361 lines
12 KiB
Idris
361 lines
12 KiB
Idris
module Quox.Syntax.Term.Tighten
|
||
|
||
import Quox.Syntax.Term.Base
|
||
import Quox.Syntax.Term.Subst
|
||
import public Quox.OPE
|
||
import Quox.No
|
||
|
||
%default total
|
||
|
||
|
||
export
|
||
Tighten Dim where
|
||
tighten p (K e loc) = pure $ K e loc
|
||
tighten p (B i loc) = B <$> tighten p i <*> pure loc
|
||
|
||
export
|
||
tightenScope : (forall m, n. OPE m n -> f n -> Maybe (f m)) ->
|
||
{s : Nat} -> OPE m n -> Scoped s f n -> Maybe (Scoped s f m)
|
||
tightenScope f p (S names (Y body)) = SY names <$> f (keepN s p) body
|
||
tightenScope f p (S names (N body)) = S names . N <$> f p body
|
||
|
||
export
|
||
tightenDScope : {0 f : Nat -> Nat -> Type} ->
|
||
(forall m, n, k. OPE m n -> f n k -> Maybe (f m k)) ->
|
||
OPE m n -> Scoped s (f n) k -> Maybe (Scoped s (f m) k)
|
||
tightenDScope f p (S names (Y body)) = SY names <$> f p body
|
||
tightenDScope f p (S names (N body)) = S names . N <$> f p body
|
||
|
||
|
||
mutual
|
||
private
|
||
tightenT : OPE n1 n2 -> Term d n2 -> Maybe (Term d n1)
|
||
tightenT p s =
|
||
let Element s' _ = pushSubsts s in
|
||
tightenT' p $ assert_smaller s s'
|
||
|
||
private
|
||
tightenE : OPE n1 n2 -> Elim d n2 -> Maybe (Elim d n1)
|
||
tightenE p e =
|
||
let Element e' _ = pushSubsts e in
|
||
tightenE' p $ assert_smaller e e'
|
||
|
||
private
|
||
tightenT' : OPE n1 n2 -> (t : Term d n2) -> (0 nt : NotClo t) =>
|
||
Maybe (Term d n1)
|
||
tightenT' p (TYPE l loc) = pure $ TYPE l loc
|
||
tightenT' p (Pi qty arg res loc) =
|
||
Pi qty <$> tightenT p arg <*> tightenS p res <*> pure loc
|
||
tightenT' p (Lam body loc) =
|
||
Lam <$> tightenS p body <*> pure loc
|
||
tightenT' p (Sig fst snd loc) =
|
||
Sig <$> tightenT p fst <*> tightenS p snd <*> pure loc
|
||
tightenT' p (Pair fst snd loc) =
|
||
Pair <$> tightenT p fst <*> tightenT p snd <*> pure loc
|
||
tightenT' p (Enum cases loc) =
|
||
pure $ Enum cases loc
|
||
tightenT' p (Tag tag loc) =
|
||
pure $ Tag tag loc
|
||
tightenT' p (Eq ty l r loc) =
|
||
Eq <$> tightenDS p ty <*> tightenT p l <*> tightenT p r <*> pure loc
|
||
tightenT' p (DLam body loc) =
|
||
DLam <$> tightenDS p body <*> pure loc
|
||
tightenT' p (Nat loc) =
|
||
pure $ Nat loc
|
||
tightenT' p (Zero loc) =
|
||
pure $ Zero loc
|
||
tightenT' p (Succ s loc) =
|
||
Succ <$> tightenT p s <*> pure loc
|
||
tightenT' p (BOX qty ty loc) =
|
||
BOX qty <$> tightenT p ty <*> pure loc
|
||
tightenT' p (Box val loc) =
|
||
Box <$> tightenT p val <*> pure loc
|
||
tightenT' p (E e) =
|
||
assert_total $ E <$> tightenE p e
|
||
|
||
private
|
||
tightenE' : OPE n1 n2 -> (e : Elim d n2) -> (0 ne : NotClo e) =>
|
||
Maybe (Elim d n1)
|
||
tightenE' p (F x u loc) =
|
||
pure $ F x u loc
|
||
tightenE' p (B i loc) =
|
||
B <$> tighten p i <*> pure loc
|
||
tightenE' p (App fun arg loc) =
|
||
App <$> tightenE p fun <*> tightenT p arg <*> pure loc
|
||
tightenE' p (CasePair qty pair ret body loc) =
|
||
CasePair qty <$> tightenE p pair
|
||
<*> tightenS p ret
|
||
<*> tightenS p body
