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make coercion computation type-directed like it should be

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rhiannon morris 2023-08-26 21:00:19 +02:00
parent 0bcb8c24db
commit 22db2724ce
4 changed files with 145 additions and 114 deletions
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5
lib/Quox/No.idr
View file

@ -52,3 +52,8 @@ export %inline
nchoose : (b : Bool) -> Either (So b) (No b) nchoose : (b : Bool) -> Either (So b) (No b)
nchoose True = Left Oh nchoose True = Left Oh
nchoose False = Right Ah nchoose False = Right Ah
export
0 notYesNo : {f : Dec p} -> Not p -> No (isYes f)
notYesNo {f = Yes y} g = absurd $ g y
notYesNo {f = No n} g = Ah

146
lib/Quox/Whnf/Coercion.idr
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@ -107,92 +107,84 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
(ST body.names $ body.term // (a' ::: shift 1)) loc (ST body.names $ body.term // (a' ::: shift 1)) loc
||| pushes a coercion inside a whnf-ed term ||| pushes a coercion inside a whnf-ed term
export covering export covering
pushCoe : BindName -> pushCoe : BindName ->
(ty : Term (S d) n) -> (0 tynf : No (isRedexT defs ty)) => (ty : Term (S d) n) ->
Dim d -> Dim d -> (p, q : Dim d) -> (0 npq : Not (p `Eqv` q)) =>
(s : Term d n) -> (0 snf : No (isRedexT defs s)) => Loc -> (s : Term d n) -> (0 pc : So (canPushCoe ty s)) => Loc ->
Eff Whnf (NonRedex Elim d n defs) Eff Whnf (NonRedex Elim d n defs)
pushCoe i ty p q s loc {snf} = pushCoe i ty p q s loc =
if p == q then whnf defs ctx $ Ann s (ty // one q) loc else case ty of
case s of -- (coe ★ᵢ @_ @_ s) ⇝ (s ∷ ★ᵢ)
-- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ) TYPE l tyLoc =>
TYPE {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc whnf defs ctx $ Ann s (TYPE l tyLoc) loc
Pi {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Sig {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Enum {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Eq {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
Nat {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
BOX {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
-- just η expand it. then whnf for App will handle it later -- η expand it so that whnf for App can deal with it
-- this is how @xtt does it
-- --
-- (coe [i ⇒ A] @p @q (λ x ⇒ s)) ⇝ -- (coe (𝑖 ⇒ π.(x : A) → B) @p @q s)
-- (λ y ⇒ (coe [i ⇒ A] @p @q (λ x ⇒ s)) y) ∷ A‹q/i› ⇝ ⋯ -- ⇝
lam@(