].findIndex(p);

        return -1 !== i
            ? Just(i)
            : Nothing();
    };

// findIndexR :: (a -> Bool) -> [a] -> Maybe Int
const findIndexR = p =>
    //  Just the index of the last element in
    //  xs for which p(x) is true, or
    //  Nothing if there is no such element.
    xs => {
        const i = reverse([...xs]).findIndex(p);

        return -1 !== i
            ? Just(xs.length - (1 + i))
            : Nothing();
    };

// findIndices :: (a -> Bool) -> [a] -> [Int]
// findIndices :: (String -> Bool) -> String -> [Int]
const findIndices = p =>
    xs => {
        const ys = [...xs];

        return ys.flatMap(
            (y, i) => p(y, i, ys)
                ? [i]
                : []
        );
    };

// findTree :: (a -> Bool) -> Tree a -> Maybe a
const findTree = p => {
    // The first of any node values in the tree which match
    // the predicate p.
    // (For all matches, see treeMatches)
    const go = tree => {
        const x = tree.root;

        return p(x)
            ? Just(x)
            : (() => {
                const
                    xs = tree.nest,
                    n = xs.length;

                return 0 < n
                    ? until(
                        ([i, mb]) => n <= i || ("Just" in mb)
                    )(
                        ([i]) => [1 + i, go(xs[i])]
                    )(
                        [0, Nothing()]
                    )[1]
                    : Nothing();
            })();
    };

    return go;
};

// first :: (a -> b) -> ((a, c) -> (b, c))
const first = f =>
    // A simple function lifted to one which applies
    // to a tuple, transforming only its first item.
    ([x, y]) => Tuple(f(x))(y);

// flatten :: NestedList a -> [a]
const flatten = nest =>
    nest.flat(Infinity);

// flattenTree :: Tree a -> [a]
const flattenTree = tree => {
    const
        go = (xs, node) => [node.root].concat(
            node.nest.reduceRight(go, xs)
        );

    return go([], tree);
};

// flip :: (a -> b -> c) -> b -> a -> c
const flip = op =>
    // The binary function op with
    // its arguments reversed.
    1 !== op.length
        ? (a, b) => op(b, a)
        : (a => b => op(b)(a));

// floor :: Num -> Int
const floor = x => {
    const
        nr = (
            "Ratio" !== x.type
                ? properFraction
                : properFracRatio
        )(x),
        n = nr[0];

    return 0 > nr[1]
        ? n - 1
        : n;
};

// fmap (<$>) :: Functor f => (a -> b) -> f a -> f b
const fmap = f =>
    // f mapped over the given functor.
    x => ({
        "Either": () => fmapLR,
        "(a -> b)": () => dot,
        "List": () => map,
        "Maybe": () => fmapMay,
        "Node": () => fmapTree,
        "String": () => map,
        "Tuple": () => fmapTuple
    })[typeName(x)]()(f)(x);

// fmapDict :: (a -> b) ->
// {String :: a} -> {String :: b}
const fmapDict = f =>
    // A map of f over every value
    // in the given dictionary.
    dict => Object.entries(dict)
        .reduceRight(
            (a, [k, v]) => ({
                ...a,
                [k]: f(v)
            }),
            {}
        );

// fmapGen <$> :: (a -> b) -> Gen [a] -> Gen [b]
const fmapGen = f =>
    // The map of f over a stream of generator values.
    function* (gen) {
        let v = gen.next();

        while (!v.done) {
            yield f(v.value);
            v = gen.next();
        }
    };

// fmapLR (<$>) :: (b -> c) -> Either a b -> Either a c
const fmapLR = f =>
    // Either f mapped into the contents of any Right
    // value in e, or e unchanged if it is a Left value.
    e => "Left" in e
        ? e
        : Right(f(e.Right));

// fmapMay (<$>) :: (a -> b) -> Maybe a -> Maybe b
const fmapMay = f =>
    mb => mb.Nothing
        ? mb
        : Just(f(mb.Just));

// fmapTree :: (a -> b) -> Tree a -> Tree b
const fmapTree = f => {
    // A new tree. The result of a
    // structure-preserving application of f
    // to each root in the existing tree.
    const go = t => Node(
        f(root(t))
    )(
        nest(t).map(go)
    );

    return go;
};

// fmapTuple (<$>) :: (a -> b) -> (a, a) -> (a, b)
const fmapTuple = f =>
    second(f);

// fmapZL (<$>) :: (a -> b) -> ZipList a -> ZipList b
const fmapZL = f =>
    // f mapped over the contents of a ZipList
    // of finite or infinite length.
    zl => ZipList(
        (() => {
            const xs = zl.getZipList;

            return Infinity > xs.length
                ? xs.map(f)
                : fmapGen(f)(xs);
        })()
    );

// foldList :: Monoid m => [m] -> m
const foldList = xs =>
    // The elements of xs combined.
    foldMapList(x => x)(xs);

// foldMap :: Monoid m => (a -> m) -> t a -> m
const foldMap = f => t =>
    // Each element of the structure mapped to a monoid,
    // with the results combined by (<>)
    ({
        Node: () => foldMapTree(f),
        List: () => foldMapList(f)
    })[typeName(t)]()(t);

// foldMapGen :: (a -> [b]) -> [a] -> Gen [b]
const foldMapGen = f =>
    // A lazy list of concatenated values
    // obtained by mapping f over xs
    xs => concatGen(
        function* () {
            const ys = [...xs];

            while (0 < ys.length) {
                yield f(ys.shift());
            }
        }(xs)
    );

// foldMapList :: Monoid m => (a -> m) -> t a -> m
const foldMapList = f =>
    // f mapped over the combined values of a structure.
    xs => 1 < xs.length
        ? xs.slice(1).reduce(
            (a, x) => mappend(a)(f(x)),
            xs[0]
        )
        : xs.map(f);

// foldMapTree :: Monoid m => (a -> m) -> Tree a -> m
const foldMapTree = f => {
    // Result of mapping each element of the tree to
    // a monoid, and combining with mappend.
    const go = tree =>
        nest(tree).map(go)
        .reduce(
            uncurry(mappend),
            f(root(tree))
        );

    return go;
};

// foldTree :: (a -> [b] -> b) -> Tree a -> b
const foldTree = f => {
    // The catamorphism on trees. A summary
    // value obtained by a depth-first fold.
    const go = tree => f(
        root(tree)
    )(
        nest(tree).map(go)
    );

    return go;
};

// foldl :: (a -> b -> a) -> a -> [b] -> a
const foldl = f =>
    // Note that that the signature of foldl differs
    // from that of foldr - the positions of
    // accumulator and current value in f are reversed.
    a => xs => [...xs].reduce(
        (x, y) => f(x)(y),
        a
    );

// foldl1 :: (a -> a -> a) -> [a] -> a
const foldl1 = f =>
    // Left to right reduction of the non-empty list xs,
    // using the binary operator f, with the head of xs
    // as the initial acccumulator value.
    xs => 1 < xs.length
        ? xs.slice(1).reduce(
            uncurry(f),
            xs[0]
        )
        : xs[0];

// foldl1May :: (a -> a -> a) -> [a] -> Maybe a
const foldl1May = f =>
    xs => 0 < xs.length
        ? Just(
            xs.slice(1)
            .reduce(uncurry(f), xs[0])
        )
        : Nothing();

// foldlTree :: (b -> a -> b) -> b -> Tree a -> b
const foldlTree = f =>
    // A top-down left-right
    // accumulating traversal.
    acc => node => {
        const go = (a, x) =>
            x.nest.reduce(go, f(a)(x.root));

        return go(acc, node);
    };

// foldr :: (a -> b -> b) -> b -> [a] -> b
const foldr = f =>
    // Note that that the signature of foldr differs
    // from that of foldl - the positions of
    // current value and accumulator in f are reversed
    acc => xs => [...xs].reduceRight(
        (a, x) => f(x)(a),
        acc
    );

// foldr1 :: (a -> a -> a) -> [a] -> a
const foldr1 = f =>
    xs => 0 < xs.length
        ? xs.slice(0, -1).reduceRight(
            uncurry(f),
            xs.slice(-1)[0]
        )
        : [];

// foldr1May :: (a -> a -> a) -> [a] -> Maybe a
const foldr1May = f =>
    // Nothing if xs is empty, or Just a right
    // fold of f over the list using the last
    // item of xs as the initial accumulator value.
    xs => Boolean(xs.length)
        ? Just(
            xs.slice(0, -1).reduceRight(
                uncurry(f),
                xs.slice(-1)[0])
        )
        : Nothing();

// foldrTree :: (a -> b -> b) -> b -> Tree a -> b
const foldrTree = f =>
    acc => node => {
        const go = (a, x) =>
            f(x.root)(
                x.nest.reduceRight(go, a)
            );

        return go(acc, node);
    };

// foldrTree2 :: (a -> b -> b) -> b -> t a -> b
const foldrTree2 = f =>
    // A derivation of foldrTree
    // from foldMapTree
    z => t => foldMapTree(
        compose(Endo, f)
    )(t).appEndo(z);

// foldr_ :: (a -> b -> b) -> b -> t a -> b
const foldr_ = f =>
    // Reduction of a structure, in terms of a binary
    // operator, from right to left.
    // A generic foldr, applicable to trees as well
    // as to lists.
    z => t => appEndo(
        foldMap(
            compose(Endo, f)
        )(t)
    )(z);

// forestFromJSONLR ::
// JSON String -> Either String Forest a
const forestFromJSONLR = json => {
    // Either a message string or a Forest.
    // Assumes a recursive [root, nest] JSON format,
    // in which `root` is a parseable value string,
    // and `nest` is a possibly empty list of
    // [`root`, `nest`] pairs.
    const go = vxs =>
        Node(vxs[0])(
            vxs[1].map(go)
        );

    return fmapLR(
        xs => xs.map(go)
    )(
        jsonParseLR(json)
    );
};

// fromEnum :: Enum a => a -> Int
const fromEnum = x =>
    typeof x !== "string"
        ? x.constructor === Object
            ? x.value
            : parseInt(Number(x), 10)
        : x.codePointAt(0);

// fromLeft :: a -> Either a b -> a
const fromLeft = def =>
    // The contents of a 'Left' value,
    // or otherwise a default value.
    lr => isLeft(lr)
        ? lr.Left
        : def;

// fromMaybe :: a -> Maybe a -> a
const fromMaybe = v =>
    mb => "Nothing" in mb
        ? v
        : mb.Just;

// fromRight :: b -> Either a b -> b
const fromRight = def =>
    // The contents of a 'Right' value or otherwise a default value.
    lr => isRight(lr) ? (
        lr.Right
    ) : def;

// fst :: (a, b) -> a
const fst = tpl =>
    // First member of a pair.
    tpl[0];

// ft :: Int -> Int -> [Int]
const ft = m =>
    // From To.
    // An abbreviation of enumFromTo.
    n => Array.from({
        length: 1 + n - m
    }, (_, i) => m + i);

// gcd :: Integral a => a -> a -> a
const gcd = x =>
    y => {
        const zero = x.constructor(0);
        const go = (a, b) =>
            zero === b
                ? a
                : go(b, a % b);

        return go(abs(x), abs(y));
    };

// gcdApprox :: Real -> (Real, Real) -> Real
const gcdApprox = epsilon =>
    (x, y) => {
        const _gcd = (a, b) => (
            b < epsilon
                ? a
                : _gcd(b, a % b)
        );

        return _gcd(Math.abs(x), Math.abs(y));
    };

// genericIndexMay :: [a] -> Int -> Maybe a
const genericIndexMay = xs =>
    i => (i < xs.length && 0 <= i)
        ? Just(xs[i])
        : Nothing();

// group :: [a] -> [[a]]
const group = xs =>
    // A list of lists, each containing only
    // elements equal under (===), such that the
    // concatenation of these lists is xs.
    groupBy(a => b => a === b)(xs);

// groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
const groupBy = eqOp =>
    // A list of lists, each containing only elements
    // equal under the given equality operator, such
    // that the concatenation of these lists is xs.
    xs => 0 < xs.length
        ? (() => {
            const [h, ...t] = xs;
            const [groups, g] = t.reduce(
                ([gs, a], x) => eqOp(a[0])(x)
                    ? [gs, [...a, x]]
                    : [[...gs, a], [x]],
                [[], [h]]
            );

            return [...groups, g];
        })()
        : [];

// groupOn :: (a -> b) -> [a] -> [[a]]
const groupOn = f =>
    // A list of lists, each containing only elements
    // which return equal values for f,
    // such that the concatenation of these lists is xs.
    xs => 0 < xs.length
        ? groupBy(
            a => b => eq(a[0])(b[0])
        )(
            xs.map(x => [f(x), x])
        )
            .map(gp => gp.map(ab => ab[1]))
        : [];

// groupOnKey :: Eq k => (a -> k) -> [a] -> [(k, [a])]
const groupOnKey = f =>
    // A list of (k, [a]) tuples, in which each [a]
    // contains only elements for which f returns the
    // same value, and in which k is that value.
    // The concatenation of the [a] in each tuple === xs.
    xs => 0 < xs.length
        ? groupBy(a => b => a[0] === b[0])(
            xs.map(x => [f(x), x])
        )
        .map(gp => [
            gp[0][0],
            gp.map(ab => ab[1])
        ])
        : [];

// groupSortBy :: (a -> a -> Ordering) -> [a] -> [[a]]
const groupSortBy = f =>
    // e.g. groupSortBy(comparing(length))
    compose(
        groupBy(a => b => 0 === f(a)(b)),
        sortBy(f)
    );

// groupSortOn :: Ord b => (a -> b) -> [a] -> [[a]]
const groupSortOn = f =>
    compose(
        map(map(snd)),
        groupBy(on(eq)(fst)),
        sortBy(comparing(fst)),
        map(fanArrow(f)(identity))
    );

// gt :: Ord a => a -> a -> Bool
const gt = x => y =>
    "Tuple" === x.type
        ? x[0] > y[0]
        : (x > y);

// head :: [a] -> a
const head = xs =>
    // The first item (if any) in a list.
    0 < xs.length
        ? xs[0]
        : undefined;

// headDef :: a -> [a] -> a
const headDef = v =>
    // The first item of a non-empty list,
    // or a default value if the list is empty.
    xs => Boolean(xs.length) ? (
        xs[0]
    ) : v;

