131 lines
4.6 KiB
Idris
131 lines
4.6 KiB
Idris
module Quox.Reduce
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import public Quox.Syntax
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%default total
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public export
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data IsRedexT : Term d n -> Type where
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IsUpsilonT : IsRedexT $ E (_ :# _)
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IsCloT : IsRedexT $ CloT {}
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IsDCloT : IsRedexT $ DCloT {}
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public export %inline
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NotRedexT : Term d n -> Type
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NotRedexT = Not . IsRedexT
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public export
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data IsRedexE : Elim d n -> Type where
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IsUpsilonE : IsRedexE $ E _ :# _
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IsBetaLam : IsRedexE $ (Lam {} :# Pi {}) :@ _
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IsCloE : IsRedexE $ CloE {}
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IsDCloE : IsRedexE $ DCloE {}
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public export %inline
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NotRedexE : Elim d n -> Type
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NotRedexE = Not . IsRedexE
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export %inline
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isRedexT : (t : Term d n) -> Dec (IsRedexT t)
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isRedexT (E (_ :# _)) = Yes IsUpsilonT
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isRedexT (CloT {}) = Yes IsCloT
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isRedexT (DCloT {}) = Yes IsDCloT
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isRedexT (TYPE _) = No $ \x => case x of {}
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isRedexT (Pi {}) = No $ \x => case x of {}
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isRedexT (Lam {}) = No $ \x => case x of {}
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isRedexT (E (F _)) = No $ \x => case x of {}
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isRedexT (E (B _)) = No $ \x => case x of {}
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isRedexT (E (_ :@ _)) = No $ \x => case x of {}
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isRedexT (E (CloE {})) = No $ \x => case x of {}
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isRedexT (E (DCloE {})) = No $ \x => case x of {}
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export %inline
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isRedexE : (e : Elim d n) -> Dec (IsRedexE e)
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isRedexE (E _ :# _) = Yes IsUpsilonE
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isRedexE ((Lam {} :# Pi {}) :@ _) = Yes IsBetaLam
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isRedexE (CloE {}) = Yes IsCloE
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isRedexE (DCloE {}) = Yes IsDCloE
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isRedexE (F x) = No $ \x => case x of {}
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isRedexE (B i) = No $ \x => case x of {}
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isRedexE (F _ :@ _) = No $ \x => case x of {}
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isRedexE (B _ :@ _) = No $ \x => case x of {}
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isRedexE (_ :@ _ :@ _) = No $ \x => case x of {}
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isRedexE ((TYPE _ :# _) :@ _) = No $ \x => case x of {}
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isRedexE ((Pi {} :# _) :@ _) = No $ \x => case x of {}
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isRedexE ((Lam {} :# TYPE _) :@ _) = No $ \x => case x of {}
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isRedexE ((Lam {} :# Lam {}) :@ _) = No $ \x => case x of {}
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isRedexE ((Lam {} :# E _) :@ _) = No $ \x => case x of {}
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isRedexE ((Lam {} :# CloT {}) :@ _) = No $ \x => case x of {}
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isRedexE ((Lam {} :# DCloT {}) :@ _) = No $ \x => case x of {}
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isRedexE ((E _ :# _) :@ _) = No $ \x => case x of {}
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isRedexE ((CloT {} :# _) :@ _) = No $ \x => case x of {}
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isRedexE ((DCloT {} :# _) :@ _) = No $ \x => case x of {}
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isRedexE (CloE {} :@ _) = No $ \x => case x of {}
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isRedexE (DCloE {} :@ _) = No $ \x => case x of {}
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isRedexE (TYPE _ :# _) = No $ \x => case x of {}
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isRedexE (Pi {} :# _) = No $ \x => case x of {}
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isRedexE (Lam {} :# _) = No $ \x => case x of {}
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isRedexE (CloT {} :# _) = No $ \x => case x of {}
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isRedexE (DCloT {} :# _) = No $ \x => case x of {}
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public export %inline
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RedexTerm : Nat -> Nat -> Type
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RedexTerm d n = Subset (Term d n) IsRedexT
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public export %inline
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NonRedexTerm : Nat -> Nat -> Type
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NonRedexTerm d n = Subset (Term d n) NotRedexT
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public export %inline
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RedexElim : Nat -> Nat -> Type
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RedexElim d n = Subset (Elim d n) IsRedexE
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public export %inline
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NonRedexElim : Nat -> Nat -> Type
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NonRedexElim d n = Subset (Elim d n) NotRedexE
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||| substitute a term with annotation for the bound variable of a `ScopeTerm`
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export %inline
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substScope : (arg, argTy : Term d n) -> (body : ScopeTerm d n) -> Term d n
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substScope arg argTy (TUsed body) = body // one (arg :# argTy)
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substScope arg argTy (TUnused body) = body
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export %inline
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stepT' : (s : Term d n) -> IsRedexT s -> Term d n
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stepT' (E (s :# _)) IsUpsilonT = s
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stepT' (CloT s th) IsCloT = pushSubstsTWith' id th s
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stepT' (DCloT s th) IsDCloT = pushSubstsTWith' th id s
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export %inline
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stepT : (s : Term d n) -> Either (NotRedexT s) (Term d n)
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stepT s = case isRedexT s of Yes y => Right $ stepT' s y; No n => Left n
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export %inline
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stepE' : (e : Elim d n) -> IsRedexE e -> Elim d n
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stepE' (E e :# _) IsUpsilonE = e
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stepE' ((Lam {body, _} :# Pi {arg, res, _}) :@ s) IsBetaLam =
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substScope s arg body :# substScope s arg res
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stepE' (CloE e th) IsCloE = pushSubstsEWith' id th e
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stepE' (DCloE e th) IsDCloE = pushSubstsEWith' th id e
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export %inline
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stepE : (e : Elim d n) -> Either (NotRedexE e) (Elim d n)
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stepE e = case isRedexE e of Yes y => Right $ stepE' e y; No n => Left n
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export covering
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whnfT : Term d n -> NonRedexTerm d n
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whnfT s = case stepT s of
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Right s' => whnfT s'
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Left done => Element s done
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export covering
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whnfE : Elim d n -> NonRedexElim d n
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whnfE e = case stepE e of
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Right e' => whnfE e'
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Left done => Element e done
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