Q.S.T.Reduce ⇒ Q.Reduce and make it use Definition directly
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module Quox.Syntax.Term.Reduce
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import Quox.No
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import Quox.Syntax.Term.Base
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import Quox.Syntax.Term.Subst
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import Data.Vect
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import Data.Maybe
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%default total
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namespace Elim
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public export %inline
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isClo : Elim {} -> Bool
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isClo (CloE {}) = True
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isClo (DCloE {}) = True
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isClo _ = False
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public export
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0 NotClo : Pred $ Elim {}
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NotClo = No . isClo
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namespace Term
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public export %inline
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isClo : Term {} -> Bool
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isClo (CloT {}) = True
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isClo (DCloT {}) = True
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isClo (E e) = isClo e
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isClo _ = False
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public export
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0 NotClo : Pred $ Term {}
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NotClo = No . isClo
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public export
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0 NonCloElim : TermLike
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NonCloElim q d n = Subset (Elim q d n) NotClo
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public export
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0 NonCloTerm : TermLike
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NonCloTerm q d n = Subset (Term q d n) NotClo
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public export %inline
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ncloT : (t : Term q d n) -> (0 nc : NotClo t) => NonCloTerm q d n
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ncloT t = Element t nc
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public export %inline
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ncloE : (e : Elim q d n) -> (0 nc : NotClo e) => NonCloElim q d n
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ncloE e = Element e nc
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mutual
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namespace Term
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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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pushSubsts : Term q d n -> NonCloTerm q d n
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pushSubsts s = pushSubstsWith id id s
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export
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pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to ->
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Term q dfrom from -> NonCloTerm q dto to
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pushSubstsWith th ph (TYPE l) =
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ncloT $ TYPE l
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pushSubstsWith 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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pushSubstsWith th ph (Lam x body) =
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ncloT $ Lam x $ subs body th ph
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pushSubstsWith th ph (Sig x a b) =
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ncloT $ Sig x (subs a th ph) (subs b th ph)
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pushSubstsWith th ph (Pair s t) =
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ncloT $ Pair (subs s th ph) (subs t th ph)
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pushSubstsWith 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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pushSubstsWith th ph (DLam i body) =
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ncloT $ DLam i $ subs body th ph
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pushSubstsWith th ph (E e) =
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let Element e nc = pushSubstsWith th ph e in ncloT $ E e
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pushSubstsWith th ph (CloT s ps) =
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pushSubstsWith th (comp th ps ph) s
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pushSubstsWith th ph (DCloT s ps) =
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pushSubstsWith (ps . th) ph s
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namespace Elim
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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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pushSubsts : Elim q d n -> NonCloElim q d n
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pushSubsts e = pushSubstsWith id id e
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export
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pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to ->
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Elim q dfrom from -> NonCloElim q dto to
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pushSubstsWith th ph (F x) =
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ncloE $ F x
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pushSubstsWith th ph (B i) =
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let res = ph !! i in
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case nchoose $ isClo res of
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Left yes => assert_total pushSubsts res
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Right no => Element res no
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pushSubstsWith th ph (f :@ s) =
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ncloE $ subs f th ph :@ subs s th ph
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pushSubstsWith th ph (CasePair pi p x r y z b) =
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ncloE $ CasePair pi (subs p th ph) x (subs r th ph) y z (subs b th ph)
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pushSubstsWith th ph (f :% d) =
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ncloE $ subs f th ph :% (d // th)
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pushSubstsWith th ph (s :# a) =
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ncloE $ subs s th ph :# subs a th ph
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pushSubstsWith th ph (CloE e ps) =
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pushSubstsWith th (comp th ps ph) e
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pushSubstsWith th ph (DCloE e ps) =
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pushSubstsWith (ps . th) ph e
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parameters (th : DSubst dfrom dto) (ph : TSubst q dto from to)
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namespace Term
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public export %inline
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pushSubstsWith' : Term q dfrom from -> Term q dto to
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pushSubstsWith' s = (pushSubstsWith th ph s).fst
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namespace Elim
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public export %inline
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pushSubstsWith' : Elim q dfrom from -> Elim q dto to
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pushSubstsWith' e = (pushSubstsWith th ph e).fst
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public export 0
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Lookup : TermLike
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Lookup q d n = Name -> Maybe $ Elim q d n
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public export %inline
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isLamHead : Elim {} -> Bool
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isLamHead (Lam {} :# Pi {}) = True
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isLamHead _ = False
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public export %inline
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isDLamHead : Elim {} -> Bool
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isDLamHead (DLam {} :# Eq {}) = True
