[WIP] Import and unify the rule syntax and classical pattern matching system from SymbolicUtils.jl

[0x0f0f0f]

• Pattern types
• Pattern/rule syntax eDSL
• Make RHS consequent in dynamic rule like in SU syntax
• Lower classical pattern matcher from SU
• E-Graphs pattern matcher support
• Added type assertions
• Change MT rule operators to support SU's operators
• Support segment variables in Classical rewriting
• Update tests with new syntax
• Separate SU and MT syntax in two different modules so that users can use both
• ACRule
• Predicate support in e-graphs
• Update ARCHITECTURE.md
• Bring docs over
• Benchmark suite
• Stage egraphs pattern matcher
• Capture macro add capture macro SymbolicUtils.jl#343
• Fix timer outputs
• downport add @slots macro to improve readability of rules SymbolicUtils.jl#374

[0x0f0f0f]

This is the first (and biggest) step for https://discourse.julialang.org/t/a-recap-of-the-state-of-the-symbolics-ecosystem/68022

[0x0f0f0f]

@shashi it seems downporting the pattern matcher was super easy. I have made a few improvements I'll benchmark later.

[0x0f0f0f]

Getting good progress:

julia> using SymbolicUtils, Metatheory, BenchmarkTools
[ Info: Precompiling Metatheory [e9d8d322-4543-424a-9be4-0cc815abe26c]
WARNING: could not import EGraphs.Rule into Schedulers
┌ Info: NOTE: The current implementation of the Metatheory library currently works
└ correctly only with the EGraphs backend.

julia> @syms x y
(x, y)

julia> f(x) = x^2
f (generic function with 1 method)

julia> g(x) = x/2
g (generic function with 1 method)

julia> rsymb = @btime SymbolicUtils.@rule f(~a, g(~b, 3)) => f(~b * ~a)
  4.100 μs (59 allocations: 2.03 KiB)
f(~a, g(~b, 3)) => f(~b * ~a)

julia> rmeta = @btime Metatheory.@methodrule f(~a, g(~b, 3)) => f(~b * ~a)
  7.260 μs (130 allocations: 5.81 KiB)
f(~a, g(~b, 3)) => f(~b * ~a)

julia> ex = term(f, x, term(g, y, 3))
f(x, g(y, 3))

julia> @btime rsymb(ex)
  2.863 μs (64 allocations: 2.78 KiB)
(x^2)*(y^2)

julia> @btime rmeta(ex)
  2.482 μs (64 allocations: 3.31 KiB)
(x^2)*(y^2)

[codecov-commenter]

Codecov Report

Merging #77 (1ca0e77) into master (931eda2) will decrease coverage by 0.53%.
The diff coverage is 70.90%.

@@            Coverage Diff             @@
##           master      #77      +/-   ##
==========================================
- Coverage   77.23%   76.69%   -0.54%     
==========================================
  Files          34       15      -19     
  Lines        1287     1416     +129     
==========================================
+ Hits          994     1086      +92     
- Misses        293      330      +37     

Impacted Files	Coverage Δ
src/Rewriters.jl	33.00% <33.00%> (ø)
src/utils.jl	35.71% <35.71%> (ø)
src/EGraphs/Schedulers.jl	39.24% <39.24%> (ø)
src/matchers.jl	70.93% <70.93%> (ø)
src/Rules.jl	73.61% <73.61%> (ø)
src/Patterns.jl	79.16% <79.16%> (ø)
src/Syntax.jl	79.69% <79.69%> (ø)
src/EGraphs/egraph.jl	91.01% <86.00%> (-3.21%)	⬇️
src/EGraphs/analysis.jl	91.02% <87.93%> (-8.98%)	⬇️
src/EGraphs/ematch.jl	92.12% <89.47%> (-0.74%)	⬇️
... and 5 more

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