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25 lines
558 B
Idris
25 lines
558 B
Idris
module Data.Rel.Complement
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import Data.Rel
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import Data.Fun
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import Data.Fun.Extra
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import Data.HVect
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%default total
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||| The logical complement of a relation.
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public export
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complement : {ts : Vect n Type} -> (p : Rel ts) -> Rel ts
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complement = chain Not
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||| The negation of a relation for some elements
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||| is equal to the complement of the relation.
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public export
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notToComplement :
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{0 ts : Vect n Type}
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-> (p : Rel ts)
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-> (elems : HVect ts)
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-> Not (uncurry p elems) = uncurry (complement {ts = ts} p) elems
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notToComplement p = chainUncurry p Not
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