lawz-0.0.1: Common mathematical laws.

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LanguageHaskell2010

Test.Function.Invertible

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adjoint_on :: Rel r -> Rel s -> (s -> r) -> (r -> s) -> s -> r -> Bool Source #

\( \forall a: f a \# b \Leftrightarrow a \# g b \)

For example, a Galois connection is defined by adjoint_on (<=).

invertible :: Eq r => (r -> s) -> (s -> r) -> r -> Bool Source #

\( \forall a: f (g a) \equiv a \)

invertible_on :: Rel s -> (s -> r) -> (r -> s) -> s -> Bool Source #

\( \forall a: f (g a) \doteq a \)