Should 1^x == 1?

[pagnani]

Following the discussion on Discourse on the same issue: do we want to enforce a rule to make 1^x -> 1?

There is a concern for x = ±∞ for which, I believe, the substitution although mathematically disputable should be ok.

As variables are strongly typed, a concern is what happens with one(ComplexF*)? However, it seems that

SymbolicUtils._isone(one(ComplexF64)) is true.

BTW, I tried to add toPOW_RULES something like

@rule(^(~x::_isone, ~z) => 1)

but it does not like it (stacktrace below). I do not understand how one can add more rules ....

ERROR: LoadError: ArgumentError: number of columns of each array must match (got (1, 1, 2, 1, 2, 1, 2, 1))
Stacktrace:
  [1] _typed_vcat(#unused#::Type{Metatheory.Rules.AbstractRule}, A::NTuple{8, Matrix{Metatheory.Rules.AbstractRule}})
    @ Base ./abstractarray.jl:1605
  [2] typed_vcat(::Type{Metatheory.Rules.AbstractRule}, ::Matrix{Metatheory.Rules.AbstractRule}, ::Matrix{Metatheory.Rules.AbstractRule}, ::Matrix{Metatheory.Rules.AbstractRule}, ::Vararg{Matrix{Metatheory.Rules.AbstractRule}})
    @ Base ./abstractarray.jl:1619
  [3] typed_hvcat(::Type{Metatheory.Rules.AbstractRule}, ::NTuple{8, Int64}, ::Metatheory.Rules.DynamicRule, ::Vararg{Any})
    @ Base ./abstractarray.jl:2041
  [4] hvcat(::NTuple{8, Int64}, ::Metatheory.Rules.DynamicRule, ::Vararg{Any})
    @ Base ./abstractarray.jl:2020
  [5] top-level scope
    @ ~/FORKS/SymbolicUtils.jl/src/simplify_rules.jl:4
  [6] include(mod::Module, _path::String)
    @ Base ./Base.jl:418
  [7] include(x::String)
    @ SymbolicUtils ~/FORKS/SymbolicUtils.jl/src/SymbolicUtils.jl:4
  [8] top-level scope
    @ ~/FORKS/SymbolicUtils.jl/src/SymbolicUtils.jl:55
  [9] include
    @ ./Base.jl:418 [inlined]
 [10] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt64}}, source::Nothing)
    @ Base ./loading.jl:1318
 [11] top-level scope
    @ none:1
 [12] eval
    @ ./boot.jl:373 [inlined]
 [13] eval(x::Expr)
    @ Base.MainInclude ./client.jl:453
 [14] top-level scope
    @ none:1
in expression starting at /Users/pagnani/FORKS/SymbolicUtils.jl/src/simplify_rules.jl:3
in expression starting at /Users/pagnani/FORKS/SymbolicUtils.jl/src/SymbolicUtils.jl:1
ERROR: Failed to precompile SymbolicUtils [d1185830-fcd6-423d-90d6-eec64667417b] to /Users/pagnani/.julia/compiled/v1.7/SymbolicUtils/jl_StTnCZ.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] compilecache(pkg::Base.PkgId, path::String, internal_stderr::IO, internal_stdout::IO, ignore_loaded_modules::Bool)
    @ Base ./loading.jl:1466
  [3] compilecache(pkg::Base.PkgId, path::String)
    @ Base ./loading.jl:1410
  [4] _require(pkg::Base.PkgId)
    @ Base ./loading.jl:1120
  [5] require(uuidkey::Base.PkgId)
    @ Base ./loading.jl:1013
  [6] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:997
  [7] eval
    @ ./boot.jl:373 [inlined]
  [8] eval
    @ ./Base.jl:68 [inlined]
  [9] repleval(m::Module, code::Expr, #unused#::String)
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.5.11/scripts/packages/VSCodeServer/src/repl.jl:157
 [10] (::VSCodeServer.var"#71#73"{Module, Expr, REPL.LineEditREPL, REPL.LineEdit.Prompt})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.5.11/scripts/packages/VSCodeServer/src/repl.jl:123
 [11] with_logstate(f::Function, logstate::Any)
    @ Base.CoreLogging ./logging.jl:511
 [12] with_logger
    @ ./logging.jl:623 [inlined]
 [13] (::VSCodeServer.var"#70#72"{Module, Expr, REPL.LineEditREPL, REPL.LineEdit.Prompt})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.5.11/scripts/packages/VSCodeServer/src/repl.jl:124
 [14] #invokelatest#2
    @ ./essentials.jl:716 [inlined]
 [15] invokelatest(::Any)
    @ Base ./essentials.jl:714
 [16] macro expansion
    @ ~/.vscode/extensions/julialang.language-julia-1.5.11/scripts/packages/VSCodeServer/src/eval.jl:34 [inlined]
 [17] (::VSCodeServer.var"#55#56")()
    @ VSCodeServer ./task.jl:423