// headMay :: [a] -> Maybe a
const headMay = xs =>
    // Just the first item of xs, or
    // Nothing if xs is an empty list.
    0 < xs.length
        ? Just(xs[0])
        : Nothing();

// identity :: a -> a
const identity = x =>
    // The identity function.
    x;

// if_ :: Bool -> a -> a -> a
const if_ = bln =>
    x => y => bln
        ? x
        : y;

// indented :: String -> String -> String
const indented = indent =>
    s => lines(s).map(
        x => 0 < x.length
            ? indent + x
            : x
    )
    .join("\n");

// index (!!) :: [a] -> Int -> Maybe a
// index (!!) :: Generator (Int, a) -> Int -> Maybe a
// index (!!) :: String -> Int -> Maybe Char
const index = xs =>
    i => {
        const s = xs.constructor.constructor.name;

        return "GeneratorFunction" !== s
            ? (() => {
                const v = xs[i];

                return undefined !== v
                    ? Just(v)
                    : Nothing();
            })()
            : (take(i)(xs), xs.next().value);
    };

// indexForest :: [Tree (a,  { nodeSum :: Int })] -> Int ->
// Maybe Tree (a, { nodeSum :: Int })
const indexForest = trees =>
    // Index into a forest of measured trees.
    // (see measuredTree)
    i => 0 < trees.length
        ? (() => {
            const
                headNode = trees[0],
                headSize = headNode.root[1].nodeSum;

            return i > (headSize - 1)
                ? indexForest(trees.slice(1))(i - headSize)
                : indexTree(headNode)(i);
        })()
        : Nothing();

// indexOf :: Eq a => [a] -> [a] -> Maybe Int
// indexOf :: String -> String -> Maybe Int
const indexOf = needle =>
    haystack => "string" !== typeof haystack
        ? findIndex(xs => isPrefixOf(needle)(xs))(
            tails(haystack)
        )
        : (() => {
            const i = haystack.indexOf(needle);

            return -1 !== i
                ? Just(i)
                : Nothing();
        })();

// indexTree :: Tree (a,  { nodeSum :: Int }) -> Int ->
// Maybe Tree (a,  { nodeSum :: Int })
const indexTree = tree =>
    // Index into a measured tree. (see measuredTree)
    i => 0 !== i
        ? i > (tree.root[1].nodeSum - 1)
            ? Nothing()
            : indexForest(tree.nest)(i - 1)
        : Just(tree);

// indexedTree :: Int -> Tree a -> Tree (a, Int)
const indexedTree = rootIndex =>
    // A tree in which each root value
    // is paired with a top-down
    // left-right index, where the root node
    // starts at the supplied rootIndex;
    tree => mapAccumLTree(
        i => x => Tuple(1 + i)(
            Tuple(x)({
                index: i
            })
        )
    )(rootIndex)(tree)[1];

// init :: [a] -> [a]
const init = xs =>
    // All elements of a list except the last.
    0 < xs.length
        ? xs.slice(0, -1)
        : null;

// initMay :: [a] -> Maybe [a]
const initMay = xs =>
    0 < xs.length
        ? Just(xs.slice(0, -1))
        : Nothing();

// inits :: [a] -> [[a]]
// inits :: String -> [String]
const inits = xs =>
    // All prefixes of the argument,
    // shortest first.
    [[], ...xs].map(
        (_, i, ys) => ys.slice(0, 1 + i)
    );

// insert :: Ord a => a -> [a] -> [a]
const insert = x =>
    xs => {
        const i = xs.findIndex(y => y >= x);

        return [
            ...xs.slice(0, i),
            x,
            ...xs.slice(i)
        ];
    };

// insertBy :: (a -> a -> Ordering) -> a -> [a] -> [a]
const insertBy = cmp =>
    // A new list in in which x is inserted into the
    // values of the given list at the first position
    // at which a supplied comparison function, applied
    // to x and the following value, returns LT or EQ.
    x => xs => {
        const go = (y, ys) =>
            0 < ys.length
                ? 0 < cmp(y)(ys[0])
                    ? [ys[0], ...go(y, ys.slice(1))]
                    : [y, ...ys]
                : [y];

        return go(x, xs);
    };

// insertDict :: String -> a -> Dict -> Dict
const insertDict = k =>
    v => dict => ({
        ...dict,
        [k]: v
    });

// insertWith :: Ord k => (a -> a -> a) ->
// k -> a -> Map k a -> Map k a
const insertWith = f =>
    // A new dictionary updated with a (k, f(v)(x)) pair.
    // Where there is no existing v for k, the supplied
    // x is used directly.
    k => x => dict => ({
        ...dict,
        [k]: k in dict
            ? f(dict[k])(x)
            : x
    });

// intToDigit :: Int -> Char
const intToDigit = n =>
    n >= 0 && n < 16
        ? "0123456789ABCDEF".charAt(n)
        : "?";

// intercalate :: [a] -> [[a]] -> [a]
const intercalate = sep =>
    // Flattened interspersal of a list between
    // the elements of a list of lists.
    xs => intersperse(sep)(xs).flat();

// intercalateS :: String -> [String] -> String
const intercalateS = s =>
    // The concatenation of xs
    // interspersed with copies of s.
    xs => xs.join(s);

// intersect :: (Eq a) => [a] -> [a] -> [a]
const intersect = xs =>
    // The intersection of lists xs and ys.
    ys => xs.filter(x => ys.includes(x));

// intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
const intersectBy = eqFn =>
    // The intersection of the lists xs and ys
    // in terms of the equality defined by eq.
    xs => ys => xs.filter(
        x => ys.some(eqFn(x))
    );

// intersectListsBy :: (a -> a -> Bool) -> [[a]] -> [a]
const intersectListsBy = eqFn =>
    foldr1(intersectBy(eqFn));

// intersectSet :: Set -> Set -> Set
const intersectSet = a =>
    // The intersection of two sets.
    b => new Set([...a].filter(i => b.has(i)));

// intersection :: Ord a => Set a -> Set a -> Set a
const intersection = s => s1 =>
    new Set([...s].filter(x => s1.has(x)));

// intersperse :: a -> [a] -> [a]
const intersperse = sep =>
    // intersperse(0)([1,2,3]) -> [1, 0, 2, 0, 3]
    xs => 0 < xs.length
        ? [xs[0]].concat(
            xs.slice(1).flatMap(x => [sep, x])
        )
        : [];

// isAlpha :: Char -> Bool
const isAlpha = c =>
    (/[A-Za-z\u00C0-\u00FF]/u).test(c);

// isAlphaNum :: Char -> Bool
const isAlphaNum = c => {
    const n = c.codePointAt(0);

    return (48 <= n && 57 >= n) || (
        (/[A-Za-z\u00C0-\u00FF]/u).test(c)
    );
};

// isBigInt :: Num -> Bool
const isBigInt = n =>
    ("undefined" !== typeof BigInt) && (
        "bigint" === typeof n
    );

// isChar :: a -> Bool
const isChar = x =>
    ("string" === typeof x) && (1 === x.length);

// isDigit :: Char -> Bool
const isDigit = c => {
    const n = c.codePointAt(0);

    return 48 <= n && 57 >= n;
};

// isInfixOf :: (Eq a) => [a] -> [a] -> Bool
// isInfixOf :: String -> String -> Bool
const isInfixOf = needle => haystack =>
    "string" !== typeof haystack
        ? (() => {
            const
                lng = needle.length,
                go = xs => lng <= xs.length
                    ? isPrefixOf(needle)(xs) || go(xs.slice(1))
                    : false;

            return go(haystack);
        })()
        : haystack.includes(needle);

// isLeft :: Either a b -> Bool
const isLeft = lr =>
    ("Either" === lr.type) && (undefined !== lr.Left);

// isLower :: Char -> Bool
const isLower = c =>
    // True if c is a lower case character.
    (/\p{Ll}/u).test(c);

// isMaybe :: a -> Bool
const isMaybe = x =>
    "Maybe" === x.type;

// isNull :: [a] -> Bool
// isNull :: String -> Bool
const isNull = xs =>
// True if xs is empty.
    1 > xs.length;

// isPrefixOf :: [a] -> [a] -> Bool
// isPrefixOf :: String -> String -> Bool
const isPrefixOf = xs =>
// True if and only if xs is a prefix of ys.
    ys => {
        const go = (vs, ws) => {
            const intX = vs.length;

            return 0 < intX
                ? ws.length >= intX
                    ? vs[0] === ws[0] && go(
                        vs.slice(1), ws.slice(1)
                    )
                    : false
                : true;
        };

        return "string" !== typeof xs
            ? go(xs, ys)
            : ys.startsWith(xs);
    };

// isRight :: Either a b -> Bool
const isRight = lr =>
    ("undefined" !== typeof lr) && (
        "Either" === lr.type
    ) && (undefined !== lr.Right);

// isSortedBy :: (a -> a -> Bool) -> [a] -> Bool
const isSortedBy = p =>
    // True if all adjacent pairs of elements in
    // the list return True under the predicate p.
    xs => xs.length < 2 || all(x => x < 1)(
        zipWith_(p)(
            xs
        )(tail(xs))
    );

// isSpace :: Char -> Bool
const isSpace = c =>
    // True if c is a white space character.
    (/\s/u).test(c);

// isSubsequenceOf :: Eq a => [a] -> [a] -> Bool
// isSubsequenceOf :: String -> String -> Bool
const isSubsequenceOf = xs =>
    // True if xs is a sub-sequence of ys.
    ys => {
        const go = (a, b) =>
            0 < a.length
                ? 0 < b.length
                    ? go(
                        a[0] === b[0]
                            ? a.slice(1)
                            : a,
                        b.slice(1)
                    )
                    : false
                : true;

        return go(xs, ys);
    };

// isSubsetOf :: Ord a => Set a -> Set a -> Bool
const isSubsetOf = a => b => {
    for (const x of a) {
        if (!b.has(x)) {
            return false;
        }
    }

    return true;
};

// isSuffixOf :: Eq a => [a] -> [a] -> Bool
// isSuffixOf :: String -> String -> Bool
const isSuffixOf = needle =>
    haystack => "string" !== typeof haystack
        ? bindMay(
            dropLengthMaybe(needle)(haystack)
        )(
            delta => eq(needle)(
                dropLength(delta)(haystack)
            )
        )
        : haystack.endsWith(needle);

// isUpper :: Char -> Bool
const isUpper = c =>
    // True if c is an upper case character.
    (/\p{Lu}/u).test(c);

// iso8601Local :: Date -> String
const iso8601Local = dte =>
    new Date(dte - (6E4 * dte.getTimezoneOffset()))
    .toISOString();

// iterate :: (a -> a) -> a -> Gen [a]
const iterate = f =>
    // An infinite list of repeated applications
    // of f, starting with the seed value x.
    function* (x) {
        let v = x;

        while (true) {
            yield v;
            v = f(v);
        }
    };

// iterateUntil :: (a -> Bool) -> (a -> a) -> a -> [a]
const iterateUntil = p =>
    // Like `until`, but returns a list of
    // intermediate values, where until
    // returns only a final value.
    // iterateUntil(x => 5 < x)(x => 2 * x)(1)
    // -> [1, 2, 4, 8]
    f => x => {
        const
            go = v => p(v)
                ? [v]
                : [v, ...go(f(v))];

        return go(x);
    };

// iterateUntilGen :: (a -> Bool) -> (a -> a) ->
// a -> Generator [a]
const iterateUntilGen = p =>
    f => function* (x) {
        let v = x;

        while (!p(v)) {
            yield v;
            v = f(v);
        }
    };

// join :: Monad m => m (m a) -> m a
const join = x =>
    bind(x)(identity);

// jsonFromTree :: Tree a -> String
const jsonFromTree = tree => {
    // A recursive [root, nest] JSON format,
    // in which `root` is a value string, and `nest`
    // is a possibly empty list of [`root`, `nest`] pairs.
    const go = node => [node.root, node.nest.map(go)];

    return JSON.stringify(go(tree));
};

// jsonLog :: a -> IO ()
const jsonLog = (...args) =>
    // eslint-disable-next-line no-console
    console.log(
        args
        .map(JSON.stringify)
        .join(" -> ")
    );

// jsonParseLR :: String -> Either String a
const jsonParseLR = s => {
    try {
        return Right(JSON.parse(s));
    } catch (e) {
        return Left(
            unlines([
                e.message,
                `(line:${e.line} col:${e.column})`
            ])
        );
    }
};

// justifyLeft :: Int -> Char -> String -> String
const justifyLeft = n =>
    // The string s, followed by enough padding (with
    // the character c) to reach the string length n.
    c => s => n > s.length
        ? s.padEnd(n, c)
        : s;

// justifyRight :: Int -> Char -> String -> String
const justifyRight = n =>
    // The string s, preceded by enough padding (with
    // the character c) to reach the string length n.
    c => s => n > s.length
        ? s.padStart(n, c)
        : s;

// kCompose (>=>) :: Monad m =>
// [(a -> m a)] -> (a -> m a)
const kCompose = (...fs) =>
    // Left Right composition of a sequence
    // of functions which lift a raw value
    // of the same type into the same monad.
    x => Boolean(fs.length)
        ? fs.slice(1).reduce(
            (m, f) => bind(m)(f),
            fs[0](x)
        )
        : x;

// keys :: Dict -> [String]
const keys = Object.keys;

// kleisliCompose (>=>) :: Monad m => (a -> m b) ->
// (b -> m c) -> (a -> m c)
const kleisliCompose = f =>
    // Kleisli composition of two functions which
    // each lift their values into the same monad.
    g => x => bind(f(x))(g);

// last :: [a] -> a
const last = xs => {
    // The last item of a list.
    const n = xs.length;

    return 0 < n
        ? xs[n - 1]
        : null;
};

// lastMay :: [a] -> Maybe a
const lastMay = xs =>
    // Nothing if xs is empty, otherwise
    // Just the last item of xs.
    0 < xs.length
        ? Just(xs.slice(-1)[0])
        : Nothing();

// lazyList :: [a] -> Gen [a]
const lazyList = xs => {
    // The values of a given array
    // lazily yielded one by one.
    const go = function* () {
        const vs = Array.from(xs);

        while (0 < vs.length) {
            yield vs.shift();
        }
    };

    return go();
};

// lcm :: Int -> Int -> Int
const lcm = x =>
    // The smallest positive integer divisible
    // without remainder by both x and y.
    y => (x === 0 || y === 0)
        ? 0
        : Math.abs(Math.floor(x / gcd(x)(y)) * y);

