Merge pull request #261 from JuliaSymbolics/ys/canon

Formalize canonical form

Author: shashi

src/SymbolicUtils.jl

@@ -13,7 +13,7 @@ include("types.jl")
 
 # Methods on symbolic objects
 using SpecialFunctions, NaNMath
-import IfElse: ifelse  # need to not bring IfElse name in or it will clash
+import IfElse: ifelse  # need to not bring IfElse name in or it will clash with Rewriters.IfElse
 include("methods.jl")
 
 # LinkedList, simplification utilities

src/code.jl

@@ -100,7 +100,7 @@ function_to_expr(op, args, st) = nothing
 
 function function_to_expr(::typeof(^), O, st)
     args = arguments(O)
-    if length(args) == 2 && args[2] isa Number && args[2] < 0
+    if length(args) == 2 && args[2] isa Real && args[2] < 0
         ex = args[1]
         if args[2] == -1
             return toexpr(Term{Any}(inv, [ex]), st)

src/types.jl

@@ -503,7 +503,7 @@ function show_call(io, f, args)
     if binary
         for (i, t) in enumerate(args)
             i != 1 && print(io, " $fname ")
-            print_arg(io, t)
+            print_arg(io, t, paren=true)
         end
     else
         if f isa Sym
@@ -513,7 +513,7 @@ function show_call(io, f, args)
         end
         print(io, "(")
         for i=1:length(args)
-            print(IOContext(io, :paren => false), args[i])
+            print(io, args[i])
             i != length(args) && print(io, ", ")
         end
         print(io, ")")
@@ -775,9 +775,21 @@ mul_t(a) = promote_symtype(*, symtype(a))
                         a.coeff * b.coeff,
                         _merge(+, a.dict, b.dict, filter=_iszero))
 
-*(a::Number, b::SN) = iszero(a) ? a : isone(a) ? b : Mul(mul_t(a, b), makemul(a, b)...)
+function *(a::Number, b::SN)
+    if iszero(a)
+        a
+    elseif isone(a)
+        b
+    elseif b isa Add
+        # 2(a+b) -> 2a + 2b
+        T = promote_symtype(+, typeof(a), symtype(b))
+        Add(T, b.coeff * a, Dict(k=>v*a for (k, v) in b.dict))
+    else
+        Mul(mul_t(a, b), makemul(a, b)...)
+    end
+end
 
-*(b::SN, a::Number) = iszero(a) ? a : isone(a) ? b : Mul(mul_t(a, b), makemul(a, b)...)
+*(a::SN, b::Number) = b * a
 
 /(a::Union{SN,Number}, b::SN) = a * b^(-1)
 
@@ -853,7 +865,13 @@ end
 
 *(a::Pow, b::Mul) = b * a
 
-_merge(f, d, others...; filter=x->false) = _merge!(f, copy(d), others...; filter=filter)
+function copy_similar(d, others)
+    K = promote_type(keytype(d), keytype.(others)...)
+    V = promote_type(valtype(d), valtype.(others)...)
+    Dict{K, V}(d)
+end
+
+_merge(f, d, others...; filter=x->false) = _merge!(f, copy_similar(d, others), others...; filter=filter)
 function _merge!(f, d, others...; filter=x->false)
     acc = d
     for other in others

test/basics.jl

@@ -151,7 +151,7 @@ end
     @test repr(Term(*, [1, 1])) == "*1"
     @test repr(Term(*, [2, 1])) == "2*1"
     @test repr((a + b) - (b + c)) == "a - c"
-    @test repr(a + -1*(b + c)) == "a - (b + c)"
+    @test repr(a + -1*(b + c)) == "a - b - c"
     @test repr(a + -1*b) == "a - b"
 end
 
@@ -165,7 +165,7 @@ toterm(t) = Term{symtype(t)}(operation(t), arguments(t))
 @testset "diffs" begin
     @syms a b c
     @test isequal(toterm(-1c), Term{Number}(*, [-1, c]))
-    @test isequal(toterm(-1(a+b)), Term{Number}(*, [-1, a+b]))
+    @test isequal(toterm(-1(a+b)), Term{Number}(+, [-1a, -b]))
     @test isequal(toterm((a + b) - (b + c)), Term{Number}(+, [a, -1c]))
 end
 
@@ -181,3 +181,17 @@ end
     @test_throws MethodError a * b
     @test_throws MethodError a + b
 end
+
+@testset "canonical form" begin
+    @syms a b c
+    for x in [a, a*b, a+b, a-b, a^2, sin(a)]
+        @test isequal(x * 1, x)
+        @test x * 0 === 0
+        @test isequal(x + 0, x)
+        @test isequal(x + x, 2x)
+        @test isequal(x + 2x, 3x)
+        @test x - x === 0
+        @test isequal(-x, -1x)
+        @test isequal(x^1, x)
+    end
+end

test/fuzzlib.jl

@@ -1,5 +1,9 @@
 using SymbolicUtils
+using SymbolicUtils: Term
+using SpecialFunctions
 using Test
+import IfElse: ifelse
+import IfElse
 
 using SymbolicUtils: showraw, Symbolic
 
@@ -101,6 +105,9 @@ function gen_rand_expr(inputs;
                                  min_depth=min_depth,
                                  max_depth=max_depth)
         else
+            @show f
+            @show arity
+            @show args
             rethrow(err)
         end
     end
@@ -114,9 +121,15 @@ function fuzz_test(ntrials, spec, simplify=simplify;kwargs...)
     inputs = Set()
     expr = gen_rand_expr(inputs; spec=spec, kwargs...)
     inputs = collect(inputs)
+    code = try
+        SymbolicUtils.Code.toexpr(expr)
+    catch err
+        @show expr
+        rethrow(err)
+    end
     unsimplifiedstr = """
     function $(tuple(inputs...))
-        $(sprint(io->showraw(io, expr)))
+        $(sprint(io->print(io, code)))
     end
     """