23 lines
597 B
Haskell
23 lines
597 B
Haskell
{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}
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module Coalgebra where
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import Control.Monad
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-- Definitions for (co)algebras
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class Functor f => Algebra f m where
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phi :: f m -> m
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class Functor f => Coalgebra f m where
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psi :: m -> f m
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-- Fixpoint, ie f (Mu f) = Mu f
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-- unfortunatly we need a data constructor
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data Mu f = In (f (Mu f))
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-- The fixpoint is both a algebra and coalgebra,
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-- because there is an arrow id: X -> X = FX, if X is a fixpoint
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instance Functor f => Algebra f (Mu f) where
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phi = In
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instance Functor f => Coalgebra f (Mu f) where
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psi (In x) = x
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