Merge pull request #6582 from JuliaLang/uniops-552

RFC: Add some unicode function synonyms and infix operators

base/exports.jl

@@ -190,23 +190,29 @@ export
 # Operators
     !,
     !=,
+    ≠,
     !==,
+    ≡,
+    ≢, 
     $,
     %,
     &,
     *,
     +,
     -,
     .!=,
+    .≠,
     .+,
     .-,
     .*,
     ./,
     .<,
     .<=,
+    .≤,
     .==,
     .>,
     .>=,
+    .≥,
     .\,
     .^,
     /,
@@ -215,9 +221,11 @@ export
     <:,
     <<,
     <=,
+    ≤,
     ==,
     >,
     >=,
+    ≥,
     >>,
     #.>>,
     #.<<,
@@ -227,6 +235,7 @@ export
     |,
     ~,
     :,
+    ÷,
     A_ldiv_B!,
     A_ldiv_Bc,
     A_ldiv_Bt,
@@ -442,6 +451,7 @@ export
     unsigned,
     widemul,
     zero,
+    √,
 
 # specfun
     airy,
@@ -660,6 +670,8 @@ export
     triu!,
     triu,
     vecnorm,
+    ⋅,
+    ×,
 
 # sparse
     etree,
@@ -746,6 +758,17 @@ export
     union,
     unique,
     values,
+    ∈,
+    ∉,
+    ∋,
+    ∌,
+    ⊆,
+    ⊈,
+    ⊂,
+    ⊄,
+    ⊊,
+    ∩,
+    ∪,
 
 # strings and text output
     ascii,

base/math.jl

@@ -16,7 +16,7 @@ export sin, cos, tan, sinh, cosh, tanh, asin, acos, atan,
        besselj0, besselj1, besselj, bessely0, bessely1, bessely,
        hankelh1, hankelh2, besseli, besselk, besselh,
        beta, lbeta, eta, zeta, polygamma, invdigamma, digamma, trigamma,
-       erfinv, erfcinv
+       erfinv, erfcinv, √
 
 import Base: log, exp, sin, cos, tan, sinh, cosh, tanh, asin,
              acos, atan, asinh, acosh, atanh, sqrt, log2, log10,
@@ -284,6 +284,7 @@ sqrt(x::Float64) = box(Float64,sqrt_llvm(unbox(Float64,x)))
 sqrt(x::Float32) = box(Float32,sqrt_llvm(unbox(Float32,x)))
 sqrt(x::Real) = sqrt(float(x))
 @vectorize_1arg Number sqrt
+const √=sqrt
 
 for f in (:ceil, :trunc, :significand) # :rint, :nearbyint
     @eval begin

base/operators.jl

@@ -13,14 +13,19 @@ isequal(T::Type, S::Type) = typeseq(T, S)
 isequal(x,y) = is(x,y)
 ==(x,y) = isequal(x,y)
 !=(x,y) = !(x==y)
+const ≠ = !=
+const ≡ = is
 !==(x,y) = !is(x,y)
-
+const ≢ = !==
 < (x,y) = isless(x,y)
 > (x,y) = y < x
 <=(x,y) = !(y < x)
+const ≤ = <=
 >=(x,y) = (y <= x)
+const ≥ = >=
 .> (x,y) = y.<x
 .>=(x,y) = y.<=x
+const .≥ = .>=
 
 # this definition allows Number types to implement < instead of isless,
 # which is more idiomatic:
@@ -84,6 +89,8 @@ end
 .!=(x::Number,y::Number) = x!=y
 .< (x::Real,y::Real) = x<y
 .<=(x::Real,y::Real) = x<=y
+const .≤ = .<=
+const .≠ = .!=
 
 # core << >> and >>> takes Int32 as second arg
 <<(x,y::Integer)  = x << convert(Int32,y)
@@ -104,6 +111,7 @@ fld{T<:Real}(x::T, y::T) = convert(T,round((x-mod(x,y))/y))
 # operator alias
 const % = rem
 .%(x::Real, y::Real) = x%y
+const ÷ = div
 
 # mod returns in [0,y) whereas mod1 returns in (0,y]
 mod1{T<:Real}(x::T, y::T) = y-mod(y-x,y)
@@ -343,7 +351,7 @@ function ifelse(c::AbstractArray{Bool}, x, y::AbstractArray)
 end
 
