Merge pull request #154 from JuliaSymbolics/s/fast-terms

WIP: constructor-level simplification

Author: shashi

docs/api.md

@@ -20,6 +20,12 @@ using SymbolicUtils # hide
 
 {{doc Term Term type}}
 
+{{doc Add Add type}}
+
+{{doc Mul Mul type}}
+
+{{doc Pow Pow type}}
+
 {{doc promote_symtype promote_symtype fn}}
 
 ## Interfacing

docs/index.md

@@ -12,18 +12,20 @@ where appropriate -->
 
 The main features are:
 
-- Symbols (`Sym`s) carry type information. ([read more](#symbolic_expressions))
-- Compound expressions composed of `Sym`s propagate type information. ([read more](#symbolic_expressions))
-- A flexible [rule-based rewriting language](#rule-based_rewriting) allowing liberal use of user defined matchers and rewriters.
+- Fast expressions
 - A [combinator library](#composing-rewriters) for making rewriters.
+- A [rule-based rewriting language](#rule-based_rewriting).
+- Type promotion:
+  - Symbols (`Sym`s) carry type information. ([read more](#symbolic_expressions))
+  - Compound expressions composed of `Sym`s propagate type information. ([read more](#symbolic_expressions))
 - Set of [simplification rules](#simplification). These can be remixed and extended for special purposes.
 
 
 ## Table of contents
 
 \tableofcontents <!-- you can use \toc as well -->
 
-## Symbolic expressions
+## `Sym`s
 
 First, let's use the `@syms` macro to create a few symbols.
 