// le :: Ord a => a -> a -> a
const le = x =>
    // True if x <= y;
    y => x <= y;

// lefts :: [Either a b] -> [a]
const lefts = xs =>
    xs.flatMap(
        x => ("Left" in x)
            ? [x.Left]
            : []
    );

// length :: [a] -> Int
const length = xs =>
    // Returns Infinity over objects without finite
    // length. This enables zip and zipWith to choose
    // the shorter argument when one is non-finite,
    // like cycle, repeat etc
    "Node" !== xs.type
        ? "GeneratorFunction" !== (
            xs.constructor.constructor.name
        )
            ? xs.length
            : Infinity
        : lengthTree(xs);

// lengthTree :: Tree a -> Int
const lengthTree = tree => {
    // The number of nodes in the tree.
    const go = (n, t) =>
        n + nest(t).reduce(go, 1);

    return go(0, tree);
};

// levelNodes :: Tree a -> [[Tree a]]
const levelNodes = tree =>
    iterateUntil(xs => 1 > xs.length)(
        xs => xs.flatMap(x => x.nest)
    )([tree]);

// levels :: Tree a -> [[a]]
const levels = tree => {
    // A list of lists, grouping the root
    // values of each level of the tree.
    const go = (layers, t) => {
        const
            [x, ...xs] = (
                0 < layers.length
            )
                ? layers
                : [[]];

        return [
            x.concat(root(t)),
            ...nest(t).reduce(go, xs)
        ];
    };

    return go([], tree);
};

// liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c
const liftA2 = f =>
    // Lift a binary function to actions.
    // liftA2 f a b = fmap f a <*> b
    a => b => ({
        "(a -> b)": () => liftA2Fn,
        "Either": () => liftA2LR,
        "Maybe": () => liftA2May,
        "Tuple": () => liftA2Tuple,
        "Node": () => liftA2Tree,
        "List": () => liftA2List,
        "Bottom": () => liftA2List
    }[typeName(a) || "List"]())(f)(a)(b);

// liftA2Fn :: (a0 -> b -> c) -> (a -> a0) -> (a -> b) -> a -> c
const liftA2Fn = op =>
    // Lift a binary function to a composition
    // over two other functions.
    // liftA2 (*) (+ 2) (+ 3) 7 == 90
    f => g => x => op(f(x))(
        g(x)
    );

// liftA2LR :: (a -> b -> c) -> Either d a -> Either d b -> Either d c
const liftA2LR = f =>
    // The binary function f lifted to a
    // function over two Either values.
    a => b => bindLR(a)(
        x => bindLR(b)(
            compose(Right, f(x))
        )
    );

// liftA2List :: (a -> b -> c) -> [a] -> [b] -> [c]
const liftA2List = op =>
    // The binary operator op applied to each pair of
    // arguments in the cartesian product of xs and ys.
    // A binary operator lifed to a function over two lists.
    xs => ys => xs.flatMap(
        x => ys.map(op(x))
    );

// liftA2May :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c
const liftA2May = f =>
    a => b => a.Nothing
        ? a
        : b.Nothing
            ? b
            : Just(f(a.Just)(b.Just));

// liftA2Tree :: (a -> b -> c) -> Tree a -> Tree b -> Tree c
const liftA2Tree = f =>
    tx => ty => {
        const go = t =>
            Node(f(t.root)(ty.root))(
                Boolean(ty.nest)
                    ? ty.nest.map(
                        fmapTree(f(t.root))
                    )
                    .concat(t.nest.map(go))
                    : []
            );

        return go(tx);
    };

// liftA2Tuple :: Monoid m =>
// (a -> b -> c) -> (m, a) -> (m, b) -> (m, c)
const liftA2Tuple = f =>
    ([a, b]) => ([c, d]) => Tuple(
        mappend(a)(c)
    )(
        f(b)(d)
    );

// liftA2ZL :: (a -> b -> c) -> ZipList a ->
// ZipList b -> ZipList c
const liftA2ZL = op =>
    // A ZipList formed by the pairwise application of a
    // binary op over the values of two existing ZipLists
    // up to the length of the shorter of these.
    zxs => zys => ZipList(
        zipWith(op)(
            zxs.getZipList
        )(
            zys.getZipList
        )
    );

// lines :: String -> [String]
const lines = s =>
    // A list of strings derived from a single string
    // which is delimited by \n or by \r\n or \r.
    0 < s.length
        ? s.split(/\r\n|\n|\r/u)
        : [];

// list :: StringOrArrayLike b => b -> [a]
const list = xs =>
// xs itself, if it is an Array,
// or an Array derived from xs.
    Array.isArray(xs)
        ? xs
        : Array.from(xs || []);

// listFromMaybe :: Maybe a -> [a]
const listFromMaybe = mb =>
    // A singleton list derived from a Just value,
    // or an empty list derived from Nothing.
    mb.Nothing
        ? []
        : [mb.Just];

// listFromTree :: Tree a -> [a]
const listFromTree = tree => {
    const go = x => [
        root(x),
        ...[].concat(...nest(x).map(go))
    ];

    return go(tree);
};

// listToMaybe :: [a] -> Maybe a
const listToMaybe = xs =>
    // Nothing if xs is empty, or Just the head of xs.
    0 < xs.length
        ? Just(xs[0])
        : Nothing();

// log :: Float -> Float
const log = Math.log;

// lookup :: Eq a => a -> Container -> Maybe b
const lookup = k =>
    // Just of value of the key k in m,
    // or Nothing if m does not contain k.
    m => (Array.isArray(m)
        ? lookupTuples
        : lookupDict)(k)(m);

// lookupDict :: a -> Dict -> Maybe b
const lookupDict = k =>
    dct => {
        const v = dct[k];

        return undefined !== v
            ? Just(v)
            : Nothing();
    };

// lookupTuples :: Eq a => a -> [(a, b)] -> Maybe b
const lookupTuples = k =>
    kvs => {
        const i = kvs.findIndex(kv => k === kv[0]);

        return -1 !== i
            ? Just(kvs[i][1])
            : Nothing();
    };

// lt (<) :: Ord a => a -> a -> Bool
const lt = a =>
    b => a < b;

// mReturn :: First-class m => (a -> b) -> m (a -> b)
const mReturn = x =>
    // Not required in JS, which has first functions by default.
    // Included only for comparison with AS, which has to derive
    // first class functions by lifting 'handlers' into 'scripts'
    // as anonymous |λ|() functions.
    // In JS, mReturn is just an alias of identity.
    identity(x);

// map :: (a -> b) -> [a] -> [b]
const map = f =>
    // The list obtained by applying f
    // to each element of xs.
    // (The image of xs under f).
    xs => [...xs].map(f);

// mapAccumL :: (acc -> x -> (acc, y)) -> acc ->
// [x] -> (acc, [y])
const mapAccumL = f =>
    // A tuple of an accumulation and a list
    // obtained by a combined map and fold,
    // with accumulation from left to right.
    acc => xs => [...xs].reduce(
        ([a, bs], x) => second(
            v => [...bs, v]
        )(
            f(a)(x)
        ),
        [acc, []]
    );

// mapAccumLTree :: (s -> a -> (s, b)) -> s ->
// Tree a -> (s, Tree b)
const mapAccumLTree = f => {
    // A tuple of an accumulation and a tree
    // obtained by a combined map and fold,
    // with accumulation from left to right over
    // the subForest.
    const go = a => x => {
        const [acc, v] = f(a)(root(x));

        return second(Node(v))(
            mapAccumL(go)(acc)(nest(x))
        );
    };

    return go;
};

// mapAccumR :: (acc -> x -> (acc, y)) -> acc ->
//    [x] -> (acc, [y])
const mapAccumR = f =>
    // A tuple of an accumulation and a list
    // obtained by a combined map and fold,
    // with accumulation from right to left.
    acc => xs => [...xs].reduceRight(
        ([a, b], x) => second(
            v => [v].concat(b)
        )(
            f(a)(x)
        ),
        Tuple(acc)([])
    );

// mapFromList :: [(String, a)] -> Dict
const mapFromList = kvs =>
    Object.fromEntries(kvs);

// mapKeys :: (Key -> Key) -> IntMap a -> IntMap a
const mapKeys = f =>
    // A function mapped over the keys of a record,
    // defining a new record.
    dct => Object.fromEntries(
        Object.entries(dct)
        .map(kv => [f(kv[0]), kv[1]])
    );

// mapMaybe :: (a -> Maybe b) -> [a] -> [b]
const mapMaybe = mf =>
    // A filtered map, retaining only the contents
    // of Just values. (Nothing values discarded).
    xs => xs.flatMap(x => {
        const mb = mf(x);

        return "Just" in mb
            ? [mb.Just]
            : [];
    });

// mapMaybeGen :: (a -> Maybe b) -> Gen [a] -> Gen [b]
const mapMaybeGen = mf =>
    // A filtered map over a generator, returning only the
    // contents of Just values. (Nothing values discarded).
    function*(gen) {
        let v = take(1)(gen);

        while (Boolean(v.length)) {
            const mb = mf(v[0]);

            if (!("Nothing" in mb)) {
                yield mb.Just;
            }
            v = take(1)(gen);
        }
    };

// mappEndo (<>) :: Endo a -> Endo a -> Endo a
const mappEndo = a =>
    // mappend is defined as composition
    // for the Endo type.
    b => Endo(x => a.appEndo(b.appEndo(x)));

// mappend (<>) :: Monoid a => a -> a -> a
const mappend = a =>
    // Associative operation
    // defined for various monoids.
    ({
        "(a -> b)": () => mappendFn,
        "Endo": () => mappEndo,
        "List": () => append,
        "Maybe": () => mappendMaybe,
        "Num": () => mappendOrd,
        "String": () => append,
        "Tuple": () => mappendTupleN,
        "TupleN": () => mappendTupleN
    })[typeName(a)]()(a);

// mappendComparing (<>) :: (a -> a -> Bool)
// (a -> a -> Bool) -> (a -> a -> Bool)
const mappendComparing = cmp =>
    cmp1 => a => b => {
        const x = cmp(a)(b);

        return 0 !== x
            ? x
            : cmp1(a)(b);
    };

// mappendFn (<>) :: Monoid b => (a -> b) -> (a -> b) -> (a -> b)
const mappendFn = f =>
    g => x => mappend(f(x))(
        g(x)
    );

// mappendMaybe (<>) :: Maybe a -> Maybe a -> Maybe a
const mappendMaybe = a =>
    b => a.Nothing
        ? b
        : b.Nothing
            ? a
            : Just(
                mappend(a.Just)(b.Just)
            );

// mappendOrd (<>) :: Ordering -> Ordering -> Ordering
const mappendOrd = x =>
    y => 0 !== x
        ? x
        : y;

// mappendTuple (<>) :: (a, b) -> (a, b) -> (a, b)
const mappendTuple = ([a, b]) =>
    ([c, d]) => Tuple(
        mappend(a)(c)
    )(
        mappend(b)(d)
    );

// mappendTupleN (<>) ::
// (a, b, ...) -> (a, b, ...) -> (a, b, ...)
const mappendTupleN = t => t1 => {
    const n = t.length;

    return n === t1.length
        ? TupleN(
            [...t].map(
                (x, i) => mappend(x)(t1[i])
            )
        )
        : undefined;
};

// matching :: [a] -> (a -> Int -> [a] -> Bool)
const matching = pat => {
    // A sequence-matching function for findIndices etc
    // findIndices(matching([2, 3]), [1, 2, 3, 1, 2, 3])
    // -> [1, 4]
    const
        n = pat.length,
        bln = 0 < n,
        h = bln
            ? pat[0]
            : undefined;

    return x => i => src =>
        bln && h === x && eq(pat)(
            src.slice(i, n + i)
        );
};

// matrix Int -> Int -> (Int -> Int -> a) -> [[a]]
const matrix = nRows =>
    // A matrix of a given number of columns and rows,
    // in which each value is a given function of its
    // (zero-based) column and row indices.
    nCols => f => Array.from(
        {length: nRows}, (_, iRow) =>
            Array.from(
                {length: nCols},
                (__, iCol) => f(iRow)(iCol)
            )
    );

// max :: Ord a => a -> a -> a
const max = a =>
    // b if greater than a,
    // otherwise a.
    b => gt(b)(a)
        ? b
        : a;

// maxBound :: a -> a
const maxBound = x => {
    const e = x.enum;

    return Boolean(e)
        ? e[e[x.max]]
        : {
            "number": Number.MAX_SAFE_INTEGER,
            "string": String.fromCodePoint(0x10FFFF),
            "boolean": true
        }[typeof x];
};

// maximum :: Ord a => [a] -> a
const maximum = xs =>
    // The largest value in a non-empty list.
    0 < xs.length
        ? xs.slice(1).reduce(
            (a, x) => x > a
                ? x
                : a,
            xs[0]
        )
        : undefined;

// maximumBy :: (a -> a -> Ordering) -> [a] -> a
const maximumBy = f =>
    xs => 0 < xs.length
        ? xs.slice(1).reduce(
            (a, x) => 0 < f(x)(a)
                ? x
                : a,
            xs[0]
        )
        : undefined;

// maximumByMay :: (a -> a -> Ordering) ->
// [a] -> Maybe a
const maximumByMay = f =>
    // Nothing, if the list is empty,
    // or just the maximum value when compared
    // in terms of f.
    xs => 0 < xs.length
        ? Just(xs.slice(1).reduce(
            (a, x) => 0 < f(a)(x)
                ? a
                : x,
            xs[0]
        ))
        : Nothing();

// maximumMay :: Ord a => [a] -> Maybe a
const maximumMay = xs =>
    0 < xs.length
        ? Just(xs.slice(1).reduce(
            (a, x) => x > a
                ? x
                : a,
            xs[0]
        ))
        : Nothing();

// maximumOn :: (Ord b) => (a -> b) -> [a] -> a
const maximumOn = f =>
    // The item in xs for which f
    // returns the highest value.
    xs => 0 < xs.length
        ? xs.slice(1).reduce(
            (tpl, x) => {
                const v = f(x);

                return v > tpl[1]
                    ? Tuple(x)(v)
                    : tpl;
            },
            (h => Tuple(h)(f(h)))(xs[0])
        )[0]
        : undefined;

// maybe :: b -> (a -> b) -> Maybe a -> b
const maybe = v =>
    // Default value (v) if m is Nothing, or f(m.Just)
    f => m => "Just" in m
        ? f(m.Just)
        : v;

