module Quox.Reduce import Quox.No import Quox.Syntax import Quox.Definition import Data.Vect import Data.Maybe import Data.List %default total public export 0 CloTest : TermLike -> Type CloTest tm = forall q, d, n. tm q d n -> Bool interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where pushSubstsWith : DSubst dfrom dto -> TSubst q dto from to -> tm q dfrom from -> Subset (tm q dto to) (No . isClo) public export 0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm q d n) NotClo = No . isClo public export 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} -> PushSubsts tm isClo => TermLike NonClo tm q d n = Subset (tm q d n) NotClo public export %inline nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) => (t : tm q d n) -> (0 nc : NotClo t) => NonClo tm q d n nclo t = Element t nc parameters {0 isClo : CloTest tm} {auto _ : PushSubsts tm isClo} ||| if the input term has any top-level closures, push them under one layer of ||| syntax export %inline pushSubsts : tm q d n -> NonClo tm q d n pushSubsts s = pushSubstsWith id id s export %inline pushSubstsWith' : DSubst dfrom dto -> TSubst q dto from to -> tm q dfrom from -> tm q dto to pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x mutual public export isCloT : CloTest Term isCloT (CloT {}) = True isCloT (DCloT {}) = True isCloT (E e) = isCloE e isCloT _ = False public export isCloE : CloTest Elim isCloE (CloE {}) = True isCloE (DCloE {}) = True isCloE _ = False mutual export PushSubsts Term Reduce.isCloT where pushSubstsWith th ph (TYPE l) = nclo $ TYPE l pushSubstsWith th ph (Pi qty a body) = nclo $ Pi qty (a // th // ph) (body // th // ph) pushSubstsWith th ph (Lam body) = nclo $ Lam (body // th // ph) pushSubstsWith th ph (Sig a b) = nclo $ Sig (a // th // ph) (b // th // ph) pushSubstsWith th ph (Pair s t) = nclo $ Pair (s // th // ph) (t // th // ph) pushSubstsWith th ph (Enum tags) = nclo $ Enum tags pushSubstsWith th ph (Tag tag) = nclo $ Tag tag pushSubstsWith th ph (Eq ty l r) = nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) pushSubstsWith th ph (DLam body) = nclo $ DLam (body // th // ph) pushSubstsWith th ph (E e) = let Element e nc = pushSubstsWith th ph e in nclo $ E e pushSubstsWith th ph (CloT s ps) = pushSubstsWith th (comp th ps ph) s pushSubstsWith th ph (DCloT s ps) = pushSubstsWith (ps . th) ph s export PushSubsts Elim Reduce.isCloE where pushSubstsWith th ph (F x) = nclo $ F x pushSubstsWith th ph (B i) = let res = ph !! i in case nchoose $ isCloE res of Left yes => assert_total pushSubsts res Right no => Element res no pushSubstsWith th ph (f :@ s) = nclo $ (f // th // ph) :@ (s // th // ph) pushSubstsWith th ph (CasePair pi p r b) = nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) pushSubstsWith th ph (CaseEnum pi t r arms) = nclo $ CaseEnum pi (t // th // ph) (r // th // ph) (map (\b => b // th // ph) arms) pushSubstsWith th ph (f :% d) = nclo $ (f // th // ph) :% (d // th) pushSubstsWith th ph (s :# a) = nclo $ (s // th // ph) :# (a // th // ph) pushSubstsWith th ph (CloE e ps) = pushSubstsWith th (comp th ps ph) e pushSubstsWith th ph (DCloE e ps) = pushSubstsWith (ps . th) ph e ||| errors that might happen if you pass an ill typed expression into ||| whnf. don't do that please public export data WhnfErr = MissingEnumArm TagVal (List TagVal) public export 0 RedexTest : TermLike -> Type RedexTest tm = forall q, d, n, g. Definitions' q g -> tm q d n -> Bool public export interface Whnf (0 tm : TermLike) (0 isRedex : RedexTest tm) (0 err : Type) | tm where whnf : (defs : Definitions' q g) -> tm q d n -> Either err (Subset (tm q d n) (No . isRedex defs)) public export 0 IsRedex, NotRedex : {isRedex : RedexTest tm} -> Whnf tm isRedex err => Definitions' q g -> Pred (tm q d n) IsRedex defs = So . isRedex defs NotRedex defs = No . isRedex defs public export 0 NonRedex : (tm : TermLike) -> {isRedex : RedexTest tm} -> Whnf tm isRedex err => (q : Type) -> (d, n : Nat) -> {g : _} -> (defs : Definitions' q