Provide Collection of Rewrite Rules

[lukem12345]

See AlgebraicJulia/Decapodes.jl#252

This branch may be affected by #74

[jpfairbanks]

Seems like overkill to use a whole decapode for this since it will always be a single LHS, RHS pair. Also the SymbolicUtils stuff will be able to use the @rule macro for defining rules.

[lukem12345]

This is to replace operations which take place directly on Decapodes. In this case, this Decapode replaces this hand-written sub-Decapode insertion: https://github.com/AlgebraicJulia/Decapodes.jl/blob/main/src/operators.jl#L320

function add_Lie_2D!(::Type{Val{1}}, d::SummationDecapode, proj1_Lie::Int, proj2_Lie::Int, res_Lie::Int)

  ## Outputs result of dual derivative Dual1 to Dual2
  dual_d_1_tgt = add_part!(d, :Var, type=:infer, name=nothing)
  add_part!(d, :Op1, src=proj2_Lie, tgt=dual_d_1_tgt, op1=:d)

  ## Takes interior product of Primal1 and Dual2 to Dual1
  inter_product_2_res = add_part!(d, :Var, type=:infer, name=nothing)
  add_Inter_Prod_2D!(Val{2}, d, dual_d_1_tgt, proj1_Lie, inter_product_2_res)

  ## Takes interior product of Primal1 and Dual1 to Dual0
  inter_product_1_res = add_part!(d, :Var, type=:infer, name=nothing)
  add_Inter_Prod_2D!(Val{1}, d, proj2_Lie, proj1_Lie, inter_product_1_res)

  ## Outputs result of dual derivative Dual0 to Dual1
  dual_d_0_tgt = add_part!(d, :Var, type=:infer, name=nothing)
  add_part!(d, :Op1, src=inter_product_1_res, tgt=dual_d_0_tgt, op1=:d)

  ## Outputs sum of both dual_d_0 and inter_product_2
  summation_tgt = add_part!(d, :Σ, sum=res_Lie)

  add_part!(d, :Summand, summand=inter_product_2_res, summation=summation_tgt)
  add_part!(d, :Summand, summand=dual_d_0_tgt, summation=summation

[lukem12345]

This PR is low-priority, because it is a Developer Experience PR, and would require an unknown amount of developer time to resolve issues relating to segfaults when using Decapode ACSets in source code.