// mconcatOrd :: [Ordering] -> Ordering
const mconcatOrd = cmps =>
    // A sort compare function derived from
    // a list of such functions, providing
    // for composition of n-ary sorts.
    0 < cmps.length
        ? foldl(
            mappendOrd
        )(cmps[0])(cmps.slice(1))
        : compare;

// mean :: [Num] -> Num
const mean = xs =>
    xs.reduce(
        (a, x) => a + x,
        0
    ) / xs.length;

// measuredTree :: Tree a ->
// Tree (a, {leafSum::Int, layerSum::Int,
//           nodeSum::Int, index::Int})
// eslint-disable-next-line max-lines-per-function
const measuredTree = tree => {
    // A tree in which each node is tupled with
    // a (leafSum, layerSum, nodeSum) measure of its sub-tree,
    // where leafSum is the number of descendant leaves,
    // and layerSum is the number of descendant levels,
    // and nodeSum counts all nodes, including the root.
    // Index is a position in a zero-based top-down
    // left to right series.
    // For additional parent indices, see parentIndexedTree.
    const whni = (leafSum, layerSum, nodeSum, ndx) => ({
        leafSum,
        layerSum,
        nodeSum,
        index : ndx
    });
    let i = 0;

    return foldTree(
        x => {
        // eslint-disable-next-line no-plusplus
            const topDown = i++;

            return xs => Node(
                Tuple(x)(
                    0 < xs.length
                        ? (() => {
                            const dct = xs.reduce(
                                (a, node) => {
                                    const dimns = node.root[1];

                                    return whni(
                                        a.leafSum + dimns.leafSum,
                                        Math.max(a.layerSum)(
                                            dimns.layerSum
                                        ),
                                        a.nodeSum + dimns.nodeSum,
                                        topDown
                                    );
                                }, whni(0, 0, 0, topDown)
                            );

                            return whni(
                                dct.leafSum,
                                1 + dct.layerSum,
                                1 + dct.nodeSum,
                                topDown
                            );
                        })()
                        : whni(1, 0, 1, topDown)
                )
            )(xs);
        }
    )(tree);
};

// member :: Key -> Dict -> Bool
const member = k =>
    // True if dict contains the key k.
    dict => k in dict;

// mempty :: a -> a
const mempty = v => {
    const t = typeName(v);

    return ({
        "List": () => [],
        "Maybe": () => Nothing(),
        "Num": () => 0,
        "String": () => "",
        "Tuple": () => Tuple(
            mempty(v[0])
        )(
            mempty(v[1])
        ),
        "Node": () => Node(mempty(root(v)))([])
    })[t]();
};

// merge :: Ord a => [a] -> [a] -> [a]
const merge = xs =>
    // An ordered list derived by merging
    // two other ordered lists.
    mergeBy(compare)(xs);

// mergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]
const mergeBy = f =>
// A single list defined by the ordered
// merging of xs and ys in terms of the
// given comparator function.
    xs => ys => {
        const go = (as, bs) =>
            0 < bs.length
                ? 0 < as.length
                    ? 1 !== f(as[0])(bs[0])
                        ? [as[0]].concat(
                            go(as.slice(1), bs)
                        )
                        : [bs[0]].concat(
                            go(as, bs.slice(1))
                        )
                    : bs
                : as;

        return [].concat(...go(xs, ys));
    };

// min :: Ord a => a -> a -> a
const min = a =>
    b => b < a
        ? b
        : a;

// minBound :: a -> a
const minBound = x => {
    const e = x.enum;

    return Boolean(e)
        ? e[e[0]]
        : {
            "number": Number.MIN_SAFE_INTEGER,
            "string": String.fromCodePoint(0),
            "boolean": false
        }[typeof x];
};

// minimum :: Ord a => [a] -> a
const minimum = xs =>
    // The least value of xs.
    0 < xs.length
        ? xs.slice(1).reduce(
            (a, x) => x < a
                ? x
                : a,
            xs[0]
        )
        : null;

// minimumBy :: (a -> a -> Ordering) -> [a] -> a
const minimumBy = f =>
    xs => 0 < xs.length
        ? xs.slice(1).reduce(
            (a, x) => 0 > f(x)(a)
                ? x
                : a,
            xs[0]
        )
        : undefined;

// minimumByMay :: (a -> a -> Ordering) -> [a] -> Maybe a
const minimumByMay = f =>
    xs => xs.reduce(
        (a, x) => a.Nothing
            ? Just(x)
            : f(x)(a.Just) < 0
                ? Just(x)
                : a,
        Nothing()
    );

// minimumMay :: [a] -> Maybe a
const minimumMay = xs =>
    0 < xs.length
        ? Just(xs.slice(1).reduce(
            (a, x) => x < a
                ? x
                : a,
            xs[0]
        ))
        : Nothing();

// minimumOn :: (Ord b) => (a -> b) -> [a] -> a
const minimumOn = f =>
    // The item in xs for which f
    // returns the highest value.
    xs => 0 < xs.length
        ? xs.slice(1).reduce(
            (tpl, x) => {
                const v = f(x);

                return v < tpl[1]
                    ? Tuple(x)(v)
                    : tpl;
            },
            (h => Tuple(h)(f(h)))(xs[0])
        )[0]
        : undefined;

// mod :: Int -> Int -> Int
const mod = n =>
    // Inherits the sign of the *divisor* for non zero
    // results. Compare with `rem`, which inherits
    // the sign of the *dividend*.
    d => (n % d) + (
        signum(n) === signum(-d)
            ? d
            : 0
    );

// mul (*) :: Num a => a -> a -> a
const mul = a =>
    b => a * b;

// ne :: a -> a -> Bool
const ne = a =>
    b => a !== b;

// negate :: Num -> Num
const negate = n =>
    -n;

// nest :: Tree a -> [a]
const nest = tree => {
    // Allowing for lazy (on-demand) evaluation.
    // If the nest turns out to be a function –
    // rather than a list – that function is applied
    // here to the root, and returns a list.
    const xs = tree.nest;

    return "function" !== typeof xs
        ? xs
        : xs(root(tree));
};

// not :: Bool -> Bool
const not = b =>
    !b;

// notElem :: Eq a => a -> [a] -> Bool
const notElem = x =>
    xs => !xs.includes(x);

// nub :: Eq a => [a] -> [a]
const nub = xs =>
    [...new Set(xs)];

// nubBy :: (a -> a -> Bool) -> [a] -> [a]
const nubBy = pEq =>
    // A sublist of xs from which all duplicates,
    // (as defined by the equality predicate pEq)
    // are excluded.
    xs => xs.reduce(
        (seen, x) => seen.some(pEq(x))
            ? seen
            : seen.concat([x]),
        []
    );

// odd :: Int -> Bool
const odd = n =>
    !even(n);

// on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
const on = f =>
    // e.g. groupBy(on(eq)(length))
    g => a => b => f(g(a))(g(b));

// or :: [Bool] -> Bool
const or = xs =>
    xs.some(Boolean);

// ord :: Char -> Int
const ord = c =>
    // Unicode ordinal value of the character.
    c.codePointAt(0);

// outdented :: String -> String
const outdented = s => {
    // All lines in the string outdented by the same amount
    // (just enough to ensure that the least indented lines
    //  have no remaining indent)
    // All relative indents are left unchanged
    const
        // Leading indentation characters.
        rgx = /^\s*/u,
        xs = lines(s),
        n = Math.min(
            ...xs.map(txt => rgx.exec(txt)[0].length)
        );

    return 0 < n ? (
        xs.map(x => x.slice(n)).join("\n")
    ) : s.slice(0);
};

// parentIndexedTree :: Tree (a, {...index :: Int}) ->
// Tree (a, {...index :: Int, parent :: Maybe Int})
const parentIndexedTree = tree => {
    // A tree additionally decorated with parent indices,
    // derived from a measured tree already decorated with
    // node indices. (See measuredTree).
    const go = mb => node => {
        const
            x = root(node),
            measures = x[1];

        return Node(
            Tuple(x[0])({
                ...measures,
                parent: mb
            })
        )(nest(node).map(go(Just(measures.index))));
    };

    return go(Nothing())(tree);
};

// partition :: (a -> Bool) -> [a] -> ([a], [a])
const partition = p =>
    // A tuple of two lists - those elements in
    // xs which match p, and those which do not.
    xs => [...xs].reduce(
        (a, x) => (
            p(x)
                ? first
                : second
        )(ys => [...ys, x])(a),
        Tuple([])([])
    );

// partitionEithers :: [Either a b] -> ([a],[b])
const partitionEithers = xs =>
    // A tuple of two lists:
    // first all the Left values in xs,
    // and then all the Right values in xs.
    xs.reduce(
        (a, x) => (
            "Left" in x
                ? first(ys => [...ys, x.Left])
                : second(ys => [...ys, x.Right])
        )(a),
        Tuple([])([])
    );

// partitionTree :: (a -> Bool) -> 
// Tree a -> ([Tree a], [Tree a])
const partitionTree = p =>
    // A list of matching subtrees, tupled with a list 
    // which contains the unmatched residue, if any, 
    // of the input tree.
    foldTree(x => vs => {
        const
            [matches, residues] = [...unzip(vs)].map(
                v => v.flat()
            ),
            subTree = Node(x)(residues);

        return p(x)
            ? Tuple([subTree, ...matches])([])
            : Tuple(matches)([subTree]);
    });

// pathAccessor :: String -> Dict -> a
const pathAccessor = path =>
    // Value if any, at supplied dot path in object.
    // Null if no such path is found.
    obj => path.split(".").reduce(
        (v, k) => v instanceof Object
            ? k in v
                ? v[k]
                : undefined
            : v,
        obj
    );

// permutations :: [a] -> [[a]]
const permutations = xs =>
    // All possible orderings of the items in xs.
    // N factorial permutations, where N === length(xs).
    xs.reduceRight(
        (orderings, x) => orderings.flatMap(
            ordering => Array.from({
                length: 1 + ordering.length
            }, (_, i) => i)
            // One additional permutation for each
            // possible position of x in each
            // existing permutation.
            .map(position => [
                ...ordering.slice(0, position),
                x,
                ...ordering.slice(position)
            ])
        ), [
            []
        ]
    );

// pi :: Float
const pi = Math.PI;

// plural :: Int -> String -> String
const plural = n =>
    // Singular or plural EN inflection
    // of a given word, preceded by digits.
    k => 1 === n
        ? `${k}`
        : `${k}s`;

// plus :: Num -> Num -> Num
const plus = a =>
    // The sum of a and b.
    b => a + b;

// postorder :: Tree a -> [a]
const postorder = t => {
    // List of root elements of tree flattened
    // bottom-up into a postorder list.
    const go = (xs, x) =>
        nest(x).reduce(go, xs)
        .concat(root(x));

    return go([], t);
};

// pred :: Enum a => a -> a
const pred = x => {
    const t = typeof x;

    return "number" !== t ? (() => {
        const [i, mn] = [x, minBound(x)].map(fromEnum);

        return i > mn ? (
            toEnum(x)(i - 1)
        ) : Error("succ :: enum out of range.");
    })() : x > Number.MIN_SAFE_INTEGER ? (
        x - 1
    ) : Error("succ :: Num out of range.");
};

// predMay :: Enum a => a -> Maybe a
const predMay = x => {
    const t = typeof x;

    return "number" !== t ? (() => {
        const [i, mn] = [x, minBound(x)].map(fromEnum);

        return i > mn ? (
            Just(toEnum(x)(i - 1))
        ) : Nothing();
    })() : x > Number.MIN_SAFE_INTEGER ? (
        Just(x - 1)
    ) : Nothing();
};

// prependToAll :: a -> [a] -> [a]
const prependToAll = sep =>
    // prependToAll(0)([1,2,3]) -> [0, 1, 0, 2, 0, 3]
    xs => 0 < xs.length ? [
        sep, xs[0],
        ...prependToAll(sep)(xs.slice(1))
    ] : [];

// product :: [Num] -> Num
const product = xs =>
    xs.reduce((a, x) => a * x, 1);

// properFracRatio :: Ratio -> (Int, Ratio)
const properFracRatio = nd => {
    const [q, r] = quotRem(nd.n)(nd.d);

    return Tuple(q)(Ratio(r)(nd.d));
};

// properFraction :: Real -> (Int, Real)
const properFraction = n => {
    const i = Math.floor(n) + (n < 0 ? 1 : 0);

    return Tuple(i)(n - i);
};

// prunedForest (a -> Bool) -> Forest a -> Forest a
const prunedForest = p => {
    // A forest of trees in which every node matches p.
    // That is, a forest including only nodes which:
    // 1. match the predicate p, AND
    // 2. descend from ancestors which all match p.
    const
        go = trees => trees.flatMap(tree => {
            const x = root(tree);

            return p(x)
                ? [
                    Node(x)(
                        go(nest(tree))
                    )
                ]
                : [];
        });

    return go;
};

// pureLR :: a -> Either e a
const pureLR = x =>
    // The value x lifted into the Either monad.
    Right(x);

// pureList :: a -> [a]
const pureList = x =>
    [x];

// pureMay :: a -> Maybe a
const pureMay = x =>
    Just(x);

// pureT :: String -> (a -> f a)
const pureT = t =>
    // Given a type name string, returns a
    // specialised "pure", where
    // "pure" lifts a value into a particular functor.
    ({
        "Either": () => pureLR,
        "(a -> b)": () => constant,
        "Maybe": () => pureMay,
        "Node": () => pureTree,
        "Tuple": () => pureTuple,
        "List": () => pureList
    })[t || "List"]();

// pureTree :: a -> Tree a
const pureTree = x =>
    Node(x)([]);

// pureTuple :: a -> (a, a)
const pureTuple = x =>
    Tuple("")(x);

// pureZL :: a -> ZipList a
const pureZL = x =>
    // A value lifted into a ZipList
    ZipList(repeat(x));

// quickSort :: (Ord a) => [a] -> [a]
const quickSort = xs =>
    // Included only for comparison with AppleScript
    // sort and sortBy are faster and more flexible
    xs.length > 1 ? (() => {
        const
            h = xs[0],
            lessMore = partition(x => x <= h)(
                xs.slice(1)
            );

        return [].concat(...[
            quickSort(lessMore[0]),
            h,
            quickSort(lessMore[1])
        ]);
    })() : xs;