g) -> Type NonRedex tm q d n defs = Subset (tm q d n) (NotRedex defs) public export %inline nred : {0 isRedex : RedexTest tm} -> (0 _ : Whnf tm isRedex err) => (t : tm q d n) -> (0 nr : NotRedex defs t) => NonRedex tm q d n defs nred t = Element t nr public export %inline isLamHead : Elim {} -> Bool isLamHead (Lam {} :# Pi {}) = True isLamHead _ = False public export %inline isDLamHead : Elim {} -> Bool isDLamHead (DLam {} :# Eq {}) = True isDLamHead _ = False public export %inline isPairHead : Elim {} -> Bool isPairHead (Pair {} :# Sig {}) = True isPairHead _ = False public export %inline isTagHead : Elim {} -> Bool isTagHead (Tag t :# Enum _) = True isTagHead _ = False public export %inline isE : Term {} -> Bool isE (E _) = True isE _ = False public export %inline isAnn : Elim {} -> Bool isAnn (_ :# _) = True isAnn _ = False mutual public export isRedexE : RedexTest Elim isRedexE defs (F x) {d, n} = isJust $ lookupElim x defs {d, n} isRedexE _ (B _) = False isRedexE defs (f :@ _) = isRedexE defs f || isLamHead f isRedexE defs (CasePair {pair, _}) = isRedexE defs pair || isPairHead pair isRedexE defs (CaseEnum {tag, _}) = isRedexE defs tag || isTagHead tag isRedexE defs (f :% _) = isRedexE defs f || isDLamHead f isRedexE defs (t :# a) = isE t || isRedexT defs t || isRedexT defs a isRedexE _ (CloE {}) = True isRedexE _ (DCloE {}) = True public export isRedexT : RedexTest Term isRedexT _ (CloT {}) = True isRedexT _ (DCloT {}) = True isRedexT defs (E e) = isAnn e || isRedexE defs e isRedexT _ _ = False mutual export covering Whnf Elim Reduce.isRedexE WhnfErr where whnf defs (F x) with (lookupElim x defs) proof eq _ | Just y = whnf defs y _ | Nothing = pure $ Element (F x) $ rewrite eq in Ah whnf _ (B i) = pure $ nred $ B i whnf defs (f :@ s) = do Element f fnf <- whnf defs f case nchoose $ isLamHead f of Left _ => let Lam body :# Pi {arg, res, _} = f s = s :# arg in whnf defs $ sub1 body s :# sub1 res s Right nlh => pure $ Element (f :@ s) $ fnf `orNo` nlh whnf defs (CasePair pi pair ret body) = do Element pair pairnf <- whnf defs pair case nchoose $ isPairHead pair of Left _ => let Pair {fst, snd} :# Sig {fst = tfst, snd = tsnd, _} = pair fst = fst :# tfst snd = snd :# sub1 tsnd fst in whnf defs $ subN body [fst, snd] :# sub1 ret pair Right np => pure $ Element (CasePair pi pair ret body) (pairnf `orNo` np) whnf defs (CaseEnum pi tag ret arms) = do Element tag tagnf <- whnf defs tag case nchoose $ isTagHead tag of Left t => let Tag t :# Enum ts = tag ty = sub1 ret tag in case lookup t arms of Just arm => whnf defs $ arm :# ty Nothing => Left $ MissingEnumArm t (keys arms) Right nt => pure $ Element (CaseEnum pi tag ret arms) $ tagnf `orNo` nt whnf defs (f :% p) = do Element f fnf <- whnf defs f case nchoose $ isDLamHead f of Left _ => let DLam body :# Eq {ty = ty, l, r, _} = f body = endsOr l r (dsub1 body p) p in whnf defs $ body :# dsub1 ty p Right ndlh => pure $ Element (f :% p) $ fnf `orNo` ndlh whnf defs (s :# a) = do Element s snf <- whnf defs s case nchoose $ isE s of Left _ => let E e = s in pure $ Element e $ noOr2 snf Right ne => do Element a anf <- whnf defs a pure $ Element (s :# a) $ ne `orNo` snf `orNo` anf whnf defs (CloE el th) = whnf defs $ pushSubstsWith' id th el whnf defs (DCloE el th) = whnf defs $ pushSubstsWith' th id el export covering Whnf Term Reduce.isRedexT WhnfErr where whnf _ t@(TYPE {}) = pure $ nred t whnf _ t@(Pi {}) = pure $ nred t whnf _ t@(Lam {}) = pure $ nred t whnf _ t@(Sig {}) = pure $ nred t whnf _ t@(Pair {}) = pure $ nred t whnf _ t@(Enum {}) = pure $ nred t whnf _ t@(Tag {}) = pure $ nred t whnf _ t@(Eq {}) = pure $ nred t whnf _ t@(DLam {}) = pure $ nred t whnf defs (E e) = do Element e enf <- whnf defs e case nchoose $ isAnn e of Left _ => let tm :# _ = e in pure $ Element tm $ noOr1 $ noOr2 enf Right na => pure $ Element (E e) $ na `orNo` enf whnf defs (CloT tm th) = whnf defs $ pushSubstsWith' id th tm whnf defs (DCloT tm th) = whnf defs $ pushSubstsWith' th id tm