331 lines
11 KiB
Idris
331 lines
11 KiB
Idris
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 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 .: 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 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 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
|
|
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
|
|
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) : DScopeTerm d n -> {default noLoc loc : Loc} -> Term d n
|
|
body.zero = dsub1 body $ K Zero loc
|
|
|
|
public export %inline
|
|
(.one) : DScopeTerm d n -> {default noLoc 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
|
|
|
|
mutual
|
|
export
|
|
PushSubsts Term Subst.isCloT where
|
|
pushSubstsWith th ph (TYPE l loc) =
|
|
nclo $ TYPE l 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 _ _ (Zero loc) =
|
|
nclo $ Zero loc
|
|
pushSubstsWith th ph (Succ n loc) =
|
|
nclo $ Succ (n // th // ph) 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 (CloT (Sub s ps)) =
|
|
pushSubstsWith th (comp th ps ph) s
|
|
pushSubstsWith th ph (DCloT (Sub s ps)) =
|
|
pushSubstsWith (ps . th) ph s
|
|
|
|
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
|