quox/lib/Quox/Syntax/Term/Tighten.idr

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module Quox.Syntax.Term.Tighten
import Quox.Syntax.Term.Base
import Quox.Syntax.Subst
import public Quox.OPE
%default total
export
Tighten (Shift from) where
-- `OPE m n` is a spicy `m ≤ n`,
-- and `Shift from n` is a (different) spicy `from ≤ n`
-- so the value is `from ≤ m` (as a `Shift`), if that is the case
tighten _ SZ = Nothing
tighten Id by = Just by
tighten (Drop p) (SS by) = tighten p by
tighten (Keep p) (SS by) = [|SS $ tighten p by|]
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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
tightenSub : (forall m, n. OPE m n -> env n -> Maybe (env m)) ->
OPE to1 to2 -> Subst env from to2 -> Maybe (Subst env from to1)
tightenSub f p (Shift by) = [|Shift $ tighten p by|]
tightenSub f p (t ::: th) = [|f p t !::: tightenSub f p th|]
export
Tighten env => Tighten (Subst env from) where
tighten p th = tightenSub tighten p th
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)
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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
tightenT p (CloT (Sub tm th)) = do
th <- assert_total $ tightenSub tightenE p th
pure $ CloT $ Sub tm th
tightenT p (DCloT (Sub tm th)) = do
tm <- tightenT p tm
pure $ DCloT $ Sub tm th
private
tightenE : OPE n1 n2 -> Elim d n2 -> Maybe (Elim d n1)
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tightenE p (F x u loc) =
pure $ F x u loc
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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 <$> tightenE p pair
<*> tightenS p ret
<*> tightenS p body
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<*> pure loc
tightenE p (CaseEnum qty tag ret arms loc) =
CaseEnum qty <$> tightenE p tag
<*> tightenS p ret
<*> traverse (tightenT p) arms
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<*> pure loc
tightenE p (CaseNat qty qtyIH nat ret zero succ loc) =
CaseNat qty qtyIH
<$> tightenE p nat
<*> tightenS p ret
<*> tightenT p zero
<*> tightenS p succ
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<*> pure loc
tightenE p (CaseBox qty box ret body loc) =
CaseBox qty <$> tightenE p box
<*> tightenS p ret
<*> tightenS p body
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<*> 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 <$> tightenDS p ty
<*> pure q0 <*> pure q1
<*> tightenT p val
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<*> pure loc
tightenE p (Comp ty q0 q1 val r zero one loc) =
Comp <$> tightenT p ty
<*> pure q0 <*> pure q1
<*> tightenT p val
<*> pure r
<*> tightenDS p zero
<*> tightenDS p one
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<*> pure loc
tightenE p (TypeCase ty ret arms def loc) =
TypeCase <$> tightenE p ty
<*> tightenT p ret
<*> traverse (tightenS p) arms
<*> tightenT p def
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<*> pure loc
tightenE p (CloE (Sub el th)) = do
th <- assert_total $ tightenSub tightenE p th
pure $ CloE $ Sub el th
tightenE p (DCloE (Sub el th)) = do
el <- tightenE p el
pure $ DCloE $ Sub el th
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)
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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
dtightenT p (CloT (Sub tm th)) = do
tm <- dtightenT p tm
th <- assert_total $ traverse (dtightenE p) th
pure $ CloT $ Sub tm th
dtightenT p (DCloT (Sub tm th)) = do
th <- tighten p th
pure $ DCloT $ Sub tm th
export
dtightenE : OPE d1 d2 -> Elim d2 n -> Maybe (Elim d1 n)
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dtightenE p (F x u loc) =
pure $ F x u loc
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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
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<*> pure loc
dtightenE p (CaseEnum qty tag ret arms loc) =
CaseEnum qty <$> dtightenE p tag
<*> dtightenS p ret
<*> traverse (dtightenT p) arms
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<*> pure loc
dtightenE p (CaseNat qty qtyIH nat ret zero succ loc) =
CaseNat qty qtyIH
<$> dtightenE p nat
<*> dtightenS p ret
<*> dtightenT p zero
<*> dtightenS p succ
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<*> pure loc
dtightenE p (CaseBox qty box ret body loc) =
CaseBox qty <$> dtightenE p box
<*> dtightenS p ret
<*> dtightenS p body
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<*> pure loc
dtightenE p (DApp fun arg loc) =
DApp <$> 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)
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(dtightenDS p zero) (dtightenDS p one) (pure loc)|]
dtightenE p (TypeCase ty ret arms def loc) =
[|TypeCase (dtightenE p ty) (dtightenT p ret)
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(traverse (dtightenS p) arms) (dtightenT p def) (pure loc)|]
dtightenE p (CloE (Sub el th)) = do
el <- dtightenE p el
th <- assert_total $ traverse (dtightenE p) th
pure $ CloE $ Sub el th
dtightenE p (DCloE (Sub el th)) = do
th <- tighten p th
pure $ DCloE $ Sub el th
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 [TermD] Tighten (\d => Term d n) where tighten p t = dtightenT p t
export [ElimD] Tighten (\d => Elim d n) where tighten p e = dtightenE p e
-- versions of SY, etc, that try to tighten and use SN automatically
public export
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ST : Tighten f => {s : Nat} -> BContext s -> f (s + n) -> Scoped s f n
ST names body =
case tightenN s body of
Just body => S names $ N body
Nothing => S names $ Y body
public export
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DST : {s : Nat} -> BContext s -> Term (s + d) n -> DScopeTermN s d n
DST names body =
case tightenN @{TermD} s body of
Just body => S names $ N body
Nothing => S names $ Y body
public export %inline
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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
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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
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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
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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 ->
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(k : TyConKind) -> BContext (arity k) -> Term d (arity k + n) ->
(loc : Loc) ->
{default (Nat loc) def : Term d n} ->
Elim d n
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typeCase1T ty ret k ns body loc {def} =
typeCase ty ret [(k ** ST ns body)] def loc
export
squeeze : {s : Nat} -> ScopeTermN s d n -> ScopeTermN s d n
squeeze (S names (Y body)) = S names $ maybe (Y body) N $ tightenN s body
squeeze (S names (N body)) = S names $ N body
export
dsqueeze : {s : Nat} -> DScopeTermN s d n -> DScopeTermN s d n
dsqueeze (S names (Y body)) =
S names $ maybe (Y body) N $ tightenN s body @{TermD}
dsqueeze (S names (N body)) = S names $ N body