Expression level rewriting

[GeorgeR227]

This PR is meant to create a back-and-forth between ACSets, which excel at information propagation (typing, overloading, etc.) and Symbolics, which excel at expression rewriting (open_operators, optimizations, etc.).

This should remove the need for our graph rewriting functions and make the workflow to add new rewrites into the system much more faster/cleaner.

[codecov]

Codecov Report

Attention: Patch coverage is 90.00000% with 11 lines in your changes missing coverage. Please review.

Project coverage is 82.01%. Comparing base (0a314a8) to head (67079cb).

Files with missing lines	Patch %	Lines
src/acset2symbolic.jl	91.83%	4 Missing ⚠️
src/deca/ThDEC.jl	55.55%	4 Missing ⚠️
src/graph_traversal.jl	94.28%	2 Missing ⚠️
src/sym_rewrite.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@                   Coverage Diff                    @@
##           symbolicutilsinterop      #69      +/-   ##
========================================================
+ Coverage                 74.90%   82.01%   +7.10%     
========================================================
  Files                        16       19       +3     
  Lines                      1068     1173     +105     
========================================================
+ Hits                        800      962     +162     
+ Misses                      268      211      -57     

Flag	Coverage Δ
	82.01% <90.00%> (?)

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[jpfairbanks]

The topo sort stuff is looking good. The symbolics integration should target the existing symbolics integration branch.

[jpfairbanks]

My aesthetic sense says these should be in the opposite order because of most significant digit first order. An alternative would be to use MLStyle to create a type that represents the valid elements of an ACSet. When you traverse the ACSet you create an iterable of these types. Then when you consume this list, you use @match to consume the elements of the iterable. These @data records could be automatically generated in ACSets.jl from the schema.

module ACSetElements
using MLStyle

abstract type ACSetElement end

@data PodeElement <: ACSetElement begin
  Op1(i::Int)
  Op2(i::Int)
  Var(i::Int)
  TVar(i::Int)
  Σ(i::Int)
  Summand(i::Int)
  Name(s::Symbol)
  _Type(t) # you can't use Type in ML style because Core.Type 
end
end

module ACSetRecords
using MLStyle

abstract type ACSetRecord end
@data PodeRecord <: ACSetRecord begin
  Name(s::Symbol)
  Operator(s::Symbol)
  _Type(t)
  Var(name::Name, type::Type)
  TVar(incl::Var)
  Op1(src::Var, tgt::Var, op1::Operator)
  Op2(proj1::Var, proj2::Var, res::Var, op2::Operator)
  Σ(sum::Var)
  Summand(summation::Σ, summand::Var)
end
end

[jpfairbanks]

Ok, the unitype design that you did, coupled with an Enum that captures the available symbols would be good. https://docs.julialang.org/en/v1/base/base/#Base.Enums.@enum and https://thautwarm.github.io/MLStyle.jl/latest/syntax/pattern.html#support-pattern-matching-for-julia-enums could work together to make it easy to write the generic code.

[jpfairbanks]

We can also check that when you iterate over the edges in the decapode, we never go from a later vertex to an earlier vertex.

[lukem12345]

When roundtripping to the SummationDecapode is complete, it would be good to test that the results in test/openoperators.jl give the same results up to renaming etc

[GeorgeR227]

I've rebased this branch to work off of PR #64 since the code here will be used for the rewriting using only Sort.

[lukem12345]

@quffaro It looks like your commit 2b3198f removed the check for $$\partial_t$$ in extract_symexprs, but your merge 367414d seems to have possibly errantly put the check back. Which behavior do you want. Is there a test that passes or fails depending on whether this is checked?

[GeorgeR227]

@lukem12345 We wanted to remove this check since it lead to a lot of special code to handle the final ACSet generation. I've removed it in commit 5b84cc8 and added the appropriate tests to ensure it's proper functionality.