|
||
<*> pure loc
|
||
tightenE' p (Fst pair loc) =
|
||
Fst <$> tightenE p pair <*> pure loc
|
||
tightenE' p (Snd pair loc) =
|
||
Snd <$> tightenE p pair <*> pure loc
|
||
tightenE' p (CaseEnum qty tag ret arms loc) =
|
||
CaseEnum qty <$> tightenE p tag
|
||
<*> tightenS p ret
|
||
<*> traverse (tightenT p) arms
|
||
<*> pure loc
|
||
tightenE' p (CaseNat qty qtyIH nat ret zero succ loc) =
|
||
CaseNat qty qtyIH
|
||
<$> tightenE p nat
|
||
<*> tightenS p ret
|
||
<*> tightenT p zero
|
||
<*> tightenS p succ
|
||
<*> pure loc
|
||
tightenE' p (CaseBox qty box ret body loc) =
|
||
CaseBox qty <$> tightenE p box
|
||
<*> tightenS p ret
|
||
<*> tightenS p body
|
||
<*> pure loc
|
||
tightenE' p (DApp fun arg loc) =
|
||
DApp <$> tightenE p fun <*> pure arg <*> pure loc
|
||
tightenE' p (Ann tm ty loc) =
|
||
Ann <$> tightenT p tm <*> tightenT p ty <*> pure loc
|
||
tightenE' p (Coe ty q0 q1 val loc) =
|
||
Coe <$> tightenDS p ty
|
||
<*> pure q0 <*> pure q1
|
||
<*> tightenT p val
|
||
<*> pure loc
|
||
tightenE' p (Comp ty q0 q1 val r zero one loc) =
|
||
Comp <$> tightenT p ty
|
||
<*> pure q0 <*> pure q1
|
||
<*> tightenT p val
|
||
<*> pure r
|
||
<*> tightenDS p zero
|
||
<*> tightenDS p one
|
||
<*> pure loc
|
||
tightenE' p (TypeCase ty ret arms def loc) =
|
||
TypeCase <$> tightenE p ty
|
||
<*> tightenT p ret
|
||
<*> traverse (tightenS p) arms
|
||
<*> tightenT p def
|
||
<*> pure loc
|
||
|
||
export
|
||
tightenS : {s : Nat} -> OPE m n ->
|
||
ScopeTermN s f n -> Maybe (ScopeTermN s f m)
|
||
tightenS = assert_total $ tightenScope tightenT
|
||
|
||
export
|
||
tightenDS : OPE m n -> DScopeTermN s f n -> Maybe (DScopeTermN s f m)
|
||
tightenDS = assert_total $ tightenDScope tightenT {f = \n, d => Term d n}
|
||
|
||
export Tighten (Elim d) where tighten p e = tightenE p e
|
||
export Tighten (Term d) where tighten p t = tightenT p t
|
||
|
||
|
||
mutual
|
||
export
|
||
dtightenT : OPE d1 d2 -> Term d2 n -> Maybe (Term d1 n)
|
||
dtightenT p s =
|
||
let Element s' _ = pushSubsts s in
|
||
dtightenT' p $ assert_smaller s s'
|
||
|
||
export
|
||
dtightenE : OPE d1 d2 -> Elim d2 n -> Maybe (Elim d1 n)
|
||
dtightenE p e =
|
||
let Element e' _ = pushSubsts e in
|
||
dtightenE' p $ assert_smaller e e'
|
||
|
||
private
|
||
dtightenT' : OPE d1 d2 -> (t : Term d2 n) -> (0 nt : NotClo t) =>
|
||
Maybe (Term d1 n)
|
||
dtightenT' p (TYPE l loc) =
|
||
pure $ TYPE l loc
|
||
dtightenT' p (Pi qty arg res loc) =
|
||
Pi qty <$> dtightenT p arg <*> dtightenS p res <*> pure loc
|
||
dtightenT' p (Lam body loc) =
|
||
Lam <$> dtightenS p body <*> pure loc
|
||
dtightenT' p (Sig fst snd loc) =
|
||
Sig <$> dtightenT p fst <*> dtightenS p snd <*> pure loc
|
||
dtightenT' p (Pair fst snd loc) =
|
||
Pair <$> dtightenT p fst <*> dtightenT p snd <*> pure loc
|
||
dtightenT' p (Enum cases loc) =
|
||
pure $ Enum cases loc
|
||
dtightenT' p (Tag tag loc) =
|
||
pure $ Tag tag loc
|
||
dtightenT' p (Eq ty l r loc) =
|
||
Eq <$> dtightenDS p ty <*> dtightenT p l <*> dtightenT p r <*> pure loc