@@ -66,17 +68,6 @@ expr1 + expr2
 ```
 \out{expr}
 
-### Simplified printing
-
-Tip: you can set `SymbolicUtils.show_simplified[] = true` to enable simplification on printing, or call `SymbolicUtils.showraw(expr)` to display an expression without simplification.
- In the REPL, if an expression was successfully simplified before printing, it will appear in yellow rather than white, as a visual cue that what you are looking at is not the exact datastructure. 
-
-```julia:showraw
-using SymbolicUtils: showraw
-
-showraw(expr1 + expr2)
-```
-\out{showraw}
 
 **Function-like symbols**
 
@@ -106,6 +97,20 @@ g(2//5, g(1, β))
 
 This works because `g` "returns" a `Real`.
 
+
+## Expression interface
+
+Symbolic expressions are of type `Term{T}`, `Add{T}`, `Mul{T}` or `Pow{T}` and denote some function call where one or more arguments are themselves such expressions or `Sym`s.
+
+All the expression types support the following:
+
+- `istree(x)` -- always returns `true` denoting, `x` is not a leaf node like Sym or a literal.
+- `operation(x)` -- the function being called
+- `arguments(x)` -- a vector of arguments
+- `symtype(x)` -- the "inferred" type (`T`)
+
+See more on the interface [here](/interface)
+
 ## Rule-based rewriting
 
 Rewrite rules match and transform an expression. A rule is written using either the `@rule` macro or the `@acrule` macro.
@@ -151,7 +156,7 @@ Notice that there is a subexpression `(2 * w) + (2 * w)` that could be simplifie
 
 ### Predicates for matching
 
-Matcher pattern may contain slot variables with attached predicates, written as `~x::f` where `f` is a function that takes a matched expression (a `Term` object a `Sym` or any Julia value that is in the expression tree) and returns a boolean value. Such a slot will be considered a match only if `f` returns true.
+Matcher pattern may contain slot variables with attached predicates, written as `~x::f` where `f` is a function that takes a matched expression and returns a boolean value. Such a slot will be considered a match only if `f` returns true.
 
 Similarly `~~x::g` is a way of attaching a predicate `g` to a segment variable. In the case of segment variables `g` gets a vector of 0 or more expressions and must return a boolean value. If the same slot or segment variable appears twice in the matcher pattern, then at most one of the occurance should have a predicate.
 

src/SymbolicUtils.jl

@@ -2,7 +2,10 @@ module SymbolicUtils
 
 export @syms, term, showraw
 
-# Sym, Term and other types
+# Sym, Term,
+# Add, Mul and Pow
+using DataStructures
+import Base: +, -, *, /, \, ^
 include("types.jl")
 
 # Methods on symbolic objects
@@ -32,7 +35,6 @@ include("matchers.jl")
 # Convert to an efficient multi-variate polynomial representation
 import AbstractAlgebra.Generic: MPoly, PolynomialRing, ZZ, exponent_vector
 using AbstractAlgebra: ismonomial, symbols
-using DataStructures
 include("abstractalgebra.jl")
 
 # Term ordering

src/methods.jl

@@ -4,7 +4,7 @@ import SpecialFunctions: gamma, loggamma, erf, erfc, erfcinv, erfi, erfcx,
                          besselj1, bessely0, bessely1, besselj, bessely, besseli,
                          besselk, hankelh1, hankelh2, polygamma, beta, logbeta
 
-const monadic = [deg2rad, rad2deg, transpose, -, conj, asind, log1p, acsch,
+const monadic = [deg2rad, rad2deg, transpose, conj, asind, log1p, acsch,
                  acos, asec, acosh, acsc, cscd, log, tand, log10, csch, asinh,
                  abs2, cosh, sin, cos, atan, cospi, cbrt, acosd, acoth, acotd,
                  asecd, exp, acot, sqrt, sind, sinpi, asech, log2, tan, exp10,
@@ -14,10 +14,9 @@ const monadic = [deg2rad, rad2deg, transpose, -, conj, asind, log1p, acsch,
                  trigamma, invdigamma, polygamma, airyai, airyaiprime, airybi,
                  airybiprime, besselj0, besselj1, bessely0, bessely1]
 
-const diadic = [+, -, max, min, *, /, \, hypot, atan, mod, rem, ^, copysign,
+const diadic = [max, min, hypot, atan, mod, rem, copysign,
                 besselj, bessely, besseli, besselk, hankelh1, hankelh2,
                 polygamma, beta, logbeta]
-
 const previously_declared_for = Set([])
 
 # TODO: it's not possible to dispatch on the symtype! (only problem is Parameter{})
@@ -32,13 +31,17 @@ end
 islike(a, T) = symtype(a) <: T
 
 # TODO: keep domains tighter than this
-function number_methods(T, rhs1, rhs2)
+function number_methods(T, rhs1, rhs2, options=nothing)
     exprs = []
 
+    skip_basics = !isnothing(options) ? options == :skipbasics : false
+    basic_monadic = [-, +]
+    basic_diadic = [+, -, *, /, \, ^]
+
     rhs2 = :($assert_like(f, Number, a, b); $rhs2)
     rhs1 = :($assert_like(f, Number, a); $rhs1)
 
-    for f in diadic
+    for f in (skip_basics ? diadic : vcat(basic_diadic, diadic))
         for S in previously_declared_for
             push!(exprs, quote
                       (f::$(typeof(f)))(a::$T, b::$S) = $rhs2
@@ -58,25 +61,38 @@ function number_methods(T, rhs1, rhs2)