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isDLamHead _ = False
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public export %inline
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isPairHead : Elim {} -> Bool
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isPairHead (Pair {} :# Sig {}) = True
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isPairHead _ = False
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public export %inline
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isE : Term {} -> Bool
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isE (E _) = True
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isE _ = False
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public export %inline
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isAnn : Elim {} -> Bool
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isAnn (_ :# _) = True
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isAnn _ = False
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parameters (g : Lookup q d n)
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mutual
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namespace Elim
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public export
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isRedex : Elim q d n -> Bool
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isRedex (F x) = isJust $ g x
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isRedex (B _) = False
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isRedex (f :@ _) = isRedex f || isLamHead f
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isRedex (CasePair {pair, _}) = isRedex pair || isPairHead pair
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isRedex (f :% _) = isRedex f || isDLamHead f
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isRedex (t :# a) = isE t || isRedex t || isRedex a
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isRedex (CloE {}) = True
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isRedex (DCloE {}) = True
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namespace Term
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public export
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isRedex : Term q d n -> Bool
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isRedex (CloT {}) = True
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isRedex (DCloT {}) = True
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isRedex (E e) = isAnn e || isRedex e
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isRedex _ = False
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namespace Elim
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public export
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0 IsRedex, NotRedex : Pred $ Elim q d n
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IsRedex = So . isRedex
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NotRedex = No . isRedex
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namespace Term
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public export
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0 IsRedex, NotRedex : Pred $ Term q d n
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IsRedex = So . isRedex
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NotRedex = No . isRedex
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public export
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0 NonRedexElim, NonRedexTerm : (q, d, n : _) -> Lookup q d n -> Type
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NonRedexElim q d n g = Subset (Elim q d n) (NotRedex g)
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NonRedexTerm q d n g = Subset (Term q d n) (NotRedex g)
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parameters (g : Lookup q d n)
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mutual
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namespace Elim
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export covering
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whnf : Elim q d n -> NonRedexElim q d n g
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whnf (F x) with (g x) proof eq
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_ | Just y = whnf y
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_ | Nothing = Element (F x) $ rewrite eq in Ah
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whnf (B i) = Element (B i) Ah
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whnf (f :@ s) =
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let Element f fnf = whnf f in
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case nchoose $ isLamHead f of
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Left _ =>
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let Lam {body, _} :# Pi {arg, res, _} = f
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s = s :# arg
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in
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whnf $ sub1 body s :# sub1 res s
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Right nlh => Element (f :@ s) $ fnf `orNo` nlh
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whnf (CasePair pi pair r ret x y body) =
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let Element pair pairnf = whnf pair in
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case nchoose $ isPairHead pair of
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Left _ =>
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let Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} = pair
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fst = fst :# tfst
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snd = snd :# sub1 tsnd fst
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in
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whnf $ subN body [fst, snd] :# sub1 ret pair
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Right np =>
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Element (CasePair pi pair r ret x y body) $ pairnf `orNo` np
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whnf (f :% p) =
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let Element f fnf = whnf f in
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case nchoose $ isDLamHead f of
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Left _ =>
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let DLam {body, _} :# Eq {ty, l, r, _} = f
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body = endsOr l r (dsub1 body p) p
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in
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whnf $ body :# dsub1 ty p
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Right ndlh =>
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Element (f :% p) $ fnf `orNo` ndlh
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whnf (s :# a) =
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let Element s snf = whnf s in
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case nchoose $ isE s of
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Left _ => let E e = s in Element e $ noOr2 snf
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Right ne =>
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let Element a anf = whnf a in
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Element (s :# a) $ ne `orNo` snf `orNo` anf
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whnf (CloE el th) = whnf $ pushSubstsWith' id th el
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whnf (DCloE el th) = whnf $ pushSubstsWith' th id el
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namespace Term
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export covering
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whnf : Term q d n -> NonRedexTerm q d n g
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whnf t@(TYPE {}) = Element t Ah
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whnf t@(Pi {}) = Element t Ah
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whnf t@(Lam {}) = Element t Ah
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whnf t@(Sig {}) = Element t Ah
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whnf t@(Pair {}) = Element t Ah
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whnf t@(Eq {}) = Element t Ah
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whnf t@(DLam {}) = Element t Ah
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whnf (E e) =
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let Element e enf = whnf e in
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case nchoose $ isAnn e of
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Left _ => let tm :# _ = e in Element tm $ noOr1 $ noOr2 enf
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Right na => Element (E e) $ na `orNo` enf
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whnf (CloT tm th) = whnf $ pushSubstsWith' id th tm
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whnf (DCloT tm th) = whnf $ pushSubstsWith' th id tm
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