31 lines
1.0 KiB
Haskell
31 lines
1.0 KiB
Haskell
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module LambdaCalculus.Representation where
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import Data.Functor.Foldable (cata)
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import Data.HashSet (HashSet, singleton, union, delete)
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import LambdaCalculus.Representation.Standard
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-- | `expr` is a representation of a /closed/ lambda calculus expression.
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class IsExpr expr where
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-- | Convert an expression to the standard representation.
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toStandard :: expr -> Expression
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-- | Convert an expression from the standard representation.
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fromStandard :: Expression -> expr
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-- | Convert an expression from one representation to another.
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convert :: IsExpr repr => expr -> repr
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convert = fromStandard . toStandard
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-- | Retrieve the free variables in an expression.
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freeVariables :: expr -> HashSet String
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freeVariables = freeVariables . toStandard
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instance IsExpr Expression where
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toStandard = id
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fromStandard = id
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convert = fromStandard
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freeVariables = cata \case
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VariableF name -> singleton name
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AbstractionF name body -> name `delete` body
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ApplicationF fe xe -> fe `union` xe
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