Add missing and Missing

Add basic support with special methods for operators and standard math functions.
Adapt ==(::AbstractArray, ::AbstractArray), all() and any() to support
three-valued logic. This requires defining missing and Missing early in the
bootstrap process, but other missing-related code is included relatively late
to be able to add methods to Base functions defined in various places.

base/abstractarray.jl

@@ -1554,12 +1554,16 @@ function (==)(A::AbstractArray, B::AbstractArray)
     if isa(A,AbstractRange) != isa(B,AbstractRange)
         return false
     end
+    anymissing = false
     for (a, b) in zip(A, B)
-        if !(a == b)
+        eq = (a == b)
+        if ismissing(eq)
+            anymissing = true
+        elseif !eq
             return false
         end
     end
-    return true
+    return anymissing ? missing : true
 end
 
 # sub2ind and ind2sub

base/essentials.jl

@@ -751,3 +751,26 @@ This function simply returns its argument by default, since the elements
 of a general iterator are normally considered its "values".
 """
 values(itr) = itr
+
+"""
+    Missing
+
+A type with no fields whose singleton instance [`missing`](@ref) is used
+to represent missing values.
+"""
+struct Missing end
+
+"""
+    missing
+
+The singleton instance of type [`Missing`](@ref) representing a missing value.
+"""
+const missing = Missing()
+
+"""
+    ismissing(x)
+
+Indicate whether `x` is [`missing`](@ref).
+"""
+ismissing(::Any) = false
+ismissing(::Missing) = true

base/exports.jl

@@ -76,6 +76,7 @@ export
     Irrational,
     Matrix,
     MergeSort,
+    Missing,
     NTuple,
     Nullable,
     ObjectIdDict,
@@ -150,6 +151,7 @@ export
     EOFError,
     InvalidStateException,
     KeyError,
+    MissingException,
     NullException,
     ParseError,
     SystemError,
@@ -882,6 +884,10 @@ export
     isready,
     fetch,
 
+# missing values
+    ismissing,
+    missing,
+
 # time
     sleep,
     time,

base/missing.jl

@@ -0,0 +1,115 @@
+# This file is a part of Julia. License is MIT: https://julialang.org/license
+
+# Missing, missing and ismissing are defined in essentials.jl
+
+show(io::IO, x::Missing) = print(io, "missing")
+
+"""
+    MissingException(msg)
+
+Exception thrown when a [`missing`](@ref) value is encountered in a situation
+where it is not supported. The error message, in the `msg` field
+may provide more specific details.
+"""
+struct MissingException <: Exception
+    msg::AbstractString
+end
+
+showerror(io::IO, ex::MissingException) =
+    print(io, "MissingException: ", ex.msg)
+
+promote_rule(::Type{Missing}, ::Type{T}) where {T} = Union{T, Missing}
+promote_rule(::Type{Union{S,Missing}}, ::Type{T}) where {T,S} = Union{promote_type(T, S), Missing}
+promote_rule(::Type{Any}, ::Type{T}) where {T} = Any
+promote_rule(::Type{Any}, ::Type{Missing}) = Any
+promote_rule(::Type{Missing}, ::Type{Any}) = Any
+promote_rule(::Type{Missing}, ::Type{Missing}) = Missing
+
+convert(::Type{Union{T, Missing}}, x) where {T} = convert(T, x)
+# To print more appropriate message than "T not defined"
+convert(::Type{Missing}, x) = throw(MethodError(convert, (Missing, x)))
+convert(::Type{Missing}, ::Missing) = missing
+
+# Comparison operators
+==(::Missing, ::Missing) = missing
+==(::Missing, ::Any) = missing
+==(::Any, ::Missing) = missing
+# To fix ambiguity
+==(::Missing, ::WeakRef) = missing
+==(::WeakRef, ::Missing) = missing
+isequal(::Missing, ::Missing) = true
+isequal(::Missing, ::Any) = false
+isequal(::Any, ::Missing) = false
+<(::Missing, ::Missing) = missing
+<(::Missing, ::Any) = missing
+<(::Any, ::Missing) = missing
+isless(::Missing, ::Missing) = false
+isless(::Missing, ::Any) = false
+isless(::Any, ::Missing) = true
+
+# Unary operators/functions
+for f in (:(!), :(+), :(-), :(identity), :(zero),
+          :(abs), :(abs2), :(sign),
+          :(acos), :(acosh), :(asin), :(asinh), :(atan), :(atanh),
+          :(sin), :(sinh), :(cos), :(cosh), :(tan), :(tanh),
+          :(exp), :(exp2), :(expm1), :(log), :(log10), :(log1p),
+          :(log2), :(exponent), :(sqrt), :(gamma), :(lgamma),
+          :(iseven), :(ispow2), :(isfinite), :(isinf), :(isodd),
+          :(isinteger), :(isreal), :(isnan), :(isempty),
+          :(iszero), :(transpose), :(float))
+    @eval Math.$(f)(::Missing) = missing
+end
+
+zero(::Type{Union{T, Missing}}) where {T} = zero(T)
+# To prevent StackOverflowError
+zero(::Type{Any}) = throw(MethodError(zero, (Any,)))
+
+# Binary operators/functions
+for f in (:(+), :(-), :(*), :(/), :(^),
+          :(div), :(mod), :(fld), :(rem), :(min), :(max))
+    @eval begin
+        # Scalar with missing
+        ($f)(::Missing, ::Missing) = missing
+        ($f)(d::Missing, x::Number) = missing
+        ($f)(d::Number, x::Missing) = missing
+    end
+end
+
+# Rounding and related functions
+for f in (:(ceil), :(floor), :(round), :(trunc))
+    @eval begin
+        ($f)(::Missing, digits::Integer=0, base::Integer=0) = missing
+        ($f)(::Type{>:Missing}, ::Missing) = missing
+        ($f)(::Type{T}, ::Missing) where {T} =
+            throw(MissingException("cannot convert a missing value to type $T"))
+    end
+end
+
+# to avoid ambiguity warnings
+(^)(::Missing, ::Integer) = missing
+
+# Bit operators
+(&)(::Missing, ::Missing) = missing
+(&)(a::Missing, b::Bool) = ifelse(b, missing, false)
+(&)(b::Bool, a::Missing) = ifelse(b, missing, false)
+(&)(::Missing, ::Integer) = missing
+(&)(::Integer, ::Missing) = missing
+(|)(::Missing, ::Missing) = missing
+(|)(a::Missing, b::Bool) = ifelse(b, true, missing)
+(|)(b::Bool, a::Missing) = ifelse(b, true, missing)
+(|)(::Missing, ::Integer) = missing
+(|)(::Integer, ::Missing) = missing
+xor(::Missing, ::Missing) = missing
+xor(a::Missing, b::Bool) = missing
+xor(b::Bool, a::Missing) = missing
+xor(::Missing, ::Integer) = missing
+xor(::Integer, ::Missing) = missing
+
+*(d::Missing, x::AbstractString) = missing
+*(d::AbstractString, x::Missing) = missing
+
+function float(A::AbstractArray{Union{T, Missing}}) where {T}
+    U = typeof(float(zero(T)))
+    convert(AbstractArray{Union{U, Missing}}, A)
+end
+float(A::AbstractArray{Missing}) = A

