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set_operations.jl
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struct CombinationSeparator{V, E, F} <: AbstractSeparator
vars::V
ex::E
f::F
end
# TODO: Replace intersection with composition
function ⊓(S1::AbstractSeparator, S2::AbstractSeparator)
vars = S1.vars # assume S1 and S2 have same variables
f = X -> begin
boundary1, inner1, outer1 = S1(X)
boundary2, inner2, outer2 = S2(X)
inner = inner1 ⊓ inner2
outer = outer1 ⊔ outer2
boundary = inner ⊓ outer
return (boundary, inner, outer)
end
ex = (S1.ex) ⊓ (S2.ex)
return CombinationSeparator(vars, ex, f)
end
function ∘(S1::AbstractSeparator, S2::AbstractSeparator)
vars = S1.vars # assume S1 and S2 have same variables
f = X -> begin
boundary1, inner1, outer1 = S1(X)
boundary2, inner2, outer2 = S2(X)
inner = inner1 ⊓ inner2
outer = outer1 ⊔ outer2
boundary = inner ⊓ outer
return (boundary, inner, outer)
end
ex = (S1.ex) ⊓ (S2.ex)
return CombinationSeparator(vars, ex, f)
end
function ⊔(S1::AbstractSeparator, S2::AbstractSeparator)
vars = S1.vars # assume S1 and S2 have same variables
f = X -> begin
boundary1, inner1, outer1 = S1(X)
boundary2, inner2, outer2 = S2(X)
inner = inner1 ⊔ inner2
outer = outer1 ⊓ outer2
boundary = inner ⊓ outer
return (boundary, inner, outer)
end
ex = (S1.ex) ⊔ (S2.ex)
return CombinationSeparator(vars, ex, f)
end
⊓
⊓
function ¬(S::AbstractSeparator)
vars = S.vars # assume S1 and S2 have same variables
f = X -> begin
boundary, inner, outer = S(X)
return (boundary, outer, inner)
end
ex = ¬(S.ex)
return CombinationSeparator(vars, ex, f)
end
Base.:!(S::AbstractSeparator) = ¬(S)
(S::CombinationSeparator)(X) = S.f(X)
Base.setdiff(S1::AbstractSeparator, S2::AbstractSeparator) = S1 ⊓ ¬(S2)
Base.symdiff(S1::AbstractSeparator, S2::AbstractSeparator) = setdiff(S1, S2) ⊔ setdiff(S2, S1)
## TODO: Make separate type
struct CombinationContractor{V, E, F} <: AbstractContractor
vars::V
ex::E
f::F
end
Base.:(∘)(C1::AbstractContractor, C2::AbstractContractor) =
CombinationContractor(C1.vars, C1.ex, X -> C1(C2(X)))
(CC::CombinationContractor)(X) = CC.f(X)