// quickSortBy :: (a -> a -> Ordering) -> [a] -> [a]
const quickSortBy = cmp => {
    // Included only for comparison with AppleScript.
    // sort and sortBy are faster and more flexible.
    const go = xs => xs.length > 1 ? (() => {
        const
            h = xs[0],
            lessMore = partition(
                x => 1 !== cmp(x)(h)
            )(xs.slice(1));

        return [].concat(...[
            go(lessMore[0]),
            h,
            go(lessMore[1])
        ]);
    })() : xs;

    return go;
};

// quot :: Integral a => a -> a -> a
const quot = n =>
    m => [n, m].some(isBigInt) ? (
        BigInt(n) / BigInt(m)
    ) : Math.trunc(n / m);

// quotRem :: Integral a => a -> a -> (a, a)
const quotRem = m =>
    // The quotient, tupled with the remainder.
    n => Tuple(
        Math.trunc(m / n)
    )(
        m % n
    );

// quoted :: Char -> String -> String
const quoted = c =>
    // A string flanked on both sides
    // by a specified quote character.
    s => c + s + c;

// radians :: Float x => Degrees x -> Radians x
const radians = x =>
    (Math.PI / 180) * x;

// raise :: Num -> Int -> Num
const raise = x =>
    // X to the power of n.
    n => x ** n;

// randomRInt :: Int -> Int -> (() -> IO Int)
const randomRInt = low =>
    // The return value of randomRInt is itself
    // a function, which, whenever evaluated,
    // yields a a new pseudo-random integer
    // in the range [low..high].
    high => () => low + Math.floor(
        Math.random() * (1 + (high - low))
    );

// range :: Ix a => (a, a) -> [a]
const range = (...args) => {
    // The list of values in the subrange defined by a bounding pair.
    // range([0, 2]) -> [0,1,2]
    // range([[0,0], [2,2]])
    //  -> [[0,0],[0,1],[0,2],[1,0],[1,1],[1,2],[2,0],[2,1],[2,2]]
    // range([[0,0,0],[1,1,1]])
    //  -> [[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
    const
        ab = 1 !== args.length
            ? args
            : args[0],
        [as, bs] = [ab[0], ab[1]].map(
            x => Array.isArray(x)
                ? x
                : (undefined !== x.type) && (
                    x.type.startsWith("Tuple")
                )
                    ? listFromTuple(x)
                    : [x]
        ),
        an = as.length;

    return (an === bs.length)
        ? 1 < an
            ? traverseList(x => x)(
                as.map(
                    (_, i) => enumFromTo(as[i])(bs[i])
                )
            )
            : enumFromTo(as[0])(bs[0])
        : [];
};

// ratioDiv :: Rational -> Rational -> Rational
const ratioDiv = n1 => n2 => {
    const [r1, r2] = [n1, n2].map(rational);

    return Ratio(r1.n * r2.d)(
        r1.d * r2.n
    );
};

// ratioMinus :: Rational -> Rational -> Rational
const ratioMinus = n1 => n2 => {
    const [r1, r2] = [n1, n2].map(rational);
    const d = lcm(r1.d)(r2.d);

    return Ratio(
        (r1.n * (d / r1.d)) - (r2.n * (d / r2.d))
    )(d);
};

// ratioMult :: Rational -> Rational -> Rational
const ratioMult = n1 => n2 => {
    const [r1, r2] = map(rational)(
        [n1, n2]
    );

    return ratio(r1.n * r2.n)(
        r1.d * r2.d
    );
};

// ratioPlus :: Rational -> Rational -> Rational
const ratioPlus = n1 =>
    n2 => {
        const [r1, r2] = [n1, n2].map(rational);
        const d = lcm(r1.d)(r2.d);

        return ratio(
            (r1.n * (d / r1.d)) + (
                r2.n * (d / r2.d)
            )
        )(d);
    };

// rational :: Num a => a -> Rational
const rational = x =>
    isNaN(x)
        ? x
        : Number.isInteger(x)
            ? Ratio(x)(1)
            : approxRatio(undefined)(x);

// read :: Read a => String -> a
const read = JSON.parse;

// readHex :: String -> Int
const readHex = s =>
    // Integer value of hexadecimal expression.
    parseInt(s, 16);

// readLR :: Read a => String -> Either String a
const readLR = s => {
    try {
        return Right(JSON.parse(s));
    } catch (e) {
        return Left(e.message);
    }
};

// recip :: Num -> Num
const recip = n =>
    0 !== n
        ? (1 / n)
        : undefined;

// recipMay :: Num -> Maybe Num
const recipMay = n =>
    0 === n ? (
        Nothing()
    ) : Just(1 / n);

// regexIndexedMatches :: Regex -> String -> [(Int, String)]
const regexIndexedMatches = rgx =>
    // (Index, String) tuples for all matches of a
    // regular expression in a given string.
    s => Array.from(
        s.matchAll(rgx),
        m => [m.index, m[0]]
    );

// regexMatches :: Regex String -> String -> [[String]]
const regexMatches = rgx =>
    // All matches for the given regular expression
    // in the supplied string s.
    s => [...s.matchAll(new RegExp(rgx, "gu"))];

// rem :: Integral a => a -> a -> a
const rem = n =>
    // Inherits the sign of the *dividend* for non-zero
    // results. Compare with `mod`, which inherits
    // the sign of the *divisor*.
    m => [n, m].some(isBigInt) ? (
        BigInt(n) % BigInt(m)
    ) : n % m;

// remQuot :: Integral a => a -> a -> (a, a)
const remQuot = m =>
    // The remainder, tupled with the quotient.
    n => Tuple(
        m % n
    )(
        Math.trunc(m / n)
    );

// repeat :: a -> Generator [a]
const repeat = function* (x) {
    while (true) {
        yield x;
    }
};

// replace :: String -> String -> String -> String
// replace :: Regex -> String -> String -> String
const replace = needle =>
    strNew => strHaystack => strHaystack.replace(
        "string" !== typeof needle ? (
            needle
        ) : new RegExp(needle, "gu"),
        strNew
    );

// replicate :: Int -> a -> [a]
const replicate = n =>
    // A list of n copies of x.
    x => Array.from({
        length: n
    }, () => x);

// replicateM :: Int -> [a] -> [[a]]
const replicateM = n =>
    // Instance for lists (arrays) only here.
    xs => {
        const go = x => 0 >= x ? [
            []
        ] : liftA2List(cons)(xs)(
            go(x - 1)
        );

        return go(n);
    };

// replicateString :: Int -> String -> String
const replicateString = n =>
    s => s.repeat(n);

// importedFrom :: FilePath -> IO Dict
const require = fp =>
    // eslint-disable-next-line no-new-func
    Function(
        readFile(fp)
    )();

// reverse :: [a] -> [a]
const reverse = xs =>
    "string" === typeof xs
        ? xs.split("").reverse()
        .join("")
        : xs.slice(0).reverse();

// rights :: [Either a b] -> [b]
const rights = xs =>
    xs.flatMap(
        x => ("Right" in x) ? [
            x.Right
        ] : []
    );

// root :: Tree a -> a
const root = tree =>
    // The value attached to a tree node.
    tree.root;

// rotate :: Int -> [a] -> [a]
const rotate = n => xs => {
    // Rightward rotation of xs by n positions.
    const lng = xs.length;

    return Infinity > lng ? (
        take(lng)(
            drop(lng - n)(
                cycle(xs)
            )
        )
    ) : undefined;
};

// round :: a -> Int
const round = x => {
    const
        nr = properFraction(x),
        [n, r] = [nr[0], nr[1]],
        m = n + (r < 0 ? -1 : 1),
        sign = signum(abs(r) - 0.5);

    return (-1 === sign) ? n : (
        0 === sign ? (even(n) ? n : m) : (
            1 === sign ? m : undefined
        )
    );
};

// roundTo :: Int -> Float -> Float
const roundTo = n => x => {
    const d = 10 ** n;

    return Math.round(x * d) / d;
};

// runAction :: Action a -> a
const runAction = act =>
    // Evaluation of an action.
    act.act(act.arg);

// safeMay :: (a -> Bool) -> (a -> b) -> Maybe b
const safeMay = p => f => x =>
    p(x) ? Just(f(x)) : Nothing();

// scanl :: (b -> a -> b) -> b -> [a] -> [b]
const scanl = f =>
    // The series of interim values arising
    // from a catamorphism. Parallel to foldl.
    startValue => xs =>
        "GeneratorFunction" !== (
            xs.constructor.constructor.name
        )
            ? xs.reduce(
                (a, x) => {
                    const v = f(a[0])(x);

                    return [v, a[1].concat(v)];
                }, [startValue, [startValue]]
            )[1]
            : scanlGen(f)(startValue)(xs);

// scanl1 :: (a -> a -> a) -> [a] -> [a]
const scanl1 = f =>
    // scanl1 is a variant of scanl that has no
    // starting value argument.
    xs => xs.length > 0 ? (
        scanl(f)(
            xs[0]
        )(xs.slice(1))
    ) : [];

// scanlGen :: (b -> a -> b) -> b -> Gen [a] -> [b]
const scanlGen = f =>
    // The series of interim values arising
    // from a catamorphism over an infinite list.
    startValue => function* (gen) {
        let
            a = startValue,
            x = gen.next();

        yield a;
        while (!x.done) {
            a = f(a)(x.value);
            yield a;
            x = gen.next();
        }
    };

// scanr :: (a -> b -> b) -> b -> [a] -> [b]
const scanr = f =>
    startValue => xs => xs.reduceRight(
        (a, x) => {
            const v = f(x)(a[0]);

            return Tuple(v)([v].concat(a[1]));
        }, Tuple(startValue)([startValue])
    )[1];

// scanr1 :: (a -> a -> a) -> [a] -> [a]
const scanr1 = f =>
    // scanr1 is a variant of scanr that has no
    // seed-value argument, and assumes that
    // xs is not empty.
    xs => xs.length > 0 ? (
        scanr(f)(
            xs.slice(-1)[0]
        )(xs.slice(0, -1))
    ) : [];

// second :: (a -> b) -> ((c, a) -> (c, b))
const second = f =>
    // A function over a simple value lifted
    // to a function over a tuple.
    // f (a, b) -> (a, f(b))
    xy => Tuple(
        xy[0]
    )(
        f(xy[1])
    );

// sequenceA :: (Applicative f, Traversable t) => t (f a) -> f (t a)
const sequenceA = tfa =>
    traverse(x => x)(
        tfa
    );

// setFromList :: Ord a => [a] -> Set a
const setFromList = xs =>
    new Set(xs);

// setInsert :: Ord a => a -> Set a -> Set a
const setInsert = x => oSet =>
    oSet.add(x);

// setMember :: Ord a => a -> Set a -> Bool
const setMember = x => oSet =>
    oSet.has(x);

// setSize :: Set a -> Int
const setSize = oSet =>
    oSet.size;

// shift :: Int -> [a] -> [a]
const shift = n => xs => {
    const lng = length(xs);

    return Infinity > lng ? (
        take(lng)(
            drop(n)(cycle(xs))
        )
    ) : (drop(n)(xs), xs);
};

// show :: a -> String
// show :: a -> Int -> Indented String
const show = x => {
    const
        instances = {
            "(a -> b)": () => showFn,
            "Bool": () => str,
            "Bottom": () => showUndefined,
            "Date": () => a => a,
            "Dict": () => a => a,
            "Either": () => showLR,
            "List": () => showList,
            "Maybe": () => showMaybe,
            "Node": () => a => a,
            "Num": () => str,
            "Ratio": () => showRatio,
            "String": () => str,
            "Tuple": () => showTuple
        },
        str = y => y.toString(),
        t = typeName(x);

    const instance = instances[
        (/^Tuple/u).test(t) ? (
            "Tuple"
        ) : t
    ];

    return Boolean(instance) ? (
        JSON.stringify(
            x,
            (_, v) => instance()(v)
        )
    ) : `No Show instance has been defined for ${t}.`;
};

// showBinary :: Int -> String
const showBinary = n => {
    const
        binaryChar = m => 0 !== m ? (
            "1"
        ) : "0";

    return showIntAtBase(2)(
        binaryChar
    )(n)("");
};

// showDate :: Date -> String
const showDate = dte =>
    dte.toJSON;

// showDict :: Dict -> String
const showDict = x =>
    show(x);

// showFn :: (a -> b) -> String
const showFn = f =>
    `λ${f}`;

// showForest :: [Tree a] -> String
const showForest = xs =>
    unlines(xs.map(x => drawTree2(false)(true)(
        fmapTree(show)(
            x
        )
    )));

// showHex :: Int -> String
const showHex = n =>
    // Hexadecimal string for a given integer.
    `0x${n.toString(16)}`;

// showIntAtBase :: Int -> (Int -> Char) ->
// Int -> String -> String
const showIntAtBase = base =>
    // A string representation of n, in the given base,
    // using a supplied (Int -> Char) function for
    // digits, and a supplied suffix string.
    toChr => n => rs => {
        const go = ([x, d], r) => {
            const r_ = toChr(d) + r;

            return 0 !== x ? (
                go(quotRem(x)(base), r_)
            ) : r_;
        };

        const e = "error: showIntAtBase applied to";

        return 1 >= base ? (
            `${e} unsupported base`
        ) : 0 > n ? (
            `${e} negative number`
        ) : go(quotRem(n)(base), rs);
    };

// showJSON :: a -> String
const showJSON = x =>
    // Indented JSON representation of the value x.
    JSON.stringify(x, null, 2);

// showLR :: Either a b -> String
const showLR = lr => {
    const k = undefined !== lr.Left ? (
        "Left"
    ) : "Right";

    return `${k}(${unQuoted(show(lr[k]))})`;
};

// showList :: [a] -> String
const showList = xs => {
    const
        s = xs.map(show)
        .join(", ")
        .replace(/[\\"]/gu, "");

    return `[${s}]`;
};

// showLog :: a -> IO ()
const showLog = (...args) =>
    // eslint-disable-next-line no-console
    console.log(
        args
        .map(JSON.stringify)
        .join(" -> ")
    );

// showMatrix :: (a -> String) -> [[a]] -> String
const showMatrix = fShow =>
    rows => Boolean(rows.length) ? (() => {
        const w = fShow(Math.max(...rows.flat())).length;

        return rows.map(
            cells => cells.map(
                x => fShow(x).padStart(w, " ")
            ).join(" ")
        ).join("\n");
    })() : "";

