339 lines
12 KiB
Idris
339 lines
12 KiB
Idris
module Quox.Syntax.Term.Reduce
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import Quox.Syntax.Term.Base
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import Quox.Syntax.Term.Subst
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%default total
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mutual
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public export
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data NotCloT : Term {} -> Type where
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NCTYPE : NotCloT $ TYPE _
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NCPi : NotCloT $ Pi {}
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NCLam : NotCloT $ Lam {}
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NCEq : NotCloT $ Eq {}
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NCDLam : NotCloT $ DLam {}
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NCE : NotCloE e -> NotCloT $ E e
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public export
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data NotCloE : Elim {} -> Type where
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NCF : NotCloE $ F _
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NCB : NotCloE $ B _
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NCApp : NotCloE $ _ :@ _
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NCDApp : NotCloE $ _ :% _
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NCAnn : NotCloE $ _ :# _
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mutual
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export
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notCloT : (t : Term {}) -> Dec (NotCloT t)
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notCloT (TYPE _) = Yes NCTYPE
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notCloT (Pi {}) = Yes NCPi
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notCloT (Lam {}) = Yes NCLam
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notCloT (Eq {}) = Yes NCEq
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notCloT (DLam {}) = Yes NCDLam
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notCloT (E e) = case notCloE e of
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Yes nc => Yes $ NCE nc
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No c => No $ \case NCE nc => c nc
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notCloT (CloT {}) = No $ \case _ impossible
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notCloT (DCloT {}) = No $ \case _ impossible
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export
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notCloE : (e : Elim {}) -> Dec (NotCloE e)
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notCloE (F _) = Yes NCF
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notCloE (B _) = Yes NCB
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notCloE (_ :@ _) = Yes NCApp
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notCloE (_ :% _) = Yes NCDApp
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notCloE (_ :# _) = Yes NCAnn
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notCloE (CloE {}) = No $ \case _ impossible
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notCloE (DCloE {}) = No $ \case _ impossible
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||| a term which is not a top level closure
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public export
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NonCloTerm : Type -> Nat -> Nat -> Type
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NonCloTerm q d n = Subset (Term q d n) NotCloT
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||| an elimination which is not a top level closure
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public export
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NonCloElim : Type -> Nat -> Nat -> Type
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NonCloElim q d n = Subset (Elim q d n) NotCloE
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public export %inline
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ncloT : (t : Term q d n) -> (0 _ : NotCloT t) => NonCloTerm q d n
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ncloT t @{p} = Element t p
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public export %inline
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ncloE : (e : Elim q d n) -> (0 _ : NotCloE e) => NonCloElim q d n
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ncloE e @{p} = Element e p
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mutual
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||| if the input term has any top-level closures, push them under one layer of
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||| syntax
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export %inline
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pushSubstsT : Term q d n -> NonCloTerm q d n
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pushSubstsT s = pushSubstsTWith id id s
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||| if the input elimination has any top-level closures, push them under one
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||| layer of syntax
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export %inline
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pushSubstsE : Elim q d n -> NonCloElim q d n
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pushSubstsE e = pushSubstsEWith id id e
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export
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pushSubstsTWith : DSubst dfrom dto -> TSubst q dto from to ->
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Term q dfrom from -> NonCloTerm q dto to
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pushSubstsTWith th ph (TYPE l) =
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ncloT $ TYPE l
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pushSubstsTWith th ph (Pi qty x a body) =
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ncloT $ Pi qty x (subs a th ph) (subs body th ph)
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pushSubstsTWith th ph (Lam x body) =
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ncloT $ Lam x $ subs body th ph
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pushSubstsTWith th ph (Eq i ty l r) =
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ncloT $ Eq i (subs ty th ph) (subs l th ph) (subs r th ph)
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pushSubstsTWith th ph (DLam i body) =
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ncloT $ DLam i $ subs body th ph
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pushSubstsTWith th ph (E e) =
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let Element e nc = pushSubstsEWith th ph e in ncloT $ E e
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pushSubstsTWith th ph (CloT s ps) =
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pushSubstsTWith th (comp th ps ph) s
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pushSubstsTWith th ph (DCloT s ps) =
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pushSubstsTWith (ps . th) ph s
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export
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pushSubstsEWith : DSubst dfrom dto -> TSubst q dto from to ->
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Elim q dfrom from -> NonCloElim q dto to
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pushSubstsEWith th ph (F x) =
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ncloE $ F x
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pushSubstsEWith th ph (B i) =
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let res = ph !! i in
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case notCloE res of
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Yes _ => ncloE res