|
||
dtightenT' p (DLam body loc) =
|
||
DLam <$> dtightenDS p body <*> pure loc
|
||
dtightenT' p (Nat loc) =
|
||
pure $ Nat loc
|
||
dtightenT' p (Zero loc) =
|
||
pure $ Zero loc
|
||
dtightenT' p (Succ s loc) =
|
||
Succ <$> dtightenT p s <*> pure loc
|
||
dtightenT' p (BOX qty ty loc) =
|
||
BOX qty <$> dtightenT p ty <*> pure loc
|
||
dtightenT' p (Box val loc) =
|
||
Box <$> dtightenT p val <*> pure loc
|
||
dtightenT' p (E e) =
|
||
assert_total $ E <$> dtightenE p e
|
||
|
||
export
|
||
dtightenE' : OPE d1 d2 -> (e : Elim d2 n) -> (0 ne : NotClo e) =>
|
||
Maybe (Elim d1 n)
|
||
dtightenE' p (F x u loc) =
|
||
pure $ F x u loc
|
||
dtightenE' p (B i loc) =
|
||
pure $ B i loc
|
||
dtightenE' p (App fun arg loc) =
|
||
App <$> dtightenE p fun <*> dtightenT p arg <*> pure loc
|
||
dtightenE' p (CasePair qty pair ret body loc) =
|
||
CasePair qty <$> dtightenE p pair
|
||
<*> dtightenS p ret
|
||
<*> dtightenS p body
|
||
<*> pure loc
|
||
dtightenE' p (Fst pair loc) =
|
||
Fst <$> dtightenE p pair <*> pure loc
|
||
dtightenE' p (Snd pair loc) =
|
||
Snd <$> dtightenE p pair <*> pure loc
|
||
dtightenE' p (CaseEnum qty tag ret arms loc) =
|
||
CaseEnum qty <$> dtightenE p tag
|
||
<*> dtightenS p ret
|
||
<*> traverse (dtightenT p) arms
|
||
<*> pure loc
|
||
dtightenE' p (CaseNat qty qtyIH nat ret zero succ loc) =
|
||
CaseNat qty qtyIH
|
||
<$> dtightenE p nat
|
||
<*> dtightenS p ret
|
||
<*> dtightenT p zero
|
||
<*> dtightenS p succ
|
||
<*> pure loc
|
||
dtightenE' p (CaseBox qty box ret body loc) =
|
||
CaseBox qty <$> dtightenE p box
|
||
<*> dtightenS p ret
|
||
<*> dtightenS p body
|
||
<*> pure loc
|
||
dtightenE' p (DApp fun arg loc) =
|
||
DApp <$> dtightenE p fun <*> tighten p arg <*> pure loc
|
||
dtightenE' p (Ann tm ty loc) =
|
||
Ann <$> dtightenT p tm <*> dtightenT p ty <*> pure loc
|
||
dtightenE' p (Coe ty q0 q1 val loc) =
|
||
[|Coe (dtightenDS p ty) (tighten p q0) (tighten p q1) (dtightenT p val)
|
||
(pure loc)|]
|
||
dtightenE' p (Comp ty q0 q1 val r zero one loc) =
|
||
[|Comp (dtightenT p ty) (tighten p q0) (tighten p q1)
|
||
(dtightenT p val) (tighten p r)
|
||
(dtightenDS p zero) (dtightenDS p one) (pure loc)|]
|
||
dtightenE' p (TypeCase ty ret arms def loc) =
|
||
[|TypeCase (dtightenE p ty) (dtightenT p ret)
|
||
(traverse (dtightenS p) arms) (dtightenT p def) (pure loc)|]
|
||
|
||
export
|
||
dtightenS : OPE d1 d2 -> ScopeTermN s d2 n -> Maybe (ScopeTermN s d1 n)
|
||
dtightenS = assert_total $ tightenDScope dtightenT {f = Term}
|
||
|
||
export
|
||
dtightenDS : {s : Nat} -> OPE d1 d2 ->
|
||
DScopeTermN s d2 n -> Maybe (DScopeTermN s d1 n)
|
||
dtightenDS = assert_total $ tightenScope dtightenT
|
||
|
||
|
||
export Tighten (\d => Term d n) where tighten p t = dtightenT p t
|
||
export Tighten (\d => Elim d n) where tighten p e = dtightenE p e
|
||
|
||
|
||
parameters {auto _ : Tighten f} {s : Nat}
|
||
export
|
||
squeeze : Scoped s f n -> (BContext s, Either (f (s + n)) (f n))
|
||
squeeze (S ns (N t)) = (ns, Right t)
|
||