base/operators.jl

@@ -155,7 +155,7 @@ julia> "foo" ≠ "foo"
 false
 ```
 """
-!=(x, y) = !(x == y)::Bool
+!=(x, y) = !(x == y)
 const ≠ = !=
 
 """

base/reduce.jl

@@ -610,10 +610,16 @@ true
 ```
 """
 function any(f, itr)
+    anymissing = false
     for x in itr
-        f(x) && return true
+        v = f(x)
+        if ismissing(v)
+            anymissing = true
+        elseif v
+            return true
+        end
     end
-    return false
+    return anymissing ? missing : false
 end
 
 """
@@ -635,12 +641,22 @@ false
 ```
 """
 function all(f, itr)
+    anymissing = false
     for x in itr
-        f(x) || return false
+        v = f(x)
+        if ismissing(v)
+            anymissing = true
+        # this syntax allows throwing a TypeError for non-Bool, for consistency with any
+        elseif v
+            continue
+        else
+            return false
+        end
     end
-    return true
+    return anymissing ? missing : true
 end
 
+
 ## in & contains
 
 """

base/reducedim.jl

@@ -112,7 +112,7 @@ function reducedim_init(f, op::typeof(*), A::AbstractArray, region)
 end
 function _reducedim_init(f, op, fv, fop, A, region)
     T = promote_union(eltype(A))
-    if applicable(zero, T)
+    if T !== Any && applicable(zero, T)
         x = f(zero(T))
         z = op(fv(x), fv(x))
         Tr = typeof(z) == typeof(x) && !isbits(T) ? T : typeof(z)

base/sysimg.jl

@@ -394,6 +394,9 @@ const × = cross
 # statistics
 include("statistics.jl")
 
+# missing values
+include("missing.jl")
+
 # libgit2 support
 include("libgit2/libgit2.jl")
 

test/ambiguous.jl

@@ -280,6 +280,10 @@ end
         pop!(need_to_handle_undef_sparam, which(Base.SparseArrays._absspvec_vcat, (AbstractSparseArray{Tv, Ti, 1} where {Tv, Ti},)))
         pop!(need_to_handle_undef_sparam, which(Base.SparseArrays._absspvec_hcat, (AbstractSparseArray{Tv, Ti, 1} where {Tv, Ti},)))
         pop!(need_to_handle_undef_sparam, which(Base.cat, (Any, Base.SparseArrays._TypedDenseConcatGroup{T} where T)))
+        pop!(need_to_handle_undef_sparam, which(Base.float, Tuple{AbstractArray{Union{Missing, T},N} where {T, N}}))
+        pop!(need_to_handle_undef_sparam, which(Base.convert, Tuple{Type{Union{Missing, T}} where T, Any}))
+        pop!(need_to_handle_undef_sparam, which(Base.promote_rule, Tuple{Type{Union{Missing, S}} where S, Type{T} where T}))
+        pop!(need_to_handle_undef_sparam, which(Base.zero, Tuple{Type{Union{Missing, T}} where T}))
         @test need_to_handle_undef_sparam == Set()
     end
 end

test/choosetests.jl

@@ -49,7 +49,7 @@ function choosetests(choices = [])
         "checked", "bitset", "floatfuncs", "compile", "distributed", "inline",
         "boundscheck", "error", "ambiguous", "cartesian", "asmvariant", "osutils",
         "channels", "iostream", "specificity", "codegen", "codevalidation",
-        "reinterpretarray", "syntax"
+        "reinterpretarray", "syntax", "missing"
     ]
 
     if isdir(joinpath(JULIA_HOME, Base.DOCDIR, "examples"))