380 lines
12 KiB
Idris
380 lines
12 KiB
Idris
module Quox.Syntax.Term.Subst
|
||
|
||
import Quox.No
|
||
import Quox.Syntax.Term.Base
|
||
import Quox.Syntax.Term.Tighten
|
||
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 loc // _ = TYPE l loc
|
||
DCloT (Sub s ph) // th = DCloT $ Sub s $ ph . th
|
||
s // th = DCloT $ Sub s th
|
||
|
||
private
|
||
subDArgs : Elim dfrom n -> DSubst dfrom dto -> Elim dto 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 loc // _ = F x 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 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 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 loc // _ = F x 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 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 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 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 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 {s : Nat}
|
||
namespace ScopeTermBody
|
||
export %inline
|
||
(.term) : ScopedBody s (Term d) n -> Term d (s + n)
|
||
(Y b).term = b
|
||
(N b).term = weakT s b
|
||
|
||
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 s b
|
||
|
||
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 -> {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
|
||
|
||
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
|
||
|
||
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 loc) =
|
||
nclo $ F x 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 (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
|
||
|
||
|
||
private %inline
|
||
CompHY : (ty : DScopeTerm d n) -> (p, q : Dim d) -> (val : Term d n) ->
|
||
(r : Dim d) -> (zero, one : DScopeTerm d n) -> (loc : Loc) -> Elim d n
|
||
CompHY {ty, p, q, val, r, zero, one, loc} =
|
||
-- [fixme] maintain location of existing B VZ
|
||
let ty' = SY ty.names $ ty.term // (B VZ noLoc ::: shift 2) in
|
||
Comp {
|
||
ty = dsub1 ty q, p, q,
|
||
val = E $ Coe ty p q val val.loc, r,
|
||
-- [fixme] better locations for these vars?
|
||
zero = SY zero.names $ E $
|
||
Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
|
||
one = SY one.names $ E $
|
||
Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
|
||
loc
|
||
}
|
||
|
||
public export %inline
|
||
CompH' : (ty : DScopeTerm d n) ->
|
||
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
|
||
(zero : DScopeTerm d n) ->
|
||
(one : DScopeTerm d n) ->
|
||
(loc : Loc) ->
|
||
Elim d n
|
||
CompH' {ty, p, q, val, r, zero, one, loc} =
|
||
case dsqueeze ty of
|
||
S _ (N ty) => Comp {ty, p, q, val, r, zero, one, loc}
|
||
S _ (Y _) => CompHY {ty, p, q, val, r, zero, one, loc}
|
||
|
||
||| heterogeneous composition, using Comp and Coe (and subst)
|
||
|||
|
||
||| comp [i ⇒ A] @p @q s @r { 0 j ⇒ t₀; 1 j ⇒ t₁ }
|
||
||| ≔
|
||
||| comp [A‹q/i›] @p @q (coe [i ⇒ A] @p @q s) @r {
|
||
||| 0 j ⇒ coe [i ⇒ A] @j @q t₀;
|
||
||| 1 j ⇒ coe [i ⇒ A] @j @q t₁
|
||
||| }
|
||
public export %inline
|
||
CompH : (i : BindName) -> (ty : Term (S d) n) ->
|
||
(p, q : Dim d) -> (val : Term d n) -> (r : Dim d) ->
|
||
(j0 : BindName) -> (zero : Term (S d) n) ->
|
||
(j1 : BindName) -> (one : Term (S d) n) ->
|
||
(loc : Loc) ->
|
||
Elim d n
|
||
CompH {i, ty, p, q, val, r, j0, zero, j1, one, loc} =
|
||
CompH' {ty = SY [< i] ty, p, q, val, r,
|
||
zero = SY [< j0] zero, one = SY [< j0] one, loc}
|