// showMaybe :: Maybe a -> String
const showMaybe = mb =>
    mb.Nothing ? (
        "Nothing"
    ) : `Just(${unQuoted(show(mb.Just))})`;

// showMenuLR :: Bool -> String -> String ->
// [String] -> String -> Either String [String]
const showMenuLR = blnMult =>
    // An optionally multi-choice menu, with
    // a given title and prompt string.
    // Listing the strings in xs, with
    // the string `selected` pre-selected
    // if found in xs.
    menuTitle => prompt => selected => xs =>
    Boolean(xs.length) ? (() => {
        const sa = Object.assign(
            Application("System Events"), {
                includeStandardAdditions: true
            });

        sa.activate();

        const v = sa.chooseFromList(xs, {
            withTitle: menuTitle,
            withPrompt: prompt,
            defaultItems: xs.includes(selected) ? (
                [selected]
            ) : [xs[0]],
            okButtonName: "OK",
            cancelButtonName: "Cancel",
            multipleSelectionsAllowed: blnMult,
            emptySelectionAllowed: false
        });

        return Array.isArray(v) ? (
            Right(v)
        ) : Left(`User cancelled ${menuTitle} menu.`);
    })() : Left(`${menuTitle}: No items to choose from.`);

// showOrdering :: Ordering -> String
const showOrdering = e =>
    0 < e.value ? (
        "GT"
    ) : 0 > e.value ? (
        "LT"
    ) : "EQ";

// showOutline :: Tree String -> String
const showOutline = tree => {
    const go = indent => x =>
        unlines(
            [indent + x.root].concat(
                x.nest.flatMap(go(`    ${indent}`))
            )
        );

    return go("")(tree);
};

// showPrecision :: Int -> Float -> String
const showPrecision = n => x => {
    // A string showing a floating point number
    // at a given degree of precision.
    const d = 10 ** n;

    return str(Math.round(d * x) / d);
};

// showRatio :: Ratio -> String
const showRatio = r =>
    "Ratio" !== r.type
        ? r.toString()
        : r.n.toString() + (
            1 !== r.d
                ? `/${r.d}`
                : ""
        );

// showSet :: Set a -> String
const showSet = oSet => {
    const
        s = Array.from(oSet)
        .map(x => x.toString())
        .join(",");

    return `{${s}}`;
};

// showTree :: Tree a -> String
const showTree = x =>
    drawTree(
        fmapTree(show)(x)
    );

// showTuple :: Tuple -> String
const showTuple = tpl => {
    const
        s = enumFromTo(0)(tpl.length - 1)
        .map(x => unQuoted(show(tpl[x])))
        .join(",");

    return `(${s})`;
};

// showUndefined :: () -> String
const showUndefined = () =>
    "(⊥)";

// signum :: Num -> Num
const signum = n =>
    // Sign of a number.
    n.constructor(
        0 > n
            ? -1
            : 0 < n
                ? 1
                : 0
    );

// sj :: a -> String
const sj = (...args) =>
    // Abbreviation of showJSON for quick testing.
    // Default indent size is two, which can be
    // overriden by any integer supplied as the
    // first argument of more than one.
    JSON.stringify.apply(
        null,
        1 < args.length && !isNaN(args[0])
            ? [args[1], null, args[0]]
            : [args[0], null, 2]
    );

// snd :: (a, b) -> b
const snd = tpl =>
    // Second member of a pair.
    tpl[1];

// snoc :: [a] -> a -> [a]
const snoc = xs =>
    // The mirror image of cons
    // A new copy of the given list,
    // with an atom appended at the end.
    x => xs.concat(x);

// sort :: Ord a => [a] -> [a]
const sort = xs =>
    // An A-Z sorted copy of xs.
    xs.slice().sort(
        (a, b) => a < b ? (
            -1
        ) : (
            a > b ? (
                1
            ) : 0
        )
    );

// sortBy :: (a -> a -> Ordering) -> [a] -> [a]
const sortBy = f =>
    // A copy of xs sorted by the comparator function f.
    xs => [...xs].sort(
        (a, b) => f(a)(b)
    );

// sortOn :: Ord b => (a -> b) -> [a] -> [a]
const sortOn = f =>
    // Equivalent to sortBy(comparing(f)), but with f(x)
    // evaluated only once for each x in xs.
    // ('Schwartzian' decorate-sort-undecorate).
    xs => sortBy(
        comparing(x => x[0])
    )(
        xs.map(x => [f(x), x])
    )
    .map(x => x[1]);

// span :: (a -> Bool) -> [a] -> ([a], [a])
const span = p =>
    // Longest prefix of xs consisting of elements which
    // all satisfy p, tupled with the remainder of xs.
    xs => {
        const i = xs.findIndex(x => !p(x));

        return -1 !== i
            ? Tuple(
                xs.slice(0, i)
            )(
                xs.slice(i)
            ) : Tuple(xs)([]);
    };

// splitArrow (***) :: (a -> b) -> (c -> d) -> ((a, c) -> (b, d))
const splitArrow = f =>
    // The functions f and g combined in a single function
    // from a tuple (x, y) to a tuple of (f(x), g(y))
    // (see bimap)
    g => ([a, b]) => Tuple(
        f(a)
    )(
        g(b)
    );

// splitAt :: Int -> [a] -> ([a], [a])
const splitAt = n =>
    xs => Tuple(xs.slice(0, n))(
        xs.slice(n)
    );

// splitBy :: (a -> a -> Bool) -> [a] -> [[a]]
// splitBy :: (String -> String -> Bool) ->
// String -> [String]
const splitBy = p =>
    // Splitting not on a delimiter, but wherever the
    // relationship between consecutive terms matches
    // a binary predicate.
    xs => 2 > xs.length
        ? [xs]
        : (() => {
            const
                [h, ...t] = xs,
                ab = t.reduce(
                    ([acc, active, prev], x) =>
                        p(prev)(x)
                            ? [acc.concat([active]), [x], x]
                            : [acc, active.concat(x), x],
                    [[], [h], h]
                );

            return ab[0].concat([ab[1]]);
        })();

// splitExtension :: FilePath -> (String, String)
const splitExtension = fp => {
    // The file path split before any extension,
    // or tupled with the empty string, if
    // no extension is seen.
    const
        lastIndex = [...fp].findLastIndex(
            c => "./".includes(c)
        );

    return (-1 !== lastIndex) && ("." === fp[lastIndex])
        ? Tuple(fp.slice(0, lastIndex))(
            fp.slice(lastIndex)
        )
        : Tuple(fp)("");
};

// splitFileName :: FilePath -> (String, String)
const splitFileName = strPath =>
    // Tuple of directory and file name,
    // derived from file path. (Inverse of combine).
    ("" !== strPath) ? (
        ("/" !== strPath[strPath.length - 1]) ? (() => {
            const
                xs = strPath.split("/"),
                stem = xs.slice(0, -1);

            return stem.length > 0 ? (
                Tuple(
                    `${stem.join("/")}/`
                )(xs.slice(-1)[0])
            ) : Tuple("./")(xs.slice(-1)[0]);
        })() : Tuple(strPath)("")
    ) : Tuple("./")("");

// splitOn :: [a] -> [a] -> [[a]]
// splitOn :: String -> String -> [String]
const splitOn = pat => src =>
    // A list of the strings delimited by
    // instances of a given pattern in s.
    ("string" === typeof src) ? (
        src.split(pat)
    ) : (() => {
        const
            lng = pat.length,
            [a, b] = findIndices(matching(pat))(src).reduce(
                ([x, y], i) => Tuple(
                    x.concat([src.slice(y, i)])
                )(lng + i),
                Tuple([])(0)
            );

        return a.concat([src.slice(b)]);
    })();

// splitRegex :: Regex -> String -> [String]
const splitRegex = needle =>
    haystack => haystack.split(needle);

// sqrt :: Num -> Num
const sqrt = n =>
    0 <= n
        ? Math.sqrt(n)
        : undefined;

// sqrtLR :: Num -> Either String Num
const sqrtLR = n =>
    0 > n ? (
        Left(`Square root of negative number: ${n}`)
    ) : Right(Math.sqrt(n));

// sqrtMay :: Num -> Maybe Num
const sqrtMay = n =>
    0 > n ? (
        Nothing()
    ) : Just(Math.sqrt(n));

// str :: a -> String
const str = x =>
    Array.isArray(x) && x.every(
        v => ("string" === typeof v) && (1 === v.length)
    )
        ? x.join("")
        : null === x
            ? "null"
            : x.toString();

// strip :: String -> String
const strip = s =>
    s.trim();

// stripEnd :: String -> String
const stripEnd = s =>
    s.trimEnd();

// stripPrefix :: Eq a => [a] -> [a] -> Maybe [a]
const stripPrefix = pfx =>
    s => {
        const
            blnString = "string" === typeof pfx,
            [vs, ws] = blnString ? (
                [pfx.split(""), s.split("")]
            ) : [pfx, s];

        const
            sp_ = (xs, ys) => 0 === xs.length ? (
                Just(blnString ? ys.join("") : ys)
            ) : (0 === ys.length || xs[0] !== ys[0]) ? (
                Nothing()
            ) : sp_(xs.slice(1), ys.slice(1));

        return sp_(vs, ws);
    };

// stripStart :: String -> String
const stripStart = s =>
    s.trimStart();

// subTreeAtPath :: Tree String -> [String] -> Maybe Tree String
const subTreeAtPath = tree => path => {
    const go = (subNest, xs) =>
        Boolean(subNest.length) && Boolean(xs.length)
            ? (() => {
                const h = xs[0];

                return bindMay(
                    find(t => h === t.root)(subNest)
                )(
                    t => 1 < xs.length
                        ? go(t.nest, xs.slice(1))
                        : Just(t)
                );
            })()
            : Nothing();

    return go([tree], path);
};

// subsequences :: [a] -> [[a]]
// subsequences :: String -> [String]
const subsequences = qs => {
    // subsequences([1,2,3]) -> [[],[1],[2],[1,2],[3],[1,3],[2,3],[1,2,3]]
    // subsequences('abc') -> ["","a","b","ab","c","ac","bc","abc"]
    const
        // nonEmptySubsequences :: [a] -> [[a]]
        nonEmptySubsequences = xxs => {
            if (xxs.length < 1) {
                return [];
            }
            const [x, xs] = [xxs[0], xxs.slice(1)];
            const f = (r, ys) => cons(ys)(cons(cons(x)(ys))(r));

            return cons([x])(nonEmptySubsequences(xs)
                .reduceRight(f, []));
        };

    return ("string" === typeof qs) ? (
        cons("")(nonEmptySubsequences(qs.split(""))
            .map(q => "".concat(...q)))
    ) : cons([])(nonEmptySubsequences(qs));
};

// subsets :: [a] -> [[a]]
const subsets = xs => {
    // The list of sublists of xs,
    // including the empty list.
    const go = ys =>
        0 < ys.length
            ? (() => {
                const
                    h = ys[0],
                    zs = go(ys.slice(1));

                return [
                    ...zs.map(z => [h, ...z]),
                    ...zs
                ];
            })()
            : [[]];

    return go(xs);
};

// subtract :: Num -> Num -> Num
const subtract = x =>
    y => y - x;

// succ :: Enum a => a -> a
const succ = x => {
    const t = typeof x;

    return "number" !== t ? (
        "bigint" !== t ? (
            (() => {
                const [i, mx] = [x, maxBound(x)].map(fromEnum);

                return i < mx ? (
                    toEnum(x)(1 + i)
                ) : Error("succ :: enum out of range.");
            })()
        ) : BigInt(1) + x
    ) : x < Number.MAX_SAFE_INTEGER ? (
        1 + x
    ) : Error("succ :: Num out of range.");
};

// succMay :: Enum a => a -> Maybe a
const succMay = x => {
    const t = typeof x;

    return "number" !== t ? (() => {
        const [i, mx] = [x, maxBound(x)].map(fromEnum);

        return i < mx ? (
            Just(toEnum(x)(1 + i))
        ) : Nothing();
    })() : x < Number.MAX_SAFE_INTEGER ? (
        Just(1 + x)
    ) : Nothing();
};

// sum :: [Num] -> Num
const sum = xs =>
    // The numeric sum of all values in xs.
    xs.reduce((a, x) => a + x, 0);

// swap :: (a, b) -> (b, a)
const swap = ab =>
    // The pair ab with its order reversed.
    Tuple(ab[1])(
        ab[0]
    );

// tail :: [a] -> [a]
const tail = xs =>
    // A new list consisting of all
    // items of xs except the first.
    "GeneratorFunction" !== xs.constructor
    .constructor.name
        ? 0 < xs.length
            ? xs.slice(1)
            : undefined
        : (take(1)(xs), xs);

// tailMay :: [a] -> Maybe [a]
const tailMay = xs =>
    Boolean(xs.length)
        ? Just(xs.slice(1))
        : Nothing();

// tails :: [a] -> [[a]]
const tails = xs =>
    xs.map((_, i) => xs.slice(i))
    .concat([
        []
    ]);

// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = n =>
    // The first n elements of a list,
    // string of characters, or stream.
    xs => "GeneratorFunction" !== xs
    .constructor.constructor.name
        ? xs.slice(0, n)
        : Array.from({length: n},
            () => {
                const x = xs.next();

                return x.done
                    ? []
                    : [x.value];
            })
        .flat();

// takeAround :: (a -> Bool) -> [a] -> [a]
const takeAround = p => xs => {
    const ys = takeWhile(p)(xs);

    return ys.length < xs.length
        ? ys.concat(takeWhileR(p)(xs))
        : ys;
};

// takeBaseName :: FilePath -> String
const takeBaseName = fp =>
    // The filename without any extension.
    ("" !== fp)
        ? ("/" !== fp[fp.length - 1])
            ? (() => {
                const fn = fp.split("/").slice(-1)[0];

                return fn.includes(".")
                    ? fn.split(".").slice(0, -1)
                    .join(".")
                    : fn;
            })()
            : ""
        : "";

// takeCycle :: Int -> [a] -> [a]
const takeCycle = n =>
    // First n elements of a non-finite cycle of xs.
    xs => {
        const lng = xs.length;

        return (
            n <= lng
                ? xs
                : Array.from(
                    {length: n},
                    () => xs
                )
                .flat(1)
        )
        .slice(0, n);
    };