 # some operators not defined yet
-global //, .>>, .<<, >:, <|, |>, hcat, hvcat
+global //, .>>, .<<, >:, <|, |>, hcat, hvcat, ⋅, ×, ∈, ∉, ∋, ∌, ⊆, ⊈, ⊊, ∩, ∪
 
 module Operators
 
@@ -380,6 +388,12 @@ export
     ==,
     >,
     >=,
+    ≥,
+    ≤,
+    ≠,
+    .≥,
+    .≤,
+    .≠,
     >>,
     .>>,
     .<<,
@@ -390,6 +404,18 @@ export
     |>,
     <|,
     ~,
+    ÷,
+    ⋅,
+    ×,
+    ∈,
+    ∉,
+    ∋,
+    ∌,
+    ⊆,
+    ⊈,
+    ⊊,
+    ∩,
+    ∪,
     colon,
     hcat,
     vcat,
@@ -402,6 +428,7 @@ export
 import Base: !, !=, $, %, .%, &, *, +, -, .!=, .+, .-, .*, ./, .<, .<=, .==, .>,
     .>=, .\, .^, /, //, <, <:, <<, <=, ==, >, >=, >>, .>>, .<<, >>>,
     <|, |>, \, ^, |, ~, !==, >:, colon, hcat, vcat, hvcat, getindex, setindex!,
-    transpose, ctranspose
+    transpose, ctranspose,
+    ≥, ≤, ≠, .≥, .≤, .≠, ÷, ⋅, ×, ∈, ∉, ∋, ∌, ⊆, ⊈, ⊊, ∩, ∪
 
 end

base/reduce.jl

@@ -121,6 +121,10 @@ function in(x, itr)
     end
     return false
 end
+const ∈ = in
+∉(x, itr)=!∈(x, itr)
+∋(itr, x)= ∈(x, itr)
+∌(itr, x)=!∋(itr, x)
 
 function contains(itr, x)
     depwarn("contains(collection, item) is deprecated, use in(item, collection) instead", :contains)

base/set.jl

@@ -50,6 +50,7 @@ function union(s::Set, sets::Set...)
     end
     return u
 end
+const ∪ = union
 
 intersect(s::Set) = copy(s)
 function intersect(s::Set, sets::Set...)
@@ -64,6 +65,7 @@ function intersect(s::Set, sets::Set...)
     end
     return i
 end
+const ∩ = intersect
 
 function setdiff(a::Set, b::Set)
     d = copy(a)
@@ -85,6 +87,9 @@ function issubset(l, r)
     end
     return true
 end
+const ⊆ = issubset
+⊊(l::Set, r::Set) = ⊆(l, r) && l!=r
+⊈(l::Set, r::Set) = !⊆(l, r)
 
 function unique(C)
     out = Array(eltype(C),0)

base/sysimg.jl

@@ -217,6 +217,8 @@ include("sparse.jl")
 importall .SparseMatrix
 include("linalg.jl")
 importall .LinAlg
+const ⋅ = dot
+const × = cross
 include("broadcast.jl")
 importall .Broadcast
 

src/julia-parser.scm

@@ -7,12 +7,12 @@
      ; the way the lexer works, every prefix of an operator must also
      ; be an operator.
      (-- -->)
-     (> < >= <= == === != !== |.>| |.<| |.>=| |.<=| |.==| |.!=| |.=| |.!| |<:| |>:|)
+     (> < >= ≥ <= ≤ == === ≡ != ≠ !== ≢ |.>| |.<| |.>=| |.≥| |.<=| |.≤| |.==| |.!=| |.≠| |.=| |.!| |<:| |>:| ∈ ∉ ∋ ∌ ⊆ ⊈ ⊂ ⊄ ⊊)
      (|\|>| |<\||)
      (: |..|)
-     (+ - |.+| |.-| |\|| $)
+     (+ - ⊕ ⊖ ⊞ ⊟ |.+| |.-| |\|| ∪ ∨ $ ⊓)
      (<< >> >>> |.<<| |.>>| |.>>>|)
-     (* / |./| % |.%| & |.*| |\\| |.\\|)
+     (* / |./| ÷ % ⋅ ∘ × |.%| |.*| |\\| |.\\| & ∩ ∧ ⊗ ⊘ ⊙ ⊚ ⊛ ⊠ ⊡ ⊔)
      (// .//)
      (^ |.^|)
      (|::|)