         push!(exprs, expr)
     end
 
-    for f in monadic
+    for f in (skip_basics ? monadic : vcat(basic_monadic, monadic))
         push!(exprs, :((f::$(typeof(f)))(a::$T)   = $rhs1))
     end
     push!(exprs, :(push!($previously_declared_for, $T)))
     Expr(:block, exprs...)
 end
 
-macro number_methods(T, rhs1, rhs2)
-    number_methods(T, rhs1, rhs2) |> esc
+macro number_methods(T, rhs1, rhs2, options=nothing)
+    number_methods(T, rhs1, rhs2, options) |> esc
 end
 
-@number_methods(Sym, term(f, a), term(f, a, b))
-@number_methods(Term, term(f, a), term(f, a, b))
+@number_methods(Sym, term(f, a), term(f, a, b), skipbasics)
+@number_methods(Term, term(f, a), term(f, a, b), skipbasics)
+@number_methods(Add, term(f, a), term(f, a, b), skipbasics)
+@number_methods(Mul, term(f, a), term(f, a, b), skipbasics)
+@number_methods(Pow, term(f, a), term(f, a, b), skipbasics)
 
 for f in diadic
     @eval promote_symtype(::$(typeof(f)),
                    T::Type{<:Number},
                    S::Type{<:Number}) = promote_type(T, S)
 end
+
+for f in [+, -, *, \, /, ^]
+    @eval promote_symtype(::$(typeof(f)),
+                   T::Type{<:Number},
+                   S::Type{<:Number}) = promote_type(T, S)
+end
+for f in [+, -, *]
+    @eval promote_symtype(::$(typeof(f)), T::Type{<:Number}) = T
+end
+
 promote_symtype(::typeof(rem2pi), T::Type{<:Number}, mode) = T
 Base.rem2pi(x::Symbolic, mode::Base.RoundingMode) = term(rem2pi, x, mode)
 
@@ -93,25 +109,6 @@ rec_promote_symtype(f, x) = promote_symtype(f, x)
 rec_promote_symtype(f, x,y) = promote_symtype(f, x,y)
 rec_promote_symtype(f, x,y,z...) = rec_promote_symtype(f, promote_symtype(f, x,y), z...)
 
-# Variadic methods
-for f in [+, *]
-
-    @eval (::$(typeof(f)))(x::Symbolic) = x
-
-    # single arg
-    @eval function (::$(typeof(f)))(x::Symbolic, w::Number...)
-        term($f, x,w...,
-             type=rec_promote_symtype($f, map(symtype, (x,w...))...))
-    end
-    @eval function (::$(typeof(f)))(x::Number, y::Symbolic, w::Number...)
-        term($f, x, y, w...,
-             type=rec_promote_symtype($f, map(symtype, (x, y, w...))...))
-    end
-    @eval function (::$(typeof(f)))(x::Symbolic, y::Symbolic, w::Number...)
-        term($f, x, y, w...,
-             type=rec_promote_symtype($f, map(symtype, (x, y, w...))...))
-    end
-end
 
 Base.:*(a::AbstractArray, b::Symbolic{<:Number}) = map(x->x*b, a)
 Base.:*(a::Symbolic{<:Number}, b::AbstractArray) = map(x->a*x, b)

src/rewriters.jl

@@ -107,19 +107,20 @@ function (rw::Fixpoint)(x)
     return x
 end
 
-struct Walk{ord, C, threaded}
+struct Walk{ord, C, F, threaded}
     rw::C
     thread_cutoff::Int
+    similarterm::F
 end
 
 using .Threads
 
-function Postwalk(rw; threaded::Bool=false, thread_cutoff=100)
-    Walk{:post, typeof(rw), threaded}(rw, thread_cutoff)
+function Postwalk(rw; threaded::Bool=false, thread_cutoff=100, similarterm=similarterm)
+    Walk{:post, typeof(rw), typeof(similarterm), threaded}(rw, thread_cutoff, similarterm)
 end
 
-function Prewalk(rw; threaded::Bool=false, thread_cutoff=100)
-    Walk{:pre, typeof(rw), threaded}(rw, thread_cutoff)
+function Prewalk(rw; threaded::Bool=false, thread_cutoff=100, similarterm=similarterm)
+    Walk{:pre, typeof(rw), typeof(similarterm), threaded}(rw, thread_cutoff, similarterm)
 end
 
 struct PassThrough{C}
@@ -128,22 +129,22 @@ end
 (p::PassThrough)(x) = (y=p.rw(x); isnothing(y) ? x : y)
 
 passthrough(x, default) = isnothing(x) ? default : x
-function (p::Walk{ord, C, false})(x) where {ord, C}
+function (p::Walk{ord, C, F, false})(x) where {ord, C, F}
     @assert ord === :pre || ord === :post
     if istree(x)
         if ord === :pre
             x = p.rw(x)
         end
         if istree(x)
-            x = similarterm(x, operation(x), map(PassThrough(p), arguments(x)))
+            x = p.similarterm(x, operation(x), map(PassThrough(p), arguments(x)))
         end
         return ord === :post ? p.rw(x) : x
     else
         return p.rw(x)
     end
 end
 
-function (p::Walk{ord, C, true})(x) where {ord, C}
+function (p::Walk{ord, C, F, true})(x) where {ord, C, F}
     @assert ord === :pre || ord === :post
     if istree(x)
         if ord === :pre
@@ -158,7 +159,7 @@ function (p::Walk{ord, C, true})(x) where {ord, C}
                 end
             end
             args = map((t,a) -> passthrough(t isa Task ? fetch(t) : t, a), _args, arguments(x))
-            t = similarterm(x, operation(x), args)
+            t = p.similarterm(x, operation(x), args)
         end
         return ord === :post ? p.rw(t) : t
     else

src/rule.jl

@@ -321,7 +321,7 @@ function (acr::ACRule)(term)
         itr = acr.sets(eachindex(args), acr.arity)
 
         for inds in itr
-            result = r(similarterm(term, f, @views args[inds]))
+            result = r(Term{T}(f, @views args[inds]))
             if !isnothing(result)
                 # Assumption: inds are unique
                 length(args) == length(inds) && return result