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No _ => assert_total pushSubstsE res
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pushSubstsEWith th ph (f :@ s) =
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ncloE $ subs f th ph :@ subs s th ph
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pushSubstsEWith th ph (f :% d) =
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ncloE $ subs f th ph :% (d // th)
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pushSubstsEWith th ph (s :# a) =
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ncloE $ subs s th ph :# subs a th ph
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pushSubstsEWith th ph (CloE e ps) =
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pushSubstsEWith th (comp th ps ph) e
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pushSubstsEWith th ph (DCloE e ps) =
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pushSubstsEWith (ps . th) ph e
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parameters (th : DSubst dfrom dto) (ph : TSubst q dto from to)
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public export %inline
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pushSubstsTWith' : Term q dfrom from -> Term q dto to
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pushSubstsTWith' s = (pushSubstsTWith th ph s).fst
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public export %inline
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pushSubstsEWith' : Elim q dfrom from -> Elim q dto to
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pushSubstsEWith' e = (pushSubstsEWith th ph e).fst
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public export %inline
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weakT : Term q d n -> Term q d (S n)
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weakT t = t //. shift 1
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public export %inline
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weakE : Elim q d n -> Elim q d (S n)
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weakE t = t //. shift 1
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mutual
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public export
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data IsRedexT : Term q 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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IsERedex : IsRedexE e -> IsRedexT $ E e
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public export
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data IsRedexE : Elim q d n -> Type where
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IsUpsilonE : IsRedexE $ E _ :# _
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IsBetaLam : IsRedexE $ (Lam {} :# Pi {}) :@ _
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IsBetaDLam : IsRedexE $ (DLam {} :# Eq {}) :% _
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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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NotRedexT : Term q d n -> Type
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NotRedexT = Not . IsRedexT
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public export %inline
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NotRedexE : Elim q d n -> Type
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NotRedexE = Not . IsRedexE
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mutual
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-- [todo] PLEASE replace these with macros omfg
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export
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isRedexT : (t : Term {}) -> Dec (IsRedexT t)
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isRedexT (E (tm :# ty)) = Yes IsUpsilonT
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isRedexT (CloT {}) = Yes IsCloT
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isRedexT (DCloT {}) = Yes IsDCloT
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isRedexT (E (CloE {})) = Yes $ IsERedex IsCloE
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isRedexT (E (DCloE {})) = Yes $ IsERedex IsDCloE
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isRedexT (E e@(_ :@ _)) with (isRedexE e)
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_ | Yes yes = Yes $ IsERedex yes
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_ | No no = No $ \case IsERedex p => no p
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isRedexT (E e@(_ :% _)) with (isRedexE e)
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_ | Yes yes = Yes $ IsERedex yes
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_ | No no = No $ \case IsERedex p => no p
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isRedexT (TYPE {}) = No $ \case _ impossible
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isRedexT (Pi {}) = No $ \case _ impossible
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isRedexT (Lam {}) = No $ \case _ impossible
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isRedexT (Eq {}) = No $ \case _ impossible
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isRedexT (DLam {}) = No $ \case _ impossible
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isRedexT (E (F _)) = No $ \case IsERedex _ impossible
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isRedexT (E (B _)) = No $ \case IsERedex _ impossible
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export
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isRedexE : (e : Elim {}) -> 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 ((DLam {} :# Eq {}) :% _) = Yes IsBetaDLam
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isRedexE (CloE {}) = Yes IsCloE
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isRedexE (DCloE {}) = Yes IsDCloE
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isRedexE (F x) = No $ \case _ impossible
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isRedexE (B i) = No $ \case _ impossible
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isRedexE (F _ :@ _) = No $ \case _ impossible
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isRedexE (B _ :@ _) = No $ \case _ impossible
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isRedexE (_ :@ _ :@ _) = No $ \case _ impossible
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isRedexE (_ :% _ :@ _) = No $ \case _ impossible
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isRedexE (CloE {} :@ _) = No $ \case _ impossible
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isRedexE (DCloE {} :@ _) = No $ \case _ impossible
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isRedexE ((TYPE _ :# _) :@ _) = No $ \case _ impossible
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isRedexE ((Pi {} :# _) :@ _) = No $ \case _ impossible
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isRedexE ((Eq {} :# _) :@ _) = No $ \case _ impossible
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isRedexE ((DLam {} :# _) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# TYPE _) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# Lam {}) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# Eq {}) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# DLam {}) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# E _) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# CloT {}) :@ _) = No $ \case _ impossible
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isRedexE ((Lam {} :# DCloT {}) :@ _) = No $ \case _ impossible
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isRedexE ((E _ :# _) :@ _) = No $ \case _ impossible
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isRedexE ((CloT {} :# _) :@ _) = No $ \case _ impossible
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isRedexE ((DCloT {} :# _) :@ _) = No $ \case _ impossible
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isRedexE ((TYPE _ :# _) :% _) = No $ \case _ impossible
