257 lines
7.7 KiB
Idris
257 lines
7.7 KiB
Idris
module Quox.Reduce
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import Quox.No
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import Quox.Syntax
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import Quox.Definition
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import Data.Vect
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import Data.Maybe
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%default total
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public export
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0 CloTest : TermLike -> Type
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CloTest tm = forall q, d, n. tm q d n -> Bool
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interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where
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pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to ->
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tm q dfrom from -> Subset (tm q dto to) (No . isClo)
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public export
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0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm q d n)
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NotClo = No . isClo
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public export
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0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} ->
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PushSubsts tm isClo => TermLike
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NonClo tm q d n = Subset (tm q d n) NotClo
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public export %inline
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nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) =>
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(t : tm q d n) -> (0 nc : NotClo t) => NonClo tm q d n
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nclo t = Element t nc
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parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo}
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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 : tm q d n -> NonClo tm q d n
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pushSubsts s = pushSubstsWith id id s
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export %inline
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pushSubstsWith' : DSubst dfrom dto -> TSubst q dto from to ->
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tm q dfrom from -> tm q dto to
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pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x
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mutual
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public export
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isCloT : CloTest Term
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isCloT (CloT {}) = True
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isCloT (DCloT {}) = True
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isCloT (E e) = isCloE e
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isCloT _ = False
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public export
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isCloE : CloTest Elim
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isCloE (CloE {}) = True
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isCloE (DCloE {}) = True
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isCloE _ = False
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mutual
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export
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PushSubsts Term Reduce.isCloT where
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pushSubstsWith th ph (TYPE l) =
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nclo $ TYPE l
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pushSubstsWith th ph (Pi qty x a body) =
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nclo $ 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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nclo $ Lam x $ subs body th ph
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pushSubstsWith th ph (Sig x a b) =
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nclo $ Sig x (subs a th ph) (subs b th ph)
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pushSubstsWith th ph (Pair s t) =
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nclo $ 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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nclo $ 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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nclo $ 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 nclo $ 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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export
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PushSubsts Elim Reduce.isCloE where
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pushSubstsWith th ph (F x) =
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nclo $ 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 $ isCloE 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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nclo $ 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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nclo $ 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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nclo $ subs f th ph :% (d // th)
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pushSubstsWith th ph (s :# a) =
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nclo $ 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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public export
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0 RedexTest : TermLike -> Type
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RedexTest tm = forall q, d, n, g. Definitions' q g -> tm q d n -> Bool
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public export
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interface Whnf (0 tm : TermLike) (0 isRedex : RedexTest tm) | tm where
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whnf : (defs : Definitions' q g) ->
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tm q d n -> Subset (tm q d n) (No . isRedex defs)
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public export
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0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex =>
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Definitions' q g -> Pred (tm q d n)
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IsRedex defs = So . isRedex defs
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NotRedex defs = No . isRedex defs
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public export
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0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} -> Whnf tm isRedex =>
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(q : Type) -> (d, n : Nat) -> {g : _} ->
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(defs : Definitions' q g) -> Type
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NonRedex tm q d n defs = Subset (tm q d n) (NotRedex defs)
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public export %inline
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nred : {0 isRedex : RedexTest tm} -> (0 _ : Whnf tm isRedex) =>
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(t : tm q d n) -> (0 nr : NotRedex defs t) =>
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NonRedex tm q d n defs
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nred t = Element t nr
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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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mutual
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public export
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isRedexE : RedexTest Elim
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isRedexE defs (F x) {d, n} =
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isJust $ lookupElim x defs {d, n}
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isRedexE _ (B _) = False
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isRedexE defs (f :@ _) =
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isRedexE defs f || isLamHead f
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isRedexE defs (CasePair {pair, _}) =
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isRedexE defs pair || isPairHead pair
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isRedexE defs (f :% _) =
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isRedexE defs f || isDLamHead f
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isRedexE defs (t :# a) =
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isE t || isRedexT defs t || isRedexT defs a
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isRedexE _ (CloE {}) = True
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isRedexE _ (DCloE {}) = True
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public export
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isRedexT : RedexTest Term
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isRedexT _ (CloT {}) = True
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isRedexT _ (DCloT {}) = True
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isRedexT defs (E e) = isAnn e || isRedexE defs e
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isRedexT _ _ = False
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mutual
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export covering
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Whnf Elim Reduce.isRedexE where
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whnf defs (F x) with (lookupElim x defs) proof eq
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_ | Just y = whnf defs y
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_ | Nothing = Element (F x) $ rewrite eq in Ah
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whnf _ (B i) = nred $ B i
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whnf defs (f :@ s) =
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let Element f fnf = whnf defs 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 defs $ sub1 body s :# sub1 res s
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Right nlh => Element (f :@ s) $ fnf `orNo` nlh
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whnf defs (CasePair pi pair r ret x y body) =
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let Element pair pairnf = whnf defs 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 defs $ 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 defs (f :% p) =
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let Element f fnf = whnf defs 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 defs $ 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 defs (s :# a) =
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let Element s snf = whnf defs 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 defs a in
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Element (s :# a) $ ne `orNo` snf `orNo` anf
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whnf defs (CloE el th) = whnf defs $ pushSubstsWith' id th el
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whnf defs (DCloE el th) = whnf defs $ pushSubstsWith' th id el
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export covering
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Whnf Term Reduce.isRedexT where
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whnf _ t@(TYPE {}) = nred t
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whnf _ t@(Pi {}) = nred t
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whnf _ t@(Lam {}) = nred t
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whnf _ t@(Sig {}) = nred t
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whnf _ t@(Pair {}) = nred t
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whnf _ t@(Eq {}) = nred t
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whnf _ t@(DLam {}) = nred t
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whnf defs (E e) =
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let Element e enf = whnf defs 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 defs (CloT tm th) = whnf defs $ pushSubstsWith' id th tm
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whnf defs (DCloT tm th) = whnf defs $ pushSubstsWith' th id tm
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