// takeDirectory :: FilePath -> FilePath
const takeDirectory = fp =>
    // The directory component of a filepath.
    "" !== fp
        ? (() => {
            const xs = fp.split("/").slice(0, -1);

            return 0 < xs.length
                ? xs.join("/")
                : ".";
        })()
        : ".";

// takeDropCycle :: Int -> [a] -> [a]
const takeDropCycle = n =>
    // N Members of an infinite cycle of xs, starting from index I
    i => xs => drop(i)(
        take(n + i)(cycle(xs))
    );

// takeExtension :: FilePath -> String
const takeExtension = fp => {
    const fn = last(fp.split("/"));

    return fn.includes(".")
        ? `.${last(fn.split("."))}`
        : "";
};

// takeFileName :: FilePath -> FilePath
const takeFileName = fp =>
    // The file name component of a filepath.
    0 < fp.length
        ? "/" !== fp[fp.length - 1]
            ? fp.split("/").slice(-1)[0]
            : ""
        : "";

// takeFromThenTo :: Int -> Int -> Int -> [a] -> [a]
const takeFromThenTo = a =>
    b => z => xs => {
        const ixs = enumFromThenTo(a)(b)(z);

        return "GeneratorFunction" !== xs.constructor
        .constructor.name
            ? ixs.map(i => xs[i])
            : (() => {
                const g = zipGen(enumFrom(0))(
                    take(z)(xs)
                );

                return ixs.flatMap(i => {
                    const mb = index(g)(i);

                    return mb.Nothing
                        ? []
                        : [mb.Just];
                });
            })();
    };

// takeIterate n f x == [x, f x, f (f x), ...]
// takeIterate :: Int -> (a -> a) -> a -> [a]
const takeIterate = n =>
    f => x => Array.from({
        length: n - 1
    }).reduce(
        ([a, vs]) => {
            const v = f(a);

            return Tuple(v)(vs.concat(v));
        },
        Tuple(x)([x])
    )[1];

// takeWhile :: (a -> Bool) -> [a] -> [a]
const takeWhile = p =>
    // The longest prefix of xs in which
    // all elements satisfy p.
    xs => {
        const i = xs.findIndex(x => !p(x));

        return -1 !== i
            ? xs.slice(0, i)
            : xs;
    };

// takeWhileEnd :: (a -> Bool) [a] -> [a]
const takeWhileEnd = p =>
    // The longest suffix of xs in which
    // all elements satisfy p.
    xs => xs.slice(
        1 + xs.findLastIndex(x => !p(x))
    );

// takeWhileGen :: (a -> Bool) -> Gen [a] -> [a]
const takeWhileGen = p =>
    xs => {
        const ys = [];
        let
            nxt = xs.next(),
            v = nxt.value;

        while (!nxt.done && p(v)) {
            ys.push(v);
            nxt = xs.next();
            v = nxt.value;
        }

        return ys;
    };

// takeWhileR :: (a -> Bool) -> [a] -> [a]
const takeWhileR = p =>
    // The longest suffix of xs in which
    // all elements satisfy p.
    xs => {
        const i = xs.findLastIndex(x => !p(x));

        return -1 !== i
            ? xs.slice(1 + i)
            : [];
    };

// taskPaperDateString :: Date -> String
const taskPaperDateString = dte =>
    [...second(t => t.slice(0, 5))(
        iso8601Local(dte).split("T")
    )].join(" ");

// taskPaperDayString :: Date -> String
const taskPaperDayString = dte =>
    taskPaperDateString(dte).slice(0, 10);

// toEnum :: a -> Int -> a
const toEnum = e =>
    // The first argument is a sample of the type
    // allowing the function to make the right mapping
    x => ({
        "number": Number,
        "string": String.fromCodePoint,
        "boolean": Boolean,
        "object": v => e.min + v
    } [typeof e])(x);

// toLower :: String -> String
const toLower = s =>
    // Lower-case version of string.
    s.toLocaleLowerCase();

// toRatio :: Real -> Ratio
const toRatio = n =>
    approxRatio(1e-12)(n);

// toSentence :: String -> String
const toSentence = s =>
    // Sentence case - first character
    // capitalized, and rest lowercase.
    0 < s.length
        ? s[0].toLocaleUpperCase() + s.slice(1)
        .toLocaleLowerCase()
        : s;

// toTitle :: String -> String
const toTitle = s =>
    0 < s.length
        ? `${toUpper(s[0])}${toLower(s.slice(1))}`
        : "";

// toUpper :: String -> String
const toUpper = s =>
    s.toLocaleUpperCase();

// transpose :: [[a]] -> [[a]]
const transpose = rows =>
    // Maximal transpose – the longest row determines
    // the number of columns.
    // If any rows are shorter than those that follow,
    // their elements are skipped:
    // transpose [[10,11],[20],[],[30,31,32]]
    //     == [[10,20,30],[11,31],[32]]
    rows.reduce(
        (cols, row) => cols.map((col, i) => {
            const v = row[i];

            return undefined !== v
                ? col.concat(v)
                : col;
        }),
        Array.from({
            length: 0 < rows.length
                ? Math.max(...rows.map(x => x.length))
                : 0
        }, () => [])
    );

// transpose_ :: [[a]] -> [[a]]
const transpose_ = rows =>
    // Minimal transpose – the shortest row
    // limits the number of ouput columns.
    // transpose_([[10, 11], [30, 31, 32]])
    //     == [[10, 30], [11, 31]]
    rows.reduce(
        (cols, row) => cols.map(
            (col, i) => col.concat(row[i])
        ),
        Array.from({
            length: 0 < rows.length
                ? Math.min(...rows.map(x => x.length))
                : 0
        }, () => [])
    );

// traverse :: (Applicative f, Traversable t) ->
// (a -> f b) -> t a -> f (t b)
const traverse = f =>
    // Each element of a structure mapped to an
    // a functor-wrapped value, with evaluation from
    // from left to right, and the results collected
    // in a single instance of the target functor.
    tx => ({
        "Either": () => traverseLR,
        "Maybe": () => traverseMay,
        "Node": () => traverseTree,
        "Tuple": () => traverseTuple,
        "List": () => traverseList
    })[tx.type || "List"]()(f)(tx);

// traverseLR :: Applicative f =>
// (t -> f b) -> Either a t -> f (Either a b)
const traverseLR = f =>
    // instance of Traversable (Either a) where
    //    traverse _ (Left x) = pure (Left x)
    //    traverse f (Right y) = Right <$> f y
    lr => "Left" in lr
        ? [lr]
        : fmap(Right)(
            f(lr.Right)
        );

// traverseList :: (Applicative f) => (a -> f b) ->
// [a] -> f [b]
const traverseList = f =>
    // Collected results of mapping each element
    // of a structure to an action, and evaluating
    // these actions from left to right.
    xs => 0 < xs.length
        ? (() => {
            const
                vLast = f(xs.slice(-1)[0]),
                t = typeName(vLast);

            return xs.slice(0, -1).reduceRight(
                (ys, x) => liftA2(cons)(f(x))(ys),
                liftA2(cons)(vLast)(pureT(t)([]))
            );
        })() 
        : fType(f)([]);

// traverseListLR (a -> Either b c) ->
// [a] -> Either b [c]
const traverseListLR = flr =>
    // Traverse over [a] with (a -> Either b c)
    // Either Left b or Right [c]
    xs => {
        const n = xs.length;

        return 0 < n
            ? until(
                ([i, lr]) => (n === i) || ("Left" in lr)
            )(
                ([i, lr]) => {
                    // Passing an optional index argument
                    // which flr can ignore or use.
                    const lrx = flr(xs[i], i);

                    return [
                        1 + i,
                        "Right" in lrx
                            ? Right(
                                lr.Right.concat([
                                    lrx.Right
                                ])
                            )
                            : lrx
                    ];
                }
            )(
                Tuple(0)(Right([]))
            )[1]
            : Right([]);
    };

// traverseMay :: Applicative f => (t -> f a) -> Maybe t -> f (Maybe a)
const traverseMay = f => mb =>
    "Nothing" in mb ? (
        [mb]
    ) : fmap(Just)(
        f(mb.Just)
    );

// traverseTree :: Applicative f => (a -> f b) ->
// Tree a -> f (Tree b)
const traverseTree = f => {
    // traverse f (Node x ts) =
    // liftA2 Node (f x) (traverse (traverse f) ts)
    const go = tree =>
        liftA2(Node)(f(tree.root))(
            traverseList(go)(
                tree.nest
            )
        );

    return go;
};

// traverseTuple :: Functor f => (t -> f b) -> (a, t) -> f (a, b)
const traverseTuple = f => ([a, b]) =>
    fmap(Tuple(a))(
        f(b)
    );

// treeFromDict :: String -> Dict -> Tree String
const treeFromDict = rootLabel =>
    dict => {
        const go = x =>
            "object" !== typeof x
                ? []
                : Array.isArray(x)
                    ? x.flatMap(go)
                    : keys(x).map(
                        k => Node(k)(
                            go(x[k])
                        )
                    );

        return Node(rootLabel)(
            go(dict)
        );
    };

// treeFromJSON :: JSON String -> Tree a
const treeFromJSON = json => {
    // Assumes a recursive [root, nest] JSON format,
    // in which `root` is a parseable value string, and `nest`
    // is a possibly empty list of [`root`, `nest`] pairs.
    const go = ([rootValue, subNest]) =>
        Node(rootValue)(subNest.map(go));

    return go(JSON.parse(json));
};

// treeFromNestedDict -> Dict -> Either String Tree Dict
const treeFromNestedDict = dict => {
    // A generic Tree structure from a dict
    // with keys assumed to include no more than
    // one key to a *list* value,
    // with this pattern applied recursively
    // to each child dictionary in such a list.
    const go = dct => {
        const
            kvs = Object.entries(dct),
            lists = kvs.filter(
                ([_, v]) => Array.isArray(v)
            ),
            lng = lists.length;

        return 0 < lng ? (
            1 < lng ? (() => {
                const
                    listing = bulleted("    ")(
                        unlines(lists.map(fst))
                    ),
                    msg = `Ambiguous structure :: ${lng}` + (
                        ` multiple sublists in:\n${dct.name}`
                    );

                return Left(`${msg}:\n${listing}`);
            })() : (() => {
                const [nestName, xs] = lists[0];

                return bindLR(traverseList(go)(xs))(
                    vs => Right(
                        Node({
                            ...deleteKey(nestName)(dct),
                            "List title": nestName
                        })(vs)
                    )
                );
            })()
        ) : Right(Node(dct)([]));
    };

    return go(dict);
};

// treeLeaves :: Tree a -> [Tree a]
const treeLeaves = tree => {
    const go = t => {
        const xs = nest(t);

        return 0 < xs.length
            ? xs.flatMap(go)
            : [t];
    };

    return go(tree);
};

// treeMatch :: (a -> Bool) -> Tree a -> [Tree a]
const treeMatch = p => {
    // Either a list containing the the first node
    // in the tree which matches the predicate p,
    // or an empty list if no match is found.
    const go = tree =>
        p(tree.root)
            ? [tree]
            : f(tree.nest);

    const f = xs => {
        const n = xs.length;

        return until(
            ([i, ms]) => (n === i) || (0 < ms.length)
        )(
            ([i]) => [1 + i, go(xs[i])]
        )(
            [0, []]
        )[1];
    };

    return go;
};

// treeMatches :: (a -> Bool) -> Tree a -> [Tree a]
const treeMatches = p => {
    // A list of all nodes in the tree which match
    // a predicate p.
    // For the first matching value only, see findTree.
    // To ignore descendants where an ancestor already matches
    // write just [tree] in lieu of [tree, ...tree.nest.flatMap(go)]
    const go = tree =>
        p(tree.root)
            ? [tree, ...tree.nest.flatMap(go)]
            : tree.nest.flatMap(go);

    return go;
};

// treeMenu :: Tree String -> IO [String]
const treeMenu = tree => {
    const go = t => {
        const
            strTitle = t.root,
            subs = t.nest,
            menu = subs.map(root),
            blnMore = 0 < subs.flatMap(nest).length;

        return until(tpl => !fst(tpl) || !isNull(snd(tpl)))(
            tpl => either(
                x => Tuple(false)([])
            )(
                Tuple(true)
            )(
                bindLR(
                    showMenuLR(!blnMore)(strTitle)(menu)
                )(ks => {
                    const
                        k = ks[0],
                        msg = `${k}: not found in ${ks}`;

                    return maybe(
                        Left(msg)
                    )(Right)(
                        bindMay(
                            find(x => k === x.root)(
                                subs
                            )
                        )(
                            chosen => Just(
                                isNull(chosen.nest) ? (
                                    ks
                                ) : go(chosen)
                            )
                        )
                    );
                })
            )
        )(Tuple(true)([]))[1];
    };

    return go(tree);
};

// treeMenuBy :: (a -> String) Tree a -> IO [a]
const treeMenuBy = fNodeKey => {
    const go = tree => {
        const
            strTitle = fNodeKey(tree.root),
            subTrees = nest(tree),
            menu = subTrees.map(
                compose(fNodeKey, root)
            ).sort();

        return until(
            ([a, b]) => !a || !isNull(b)
        )(
            () => either(
                x => Tuple(false)([])
            )(
                Tuple(true)
            )(
                bindLR(
                    showMenuLR(true)(strTitle)(menu)
                )(
                    ks => {
                        const
                            k0 = ks[0],
                            msg = `${k0}: not found in ${ks}`;

                        return maybe(
                            Left(msg)
                        )(Right)(
                            bindMay(
                                find(
                                    x => k0 === fNodeKey(
                                        x.root
                                    )
                                )(subTrees)
                            )(
                                firstChosen => Just(
                                    isNull(
                                        nest(firstChosen)
                                    )
                                        ? ks.map(
                                            k => find(
                                                x => k === fNodeKey(
                                                    x.root
                                                )
                                            )(subTrees).Just
                                        )
                                        : go(firstChosen)
                                )
                            )
                        );
                    }
                )
            )
        )(Tuple(true)([]))[1];
    };

    return go;
};

// truncate :: Num -> Int
const truncate = x =>
    "Ratio" === x.type ? (
        properFracRatio(x)[0]
    ) : properFraction(x)[0];

// tupleFromList :: [a] -> (a, a ...)
const tupleFromList = xs =>
    TupleN(...xs);

