module Quox.Syntax.Term.Subst import Quox.No import Quox.Syntax.Term.Base import Data.SnocVect %default total namespace CanDSubst public export interface CanDSubst (0 tm : TermLike) where (//) : tm dfrom n -> Lazy (DSubst dfrom dto) -> tm dto n ||| does the minimal reasonable work: ||| - deletes the closure around an atomic constant like `TYPE` ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level dim-closure ||| - otherwise, wraps in a new closure export CanDSubst Term where s // Shift SZ = s TYPE l // _ = TYPE l DCloT s ph // th = DCloT s $ ph . th s // th = DCloT s th private subDArgs : Elim dfrom n -> DSubst dfrom dto -> Elim dto n subDArgs (f :% d) th = subDArgs f th :% (d // th) subDArgs e th = DCloE e th ||| does the minimal reasonable work: ||| - deletes the closure around a term variable ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level dim-closure ||| - immediately looks up bound variables in a ||| top-level sequence of dimension applications ||| - otherwise, wraps in a new closure export CanDSubst Elim where e // Shift SZ = e F x // _ = F x B i // _ = B i f :% d // th = subDArgs (f :% d) th DCloE e ph // th = DCloE e $ ph . th e // th = DCloE e th namespace DSubst.ScopeTermN export %inline (//) : ScopeTermN s dfrom n -> Lazy (DSubst dfrom dto) -> ScopeTermN s dto n S ns (Y body) // th = S ns $ Y $ body // th S ns (N body) // th = S ns $ N $ body // th namespace DSubst.DScopeTermN export %inline (//) : {s : Nat} -> DScopeTermN s dfrom n -> Lazy (DSubst dfrom dto) -> DScopeTermN s dto n S ns (Y body) // th = S ns $ Y $ body // pushN s th S ns (N body) // th = S ns $ N $ body // th export %inline FromVar (Elim d) where fromVar = B export %inline FromVar (Term d) where fromVar = E . fromVar ||| does the minimal reasonable work: ||| - deletes the closure around a *free* name ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level closure ||| - immediately looks up a bound variable ||| - otherwise, wraps in a new closure export CanSubstSelf (Elim d) where F x // _ = F x B i // th = th !! i CloE e ph // th = assert_total CloE e $ ph . th e // th = case force th of Shift SZ => e th => CloE e th namespace CanTSubst public export interface CanTSubst (0 tm : TermLike) where (//) : tm d from -> Lazy (TSubst d from to) -> tm d to ||| does the minimal reasonable work: ||| - deletes the closure around an atomic constant like `TYPE` ||| - deletes an identity substitution ||| - composes (lazily) with an existing top-level closure ||| - goes inside `E` in case it is a simple variable or something ||| - otherwise, wraps in a new closure export CanTSubst Term where TYPE l // _ = TYPE l E e // th = E $ e // th CloT s ph // th = CloT s $ ph . th s // th = case force th of Shift SZ => s th => CloT s th namespace ScopeTermN export %inline (//) : {s : Nat} -> ScopeTermN s d from -> Lazy (TSubst d from to) -> ScopeTermN s d to S ns (Y body) // th = S ns $ Y $ body // pushN s th S ns (N body) // th = S ns $ N $ body // th namespace DScopeTermN export %inline (//) : {s : Nat} -> DScopeTermN s d from -> Lazy (TSubst d from to) -> DScopeTermN s d to S ns (Y body) // th = S ns $ Y $ body // map (// shift s) th S ns (N body) // th = S ns $ N $ body // th export %inline CanShift (Term d) where s // by = s // Shift by export %inline CanShift (Elim d) where e // by = e // Shift by export %inline {s : Nat} -> CanShift (ScopeTermN s d) where b // by = b // Shift by export %inline comp : DSubst dfrom dto -> TSubst dfrom from mid -> TSubst dto mid to -> TSubst dto from to comp th ps ph = map (// th) ps . ph public export %inline dweakT : {by : Nat} -> Term d n -> Term (by + d) n dweakT t = t // shift by public export %inline dweakE : {by : Nat} -> Elim d n -> Elim (by + d) n dweakE t = t // shift by public export %inline weakT : {default 1 by : Nat} -> Term d n -> Term d (by + n) weakT t = t // shift by public export %inline weakE : {default 1 by : Nat} -> Elim d n -> Elim d (by + n) weakE t = t // shift by parameters {s : Nat} namespace ScopeTermBody export %inline (.term) : ScopedBody s (Term d) n -> Term d (s + n) (Y b).term = b (N b).term = weakT b {by = s} namespace ScopeTermN export %inline (.term) : ScopeTermN s d n -> Term d (s + n) t.term = t.body.term namespace DScopeTermBody export %inline (.term) : ScopedBody s (\d => Term d n) d -> Term (s + d) n (Y b).term = b (N b).term = dweakT b {by = s} namespace DScopeTermN export %inline (.term) : DScopeTermN s d n -> Term (s + d) n t.term = t.body.term export %inline subN : ScopeTermN s d n -> SnocVect s (Elim d n) -> Term d n subN (S _ (Y body)) es = body // fromSnocVect es subN (S _ (N body)) _ = body export %inline sub1 : ScopeTerm d n -> Elim d n -> Term d n sub1 t e = subN t [< e] export %inline dsubN : DScopeTermN s d n -> SnocVect s (Dim d) -> Term d n dsubN (S _ (Y body)) ps = body // fromSnocVect ps dsubN (S _ (N body)) _ = body export %inline dsub1 : DScopeTerm d n -> Dim d -> Term d n dsub1 t p = dsubN t [< p] public export %inline (.zero) : DScopeTerm d n -> Term d n body.zero = dsub1 body $ K Zero public export %inline (.one) : DScopeTerm d n -> Term d n body.one = dsub1 body $ K One public export 0 CloTest : TermLike -> Type CloTest tm = forall d, n. tm d n -> Bool interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where pushSubstsWith : DSubst dfrom dto -> TSubst dto from to -> tm dfrom from -> Subset (tm dto to) (No . isClo) public export 0 NotClo : {isClo : CloTest tm} -> PushSubsts tm isClo => Pred (tm d n) NotClo = No . isClo public export 0 NonClo : (tm : TermLike) -> {isClo : CloTest tm} -> PushSubsts tm isClo => TermLike NonClo tm d n = Subset (tm d n) NotClo public export %inline nclo : {isClo : CloTest tm} -> (0 _ : PushSubsts tm isClo) => (t : tm d n) -> (0 nc : NotClo t) => NonClo tm 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 d n -> NonClo tm d n pushSubsts s = pushSubstsWith id id s export %inline pushSubstsWith' : DSubst dfrom dto -> TSubst dto from to -> tm dfrom from -> tm 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 Subst.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 _ _ Nat = nclo Nat pushSubstsWith _ _ Zero = nclo Zero pushSubstsWith th ph (Succ n) = nclo $ Succ $ n // th // ph pushSubstsWith th ph (BOX pi ty) = nclo $ BOX pi $ ty // th // ph pushSubstsWith th ph (Box val) = nclo $ Box $ val // 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 Subst.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 (CaseNat pi pi' n r z s) = nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph) (z // th // ph) (s // th // ph) pushSubstsWith th ph (CaseBox pi x r b) = nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) 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