squeeze (S ns (Y t)) = (ns, maybe (Left t) Right $ tightenN s t)
|
||
|
||
export
|
||
squeeze' : Scoped s f n -> Scoped s f n
|
||
squeeze' t = let (ns, res) = squeeze t in S ns $ either Y N res
|
||
|
||
parameters {0 f : Nat -> Nat -> Type}
|
||
{auto tt : Tighten (\d => f d n)} {s : Nat}
|
||
export
|
||
dsqueeze : Scoped s (\d => f d n) d ->
|
||
(BContext s, Either (f (s + d) n) (f d n))
|
||
dsqueeze = squeeze
|
||
|
||
export
|
||
dsqueeze' : Scoped s (\d => f d n) d -> Scoped s (\d => f d n) d
|
||
dsqueeze' = squeeze'
|
||
|
||
|
||
-- versions of SY, etc, that try to tighten and use SN automatically
|
||
|
||
public export %inline
|
||
ST : Tighten f => {s : Nat} -> BContext s -> f (s + n) -> Scoped s f n
|
||
ST names body = squeeze' $ SY names body
|
||
|
||
public export %inline
|
||
DST : {s : Nat} -> BContext s -> Term (s + d) n -> DScopeTermN s d n
|
||
DST names body = dsqueeze' {f = Term} $ SY names body
|
||
|
||
public export %inline
|
||
PiT : (qty : Qty) -> (x : BindName) ->
|
||
(arg : Term d n) -> (res : Term d (S n)) -> (loc : Loc) -> Term d n
|
||
PiT {qty, x, arg, res, loc} = Pi {qty, arg, res = ST [< x] res, loc}
|
||
|
||
public export %inline
|
||
LamT : (x : BindName) -> (body : Term d (S n)) -> (loc : Loc) -> Term d n
|
||
LamT {x, body, loc} = Lam {body = ST [< x] body, loc}
|
||
|
||
public export %inline
|
||
SigT : (x : BindName) -> (fst : Term d n) ->
|
||
(snd : Term d (S n)) -> (loc : Loc) -> Term d n
|
||
SigT {x, fst, snd, loc} = Sig {fst, snd = ST [< x] snd, loc}
|
||
|
||
public export %inline
|
||
EqT : (i : BindName) -> (ty : Term (S d) n) ->
|
||
(l, r : Term d n) -> (loc : Loc) -> Term d n
|
||
EqT {i, ty, l, r, loc} = Eq {ty = DST [< i] ty, l, r, loc}
|
||
|
||
public export %inline
|
||
DLamT : (i : BindName) -> (body : Term (S d) n) -> (loc : Loc) -> Term d n
|
||
DLamT {i, body, loc} = DLam {body = DST [< i] body, loc}
|
||
|
||
public export %inline
|
||
CoeT : (i : BindName) -> (ty : Term (S d) n) ->
|
||
(p, q : Dim d) -> (val : Term d n) -> (loc : Loc) -> Elim d n
|
||
CoeT {i, ty, p, q, val, loc} = Coe {ty = DST [< i] ty, p, q, val, loc}
|
||
|
||
public export %inline
|
||
typeCase1T : Elim d n -> Term d n ->
|
||
(k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
|
||
(loc : Loc) ->
|
||
{default (Nat loc) def : Term d n} ->
|
||
Elim d n
|
||
typeCase1T ty ret k ns body loc {def} =
|
||
typeCase ty ret [(k ** ST ns body)] def loc
|
||
|
||
|
||
public export %inline
|
||
CompH' : (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
|
||
CompH' {ty, p, q, val, r, zero, one, loc} =
|
||
let ty' = DST ty.names $ ty.term // (B VZ ty.name.loc ::: shift 2) in
|
||
Comp {
|
||
ty = dsub1 ty q, p, q,
|
||
val = E $ Coe ty p q val val.loc, r,
|
||
zero = DST zero.names $ E $
|
||
Coe ty' (B VZ zero.loc) (weakD 1 q) zero.term zero.loc,
|
||
one = DST one.names $ E $
|
||
Coe ty' (B VZ one.loc) (weakD 1 q) one.term one.loc,
|
||
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 = DST [< i] ty, p, q, val, r,
|
||
zero = DST [< j0] zero, one = DST [< j1] one, loc}
|