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add converse υ rule for elim 

i think this just means type preservation is modulo subtyping. which is
probably fine....?
This commit is contained in:
rhiannon morris 2022-04-27 20:04:29 +02:00
parent 81e1f331e0
commit 6bffd6a11c
1 changed files with 18 additions and 11 deletions
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29
src/Quox/Reduce.idr
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@ -5,9 +5,9 @@ import public Quox.Syntax
public export
data IsRedexT : Term d n -> Type where
IsUpsilon : IsRedexT $ E (_ :# _)
IsCloT : IsRedexT $ CloT {}
IsDCloT : IsRedexT $ DCloT {}
IsUpsilonT : IsRedexT $ E (_ :# _)
IsCloT : IsRedexT $ CloT {}
IsDCloT : IsRedexT $ DCloT {}
public export %inline
NotRedexT : Term d n -> Type
@ -15,9 +15,10 @@ NotRedexT = Not . IsRedexT
public export
data IsRedexE : Elim d n -> Type where
IsBetaLam : IsRedexE $ (Lam {} :# Pi {}) :@ _
IsCloE : IsRedexE $ CloE {}
IsDCloE : IsRedexE $ DCloE {}
IsUpsilonE : IsRedexE $ E _ :# _
IsBetaLam : IsRedexE $ (Lam {} :# Pi {}) :@ _
IsCloE : IsRedexE $ CloE {}
IsDCloE : IsRedexE $ DCloE {}
public export %inline
NotRedexE : Elim d n -> Type
@ -26,7 +27,7 @@ NotRedexE = Not . IsRedexE
export %inline
isRedexT : (t : Term d n) -> Dec (IsRedexT t)
isRedexT (E (_ :# _)) = Yes IsUpsilon
isRedexT (E (_ :# _)) = Yes IsUpsilonT
isRedexT (CloT {}) = Yes IsCloT
isRedexT (DCloT {}) = Yes IsDCloT
isRedexT (TYPE _) = No $ \x => case x of {}
@ -40,6 +41,7 @@ isRedexT (E (DCloE {})) = No $ \x => case x of {}
export %inline
isRedexE : (e : Elim d n) -> Dec (IsRedexE e)
isRedexE (E _ :# _) = Yes IsUpsilonE
isRedexE ((Lam {} :# Pi {}) :@ _) = Yes IsBetaLam
isRedexE (CloE {}) = Yes IsCloE
isRedexE (DCloE {}) = Yes IsDCloE
@ -60,7 +62,11 @@ isRedexE ((CloT {} :# _) :@ _) = No $ \x => case x of {}
isRedexE ((DCloT {} :# _) :@ _) = No $ \x => case x of {}
isRedexE (CloE {} :@ _) = No $ \x => case x of {}
isRedexE (DCloE {} :@ _) = No $ \x => case x of {}
isRedexE (_ :# _) = No $ \x => case x of {}
isRedexE (TYPE _ :# _) = No $ \x => case x of {}
isRedexE (Pi {} :# _) = No $ \x => case x of {}
isRedexE (Lam {} :# _) = No $ \x => case x of {}
isRedexE (CloT {} :# _) = No $ \x => case x of {}
isRedexE (DCloT {} :# _) = No $ \x => case x of {}
public export %inline
@ -89,9 +95,9 @@ substScope arg argTy (TUnused body) = body
export %inline
stepT' : (s : Term d n) -> IsRedexT s -> Term d n
stepT' (E (s :# _)) IsUpsilon = s
stepT' (CloT s th) IsCloT = pushSubstsTWith' id th s
stepT' (DCloT s th) IsDCloT = pushSubstsTWith' th id s
stepT' (E (s :# _)) IsUpsilonT = s
stepT' (CloT s th) IsCloT = pushSubstsTWith' id th s
stepT' (DCloT s th) IsDCloT = pushSubstsTWith' th id s
export %inline
stepT : (s : Term d n) -> Either (NotRedexT s) (Term d n)
@ -99,6 +105,7 @@ stepT s = case isRedexT s of Yes y => Right $ stepT' s y; No n => Left n
export %inline
stepE' : (e : Elim d n) -> IsRedexE e -> Elim d n
stepE' (E e :# _) IsUpsilonE = e
stepE' ((Lam {body, _} :# Pi {arg, res, _}) :@ s) IsBetaLam =
substScope s arg body :# substScope s arg res
stepE' (CloE e th) IsCloE = pushSubstsEWith' id th e