// typeName :: a -> String
const typeName = v => {
    const t = typeof v;

    return "object" === t
        ? null !== v
            ? Array.isArray(v)
                ? "List"
                : "Date" === v.constructor.name
                    ? "Date"
                    : null !== v
                        ? (() => {
                            const ct = v.type;

                            return Boolean(ct)
                                ? (/Tuple\d+/u).test(ct)
                                    ? "TupleN"
                                    : ct
                                : "Dict";
                        })()
                        : "Bottom"
            : "Bottom"

        : {
            "boolean": "Bool",
            "date": "Date",
            "number": "Num",
            "string": "String",
            "function": "(a -> b)"
        } [t] || "Bottom";
};

// unDigits :: [Int] -> Int
const unDigits = ds =>
    // The integer with the given digits.
    ds.reduce((a, x) => (10 * a) + x, 0);

// unQuoted :: String -> String
const unQuoted = s =>
    1 < s.length ? (
        q => s.slice(
            q !== s[0] ? 0 : 1,
            q !== s.slice(-1) ? undefined : -1
        )
    )(
        String.fromCodePoint(34)
    ) : s;

// uncons :: [a] -> Maybe (a, [a])
const uncons = xs => {
    // Just a tuple of the head of xs and its tail,
    // Or Nothing if xs is an empty list.
    const n = length(xs);

    return 0 < n
        ? Infinity > n
            // Finite list
            ? Just(Tuple(xs[0])(xs.slice(1)))

            // Lazy generator
            : (() => {
                const nxt = take(1)(xs);

                return 0 < nxt.length
                    ? Just(Tuple(nxt[0])(xs))
                    : Nothing();
            })()
        : Nothing();
};

// uncurry :: (a -> b -> c) -> ((a, b) -> c)
const uncurry = f =>
    // A function over a Tuple or argument pair, 
    // derived from a curried function.
    (...args) => {
        const [x, y] = 2 === args.length
            ? args
            : args[0]

        return f(x)(y);
    };

// uncurryN :: (a -> b ... -> e) -> (a, b ...) -> e
const uncurryN = f =>
    // A function over a tuple of values, 
    // derived from a curried function absorbing 
    // any number of arguments.
    (...args) => args.reduce(
        (g, x) => g(x),
        f
    );

// unfoldForest :: (b -> (a, [b])) -> [b] -> [Tree]
const unfoldForest = f =>
    // A forest built from a list of seed values.
    xs => xs.map(unfoldTree(f));

// unfoldTree :: (b -> (a, [b])) -> b -> Tree a
const unfoldTree = f =>
    // A tree unfolded in breadth-first order
    // from a seed value.
    // Given a seed value, f defines a tuple:
    // (Node root value, [seed])
    // Empty seed lists conclude recursion.
    b => uncurry(Node)(
        second(unfoldForest(f))(
            f(b)
        )
    );

// unfoldl :: (b -> Maybe (b, a)) -> b -> [a]
const unfoldl = f => v => {
    // Dual to reduce or foldl.
    // Where these reduce a list to a summary value, unfoldl
    // builds a list from a seed value.
    // Where f returns Just(a, b), a is appended to the list,
    // and the residual b is used as the argument for the next
    // application of f.
    // Where f returns Nothing, the completed list is returned.
    // unfoldl(x => 0 !== x ? Just([x - 1, x]) : Nothing(), 10);
    // --> [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    let
        xr = [v, v],
        xs = [];

    // eslint-disable-next-line no-constant-condition
    while (true) {
        const mb = f(xr[0]);

        if (mb.Nothing) {
            return xs;
        // eslint-disable-next-line no-else-return
        } else {
            xr = mb.Just;
            xs = [xr[1]].concat(xs);
        }
    }
};

// unfoldr :: (b -> Maybe (a, b)) -> b -> Gen [a]
const unfoldr = f =>
    // A lazy (generator) list unfolded from a seed value
    // by repeated application of f to a value until no
    // residue remains. Dual to fold/reduce.
    // f returns either Nothing or Just (value, residue).
    // For a strict output list,
    // wrap with `list` or Array.from
    x => (
        function* () {
            let maybePair = f(x);

            while (!maybePair.Nothing) {
                const valueResidue = maybePair.Just;

                yield valueResidue[0];
                maybePair = f(valueResidue[1]);
            }
        }()
    );

// union :: [a] -> [a] -> [a]
const union = xs => ys =>
    unionBy(a => b => a === b)(xs)(ys);

// unionBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
const unionBy = fnEq =>
    // The union of xs and ys in terms of the
    // equality function given in fnEq
    xs => ys => {
        const sx = nubBy(fnEq)(xs);

        return sx.concat(
            sx.reduce(
                (a, x) => deleteBy(fnEq)(
                    x
                )(a),
                nubBy(fnEq)(ys)
            )
        );
    };

// unionSet :: Ord a => Set a -> Set a -> Set a
const unionSet = s => s1 =>
    Array.from(s1.values())
    .reduce(
        (a, x) => (a.add(x), a),
        new Set(s)
    );

// unlines :: [String] -> String
const unlines = xs =>
    // A single string formed by the intercalation
    // of a list of strings with the newline character.
    xs.join("\n");

// unsnoc :: [a] -> Maybe ([a], a)
const unsnoc = xs =>
    // Nothing if the list is empty, otherwise
    // Just the init and the last.
    Boolean(xs.length) ? (
        Just(Tuple(xs.slice(0, -1))(xs.slice(-1)[0]))
    ) : Nothing();

// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = p =>
    // The value resulting from successive applications
    // of f to f(x), starting with a seed value x,
    // and terminating when the result returns true
    // for the predicate p.
    f => x => {
        let v = x;

        while (!p(v)) {
            v = f(v);
        }

        return v;
    };

// unwords :: [String] -> String
const unwords = xs =>
    // A space-separated string derived
    // from a list of words.
    xs.join(" ");

// unzip :: [(a,b)] -> ([a],[b])
const unzip = xys =>
    // A list of the first items in each pair
    // of the zip, tupled with a list of all
    // the second items.
    Tuple(
        xys.map(xy => xy[0])
    )(
        xys.map(xy => xy[1])
    );


// unzip3 :: [(a,b,c)] -> ([a],[b],[c])
const unzip3 = xyzs =>
    xyzs.reduce(
        (a, x) => TupleN(...[0, 1, 2].map(
            i => a[i].concat(x[i])
        )),
        TupleN([], [], [])
    );

// unzip4 :: [(a,b,c,d)] -> ([a],[b],[c],[d])
const unzip4 = wxyzs =>
    wxyzs.reduce(
        (a, x) => TupleN(...[0, 1, 2, 3].map(
            i => a[i].concat(x[i])
        )),
        TupleN([], [], [], [])
    );

// unzipN :: [(a,b,...)] -> ([a],[b],...)
const unzipN = tpls =>
    TupleN(
        ...tpls.reduce(
            (a, tpl) => a.map(
                (x, i) => x.concat(tpl[i])
            ),
            replicate(
                0 < tpls.length
                    ? tpls[0].length
                    : 0, []
            )
        )
    );

// variance :: [Num] -> Num
const variance = xs => {
    const
        lng = xs.length,
        avg = xs.reduce((a, b) => a + b, 0) / lng;

    return xs.reduce(
        (a, b) => a + ((b - avg) ** 2),
        0
    ) / (lng - 1);
};

// words :: String -> [String]
const words = s =>
    // List of space-delimited sub-strings.
    // Leading and trailling space ignored.
    s.split(/\s+/u).filter(Boolean);

// zeroPadded :: Int -> Int -> String
const zeroPadded = w =>
    // A string representation of the integer n,
    // zero padded at left to width w.
    n => `${n}`.padStart(w, "0");

// zip :: [a] -> [b] -> [(a, b)]
const zip = xs =>
    // The paired members of xs and ys, up to
    // the length of the shorter of the two lists.
    ys => Array.from({
        length: Math.min(xs.length, ys.length)
    }, (_, i) => [xs[i], ys[i]]);

// zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
const zip3 = xs =>
    // Triples of the values at each position of
    // xs,ys,zs up to the length of the shortest.
    ys => zs => Array.from(
        {
            length: Math.min(
                ...[xs, ys, zs].map(x => x.length)
            )
        },
        (_, i) => [xs[i], ys[i], zs[i]]
    );

// zip4 :: [a] -> [b] -> [c] -> [d] -> [(a, b, c, d)]
const zip4 = ws =>
    // List of triples of the values at each position
    // of xs,ys,zs up to the length of the shortest.
    xs => ys => zs => Array.from(
        {
            length: Math.min(
                ...[ws, xs, ys, zs].map(x => x.length)
            )
        },
        (_, i) => [ws[i], xs[i], ys[i], zs[i]]
    );

// zipGen :: (a -> b -> c) ->
// Gen [a] -> Gen [b] -> Gen [c]
const zipGen = ga =>
    // A composite generator formed by the application
    // of f to each pair of values in a zip of two
    // generators.
    gb => {
        const go = function* (ma, mb) {
            let
                a = ma,
                b = mb;

            while (!a.Nothing && !b.Nothing) {
                const [ax, axs] = a.Just;
                const [bx, bxs] = b.Just;

                yield [ax, bx];
                a = uncons(axs);
                b = uncons(bxs);
            }
        };

        return go(uncons(ga), uncons(gb));
    };

// zipList :: [a] -> [b] -> [(a, b)]
const zipList = xs => ys => {
    const
        n = Math.min(length(xs), length(ys)),
        vs = take(n)(ys);

    return take(n)(xs)
        .map((x, i) => Tuple(x)(vs[i]));
};

// zipN :: [a] -> [b] -> ... -> [(a, b ...)]
const zipN = (...xss) =>
    0 < xss.length
        ? Array.from(
            { length: Math.min(...xss.map(xs => xs.length)) },
            (_, i) => TupleN(...xss.map(xs => xs[i]))
        )
        : [];

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = f =>
    // A list with the length of the shorter of
    // xs and ys, defined by zipping with a
    // custom function, rather than with the
    // default tuple constructor.
    xs => ys => {
        const n = Math.min(...[xs, ys].map(length));

        return Infinity > n
            ? (([as, bs]) => Array.from({
                length: n
            }, (_, i) => f(as[i])(
                bs[i]
            )))([xs, ys].map(
                take(n)
            ))
            : zipWithGen(f)(xs)(ys);
    };

// zipWith3 :: (a -> b -> c -> d) ->
// [a] -> [b] -> [c] -> [d]
const zipWith3 = f =>
    xs => ys => zs => Array.from({
        length: Math.min(
            ...[xs, ys, zs].map(x => x.length)
        )
    }, (_, i) => f(xs[i])(ys[i])(zs[i]));

// zipWith4 :: (a -> b -> c -> d -> e) ->
// [a] -> [b] -> [c] -> [d] -> [e]
const zipWith4 = f =>
    ws => xs => ys => zs => Array.from({
        length: Math.min(
            ...[ws, xs, ys, zs].map(x => x.length)
        )
    }, (_, i) => f(ws[i])(xs[i])(ys[i])(zs[i]));

// zipWithGen :: (a -> b -> c) ->
// Gen [a] -> Gen [b] -> Gen [c]
const zipWithGen = f =>
    // A composite generator formed by the application
    // of f to each pair of values in a zip of two
    // generators.
    ga => gb => {
        const go = function* (ma, mb) {
            let
                a = ma,
                b = mb;

            while (!a.Nothing && !b.Nothing) {
                const [ax, axs] = a.Just;
                const [bx, bxs] = b.Just;

                yield f(ax)(bx);
                a = uncons(axs);
                b = uncons(bxs);
            }
        };

        return go(uncons(ga), uncons(gb));
    };

// zipWithList :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWithList = f =>
    // A list constructed by zipping with a
    // custom function, rather than with the
    // default tuple constructor.
    xs => ys => ((xs_, ys_) => {
        const lng = Math.min(length(xs_), length(ys_));

        return take(lng)(xs_).map(
            (x, i) => f(x)(ys_[i])
        );
    })([...xs], [...ys]);

// zipWithList_ :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWithList_ = f =>
    // A list constructed by zipping with a
    // custom function, rather than with the
    // default tuple constructor.
    xs => ys => Array.from(
        { length: Math.min(xs.length, ys.length) },
        (_, i) => f(xs[i])(ys[i])
    );

// zipWithLong :: (a -> a -> a) -> [a] -> [a] -> [a]
const zipWithLong = f => {
    // A list with the length of the *longer* of
    // xs and ys, defined by zipping with a
    // custom function, rather than with the
    // default tuple constructor.
    // Any unpaired values, where list lengths differ,
    // are simply appended.
    const go = xs =>
        ys => 0 < xs.length
            ? 0 < ys.length
                ? [f(xs[0])(ys[0])].concat(
                    go(
                        xs.slice(1)
                    )(
                        ys.slice(1)
                    )
                )
                : xs
            : ys;

    return go;
};

// zipWithM :: Applicative m => (a -> b -> m c) ->
// [a] -> [b] -> m [c]
const zipWithM = f =>
    xs => ys =>
        sequenceA(
            zipWith(f)(
                [...xs]
            )([...ys])
        );

// zipWithN :: (a -> b -> ... -> d) -> [a], [b] ... -> [d]
const zipWithN = (f, ...xss) => {
    // Generalisation of ZipWith, ZipWith3 etc.
    // f is a curried function absorbing at least 
    // N arguments, where N is the length of xss.
    const m = 0 < xss.length
        ? Math.min(...xss.map(x => x.length))
        : 0;

    return xss.reduce(
        (gs, vs) => gs.map((g, i) => g(vs[i])),
        Array.from({ length: m }, () => f)
    );
};

// zipWithN_ :: ((a, b ...) -> d) -> [a], [b] ... -> [d]
const zipWithN_ = (f, ...xss) =>
    // Generalisation of ZipWith, ZipWith3 etc.
    // f is an uncurried function with arity
    // equal to the length of xss.
    Array.from(
        {
            length: 0 < xss.length
                ? Math.min(...xss.map(x => x.length))
                : 0
        },
        (_, i) => f(
            ...xss.map(xs => xs[i])
        )
    );

// zipWith_ :: (a -> a -> b) -> [a] -> [b]
const zipWith_ = f =>
    // A list with the length of the shorter of
    // xs and ys, defined by zipping with a
    // custom function, rather than with the
    // default tuple constructor.
    xs => ys => xs.slice(
        0, Math.min(xs.length, ys.length)
    )
    .map((x, i) => f(x)(ys[i]));