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isRedexE ((Pi {} :# _) :% _) = No $ \case _ impossible
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isRedexE ((Eq {} :# _) :% _) = No $ \case _ impossible
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isRedexE ((Lam {} :# _) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# TYPE _) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# Pi {}) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# Lam {}) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# DLam {}) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# E _) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# CloT {}) :% _) = No $ \case _ impossible
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isRedexE ((DLam {} :# DCloT {}) :% _) = No $ \case _ impossible
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isRedexE ((E _ :# _) :% _) = No $ \case _ impossible
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isRedexE ((CloT {} :# _) :% _) = No $ \case _ impossible
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isRedexE ((DCloT {} :# _) :% _) = No $ \case _ impossible
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isRedexE (F _ :% _) = No $ \case _ impossible
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isRedexE (B _ :% _) = No $ \case _ impossible
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isRedexE (_ :@ _ :% _) = No $ \case _ impossible
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isRedexE (_ :% _ :% _) = No $ \case _ impossible
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isRedexE (CloE {} :% _) = No $ \case _ impossible
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isRedexE (DCloE {} :% _) = No $ \case _ impossible
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isRedexE (TYPE _ :# _) = No $ \case _ impossible
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isRedexE (Pi {} :# _) = No $ \case _ impossible
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isRedexE (Lam {} :# _) = No $ \case _ impossible
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isRedexE (Eq {} :# _) = No $ \case _ impossible
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isRedexE (DLam {} :# _) = No $ \case _ impossible
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isRedexE (CloT {} :# _) = No $ \case _ impossible
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isRedexE (DCloT {} :# _) = No $ \case _ impossible
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public export %inline
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RedexTerm : Type -> Nat -> Nat -> Type
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RedexTerm q d n = Subset (Term q d n) IsRedexT
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public export %inline
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NonRedexTerm : Type -> Nat -> Nat -> Type
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NonRedexTerm q d n = Subset (Term q d n) NotRedexT
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public export %inline
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RedexElim : Type -> Nat -> Nat -> Type
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RedexElim q d n = Subset (Elim q d n) IsRedexE
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public export %inline
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NonRedexElim : Type -> Nat -> Nat -> Type
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NonRedexElim q d n = Subset (Elim q 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 q d n) -> (body : ScopeTerm q d n) -> Term q d n
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substScope arg argTy body = sub1 body (arg :# argTy)
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mutual
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export %inline
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stepT' : (s : Term q d n) -> IsRedexT s -> Term q 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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stepT' (E e) (IsERedex p) = E $ stepE' e p
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export %inline
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stepE' : (e : Elim q d n) -> IsRedexE e -> Elim q 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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let s = s :# arg in sub1 body s :# sub1 res s
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stepE' ((DLam {body, _} :# Eq {ty, l, r, _}) :% dim) IsBetaDLam =
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case dim of
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K Zero => l :# ty.zero
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K One => r :# ty.one
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B _ => dsub1 body dim :# dsub1 ty dim
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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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stepT : (s : Term q d n) -> Either (NotRedexT s) (Term q 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 q d n) -> Either (NotRedexE e) (Elim q 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 q d n -> NonRedexTerm q d n
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whnfT s = case stepT s of Right s' => whnfT s'; Left done => Element s done
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export covering
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whnfE : Elim q d n -> NonRedexElim q d n
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whnfE e = case stepE e of Right e' => whnfE e'; Left done => Element e done
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export
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notRedexNotCloE : (e : Elim {}) -> NotRedexE e -> NotCloE e
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notRedexNotCloE (F x) f = NCF
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notRedexNotCloE (B i) f = NCB
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notRedexNotCloE (fun :@ arg) f = NCApp
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notRedexNotCloE (fun :% arg) f = NCDApp
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notRedexNotCloE (tm :# ty) f = NCAnn
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notRedexNotCloE (CloE el th) f = absurd $ f IsCloE
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notRedexNotCloE (DCloE el th) f = absurd $ f IsDCloE
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export
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notRedexNotCloT : (t : Term {}) -> NotRedexT t -> NotCloT t
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notRedexNotCloT (TYPE _) _ = NCTYPE
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notRedexNotCloT (Pi {}) _ = NCPi
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notRedexNotCloT (Lam {}) _ = NCLam
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notRedexNotCloT (Eq {}) _ = NCEq
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notRedexNotCloT (DLam {}) _ = NCDLam
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notRedexNotCloT (E e) f = NCE $ notRedexNotCloE e $ f . IsERedex
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notRedexNotCloT (CloT {}) f = absurd $ f IsCloT
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notRedexNotCloT (DCloT {}) f = absurd $ f IsDCloT
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export
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toNotCloE : NonRedexElim q d n -> NonCloElim q d n
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toNotCloE (Element e prf) = Element e $ notRedexNotCloE e prf
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export
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toNotCloT : NonRedexTerm q d n -> NonCloTerm q d n
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toNotCloT (Element t prf) = Element t $ notRedexNotCloT t prf
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