Mugda

Recursion is not an option.

-- "The Little Typer"

An implementation of the Mugda paper -- "Termination Checking for a Dependently Typed Language", 2007, by Karl Mehltretter.

The "Mu" of the name "Mugda" comes from μ-operator (mu-operator) of general recursive function.

Notes

Zero arity data constructor

When using zero arity data constructor, we must write them in (). For example, zero and (zero) are the same.

But when using zero arity data constructor in pattern, we must write them in (). For example, we should not write zero but write (zero), otherwise the interpreter can not distinguish pattern variable from this zero arity data constructor.

Syntax of inductive datatype definition

The syntax of inductive datatype definition -- (data), is learnt from "The Little Typer".

Usages

Command line tool

Install it by the following command:

npm install -g @cicada-lang/mugda

The command-line program is called mu.

open a REPL:

mu repl

or just:

mu

Run a file:

mu run tests/basic/id.test.mu

Run a file and watch file change:

mu run tests/basic/id.test.mu --watch

Examples

Please see tests/ and std/ for more examples.

Boolean

(data Boolean () ()
  [true () Boolean]
  [false () Boolean])

(fn if (Pi ([A Type]) (-> Boolean A A A))
  [(A (true) a b) a]
  [(A (false) a b) b])

(define and (-> Boolean Boolean Boolean)
  (lambda (a b)
    (if Boolean a b false)))

(define or (-> Boolean Boolean Boolean)
  (lambda (a b)
    (if Boolean a true b)))

(and true true)
(and true false)
(and false true)
(and false false)

(or true true)
(or true false)
(or false true)
(or false false)

Nat

(data Nat () ()
  [zero () Nat]
  [add1 ([prev Nat]) Nat])

(fn add (-> Nat Nat Nat)
  [(x (zero)) x]
  [(x (add1 y)) (add1 (add x y))])

add
(add (add1 zero))
(add (add1 zero) (add1 zero))

List

(data List ([+ A Type]) ()
  [null () (List A)]
  [cons ([head A] [tail (List A)]) (List A)])

(import "../nat/index.mu" Nat zero add1)

(fn length (Pi ([A Type]) (-> (List A) Nat))
  [(A (null A)) zero]
  [(A (cons A head tail)) (add1 (length A tail))])

(length Nat (null Nat))
(length Nat (cons Nat zero (null Nat)))
(length Nat (cons Nat zero (cons Nat zero (null Nat))))

Development

npm install           # Install dependencies
npm run build         # Compile `src/` to `lib/`
npm run build:watch   # Watch the compilation
npm run format        # Format the code
npm run test          # Run test
npm run test:watch    # Watch the testing

Thanks

Thank you, Karl Mehltretter, for writing this paper.

Contributions

To make a contribution, fork this project and create a pull request.

Please read the STYLE-GUIDE.md before you change the code.

Remember to add yourself to AUTHORS. Your line belongs to you, you can write a little introduction to yourself but not too long.

License

GPLv3