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 d1 n -> Lazy (DSubst d1 d2) -> tm d2 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 loc // _ = TYPE l loc DCloT (Sub s ph) // th = DCloT $ Sub s $ ph . th s // th = DCloT $ Sub s th private subDArgs : Elim d1 n -> DSubst d1 d2 -> Elim d2 n subDArgs (DApp f d loc) th = DApp (subDArgs f th) (d // th) loc subDArgs e th = DCloE $ Sub 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 u loc // _ = F x u loc B i loc // _ = B i loc e@(DApp {}) // th = subDArgs e th DCloE (Sub e ph) // th = DCloE $ Sub e $ ph . th e // th = DCloE $ Sub e th namespace DSubst.ScopeTermN export %inline (//) : ScopeTermN s d1 n -> Lazy (DSubst d1 d2) -> ScopeTermN s d2 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 d1 n -> Lazy (DSubst d1 d2) -> DScopeTermN s d2 n S ns (Y body) // th = S ns $ Y $ body // pushN s (locs $ toList' ns) th S ns (N body) // th = S ns $ N $ body // th export %inline FromVar (Elim d) where fromVarLoc = B export %inline FromVar (Term d) where fromVarLoc = E .: fromVarLoc ||| 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 u loc // _ = F x u loc B i loc // th = getLoc th i loc CloE (Sub e ph) // th = assert_total CloE $ Sub e $ ph . th e // th = case force th of Shift SZ => e th => CloE $ Sub e th namespace CanTSubst public export interface CanTSubst (0 tm : TermLike) where (//) : tm d n1 -> Lazy (TSubst d n1 n2) -> tm d n2 ||| 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 loc // _ = TYPE l loc E e // th = E $ e // th CloT (Sub s ph) // th = CloT $ Sub s $ ph . th s // th = case force th of Shift SZ => s th => CloT $ Sub s th namespace ScopeTermN export %inline (//) : {s : Nat} -> ScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> ScopeTermN s d n2 S ns (Y body) // th = S ns $ Y $ body // pushN s (locs $ toList' ns) th S ns (N body) // th = S ns $ N $ body // th namespace DScopeTermN export %inline (//) : {s : Nat} -> DScopeTermN s d n1 -> Lazy (TSubst d n1 n2) -> DScopeTermN s d n2 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 CanShift (flip Term n) where s // by = s // Shift by export %inline CanShift (flip Elim n) where e // by = e // Shift by export %inline {s : Nat} -> CanShift (ScopeTermN s d) where b // by = b // Shift by export %inline comp : DSubst d1 d2 -> TSubst d1 n1 mid -> TSubst d2 mid n2 -> TSubst d2 n1 n2 comp th ps ph = map (// th) ps . ph public export %inline dweakT : (by : Nat) -> Term d n -> Term (by + d) n dweakT by t = t // shift by public export %inline dweakS : (by : Nat) -> ScopeTermN s d n -> ScopeTermN s (by + d) n dweakS by t = t // shift by public export %inline dweakDS : {s : Nat} -> (by : Nat) -> DScopeTermN s d n -> DScopeTermN s (by + d) n dweakDS by t = t // shift by public export %inline dweakE : (by : Nat) -> Elim d n -> Elim (by + d) n dweakE by t = t // shift by public export %inline weakT : (by : Nat) -> Term d n -> Term d (by + n) weakT by t = t // shift by public export %inline weakS : {s : Nat} -> (by : Nat) -> ScopeTermN s d n -> ScopeTermN s d (by + n) weakS by t = t // shift by public export %inline weakDS : {s : Nat} -> (by : Nat) -> DScopeTermN s d n -> DScopeTermN s d (by + n) weakDS by t = t // shift by public export %inline weakE : (by : Nat) -> Elim d n -> Elim d (by + n) weakE by t = t // shift by parameters {auto _ : CanShift f} {s : Nat} export %inline getTerm : ScopedBody s f n -> f (s + n) getTerm (Y b) = b getTerm (N b) = b // fromNat s export %inline (.term) : Scoped s f n -> f (s + n) t.term = getTerm t.body namespace ScopeTermBody export %inline getTerm0 : ScopedBody 0 f n -> f n getTerm0 (Y b) = b getTerm0 (N b) = b namespace ScopeTermN export %inline (.term0) : Scoped 0 f n -> f n t.term0 = getTerm0 t.body 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) : (body : DScopeTerm d n) -> {default body.loc loc : Loc} -> Term d n body.zero = dsub1 body $ K Zero loc public export %inline (.one) : (body : DScopeTerm d n) -> {default body.loc loc : Loc} -> Term d n body.one = dsub1 body $ K One loc public export 0 CloTest : TermLike -> Type CloTest tm = forall d, n. tm d n -> Bool public export interface PushSubsts (0 tm : TermLike) (0 isClo : CloTest tm) | tm where pushSubstsWith : DSubst d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> Subset (tm d2 n2) (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 d1 d2 -> TSubst d2 n1 n2 -> tm d1 n1 -> tm d2 n2 pushSubstsWith' th ph x = fst $ pushSubstsWith th ph x export %inline pushSubsts' : tm d n -> tm d n pushSubsts' s = fst $ pushSubsts s 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 export PushSubsts Elim Subst.isCloE where pushSubstsWith th ph (F x u loc) = nclo $ F x u loc pushSubstsWith th ph (B i loc) = let res = getLoc ph i loc in case nchoose $ isCloE res of Left yes => assert_total pushSubsts res Right no => Element res no pushSubstsWith th ph (App f s loc) = nclo $ App (f // th // ph) (s // th // ph) loc pushSubstsWith th ph (CasePair pi p r b loc) = nclo $ CasePair pi (p // th // ph) (r // th // ph) (b // th // ph) loc pushSubstsWith th ph (Fst pair loc) = nclo $ Fst (pair // th // ph) loc pushSubstsWith th ph (Snd pair loc) = nclo $ Snd (pair // th // ph) loc pushSubstsWith th ph (CaseEnum pi t r arms loc) = nclo $ CaseEnum pi (t // th // ph) (r // th // ph) (map (\b => b // th // ph) arms) loc pushSubstsWith th ph (CaseNat pi pi' n r z s loc) = nclo $ CaseNat pi pi' (n // th // ph) (r // th // ph) (z // th // ph) (s // th // ph) loc pushSubstsWith th ph (CaseBox pi x r b loc) = nclo $ CaseBox pi (x // th // ph) (r // th // ph) (b // th // ph) loc pushSubstsWith th ph (DApp f d loc) = nclo $ DApp (f // th // ph) (d // th) loc pushSubstsWith th ph (Ann s a loc) = nclo $ Ann (s // th // ph) (a // th // ph) loc pushSubstsWith th ph (Coe ty p q val loc) = nclo $ Coe (ty // th // ph) (p // th) (q // th) (val // th // ph) loc pushSubstsWith th ph (Comp ty p q val r zero one loc) = nclo $ Comp (ty // th // ph) (p // th) (q // th) (val // th // ph) (r // th) (zero // th // ph) (one // th // ph) loc pushSubstsWith th ph (TypeCase ty ret arms def loc) = nclo $ TypeCase (ty // th // ph) (ret // th // ph) (map (\t => t // th // ph) arms) (def // th // ph) loc pushSubstsWith th ph (CloE (Sub e ps)) = pushSubstsWith th (comp th ps ph) e pushSubstsWith th ph (DCloE (Sub e ps)) = pushSubstsWith (ps . th) ph e export PushSubsts Term Subst.isCloT where pushSubstsWith th ph (TYPE l loc) = nclo $ TYPE l loc pushSubstsWith th ph (IOState loc) = nclo $ IOState loc pushSubstsWith th ph (Pi qty a body loc) = nclo $ Pi qty (a // th // ph) (body // th // ph) loc pushSubstsWith th ph (Lam body loc) = nclo $ Lam (body // th // ph) loc pushSubstsWith th ph (Sig a b loc) = nclo $ Sig (a // th // ph) (b // th // ph) loc pushSubstsWith th ph (Pair s t loc) = nclo $ Pair (s // th // ph) (t // th // ph) loc pushSubstsWith th ph (Enum tags loc) = nclo $ Enum tags loc pushSubstsWith th ph (Tag tag loc) = nclo $ Tag tag loc pushSubstsWith th ph (Eq ty l r loc) = nclo $ Eq (ty // th // ph) (l // th // ph) (r // th // ph) loc pushSubstsWith th ph (DLam body loc) = nclo $ DLam (body // th // ph) loc pushSubstsWith _ _ (NAT loc) = nclo $ NAT loc pushSubstsWith _ _ (Nat n loc) = nclo $ Nat n loc pushSubstsWith th ph (Succ n loc) = nclo $ Succ (n // th // ph) loc pushSubstsWith _ _ (STRING loc) = nclo $ STRING loc pushSubstsWith _ _ (Str s loc) = nclo $ Str s loc pushSubstsWith th ph (BOX pi ty loc) = nclo $ BOX pi (ty // th // ph) loc pushSubstsWith th ph (Box val loc) = nclo $ Box (val // th // ph) loc pushSubstsWith th ph (E e) = let Element e nc = pushSubstsWith th ph e in nclo $ E e pushSubstsWith th ph (Let qty rhs body loc) = nclo $ Let qty (rhs // th // ph) (body // th // ph) loc pushSubstsWith th ph (CloT (Sub s ps)) = pushSubstsWith th (comp th ps ph) s pushSubstsWith th ph (DCloT (Sub s ps)) = pushSubstsWith (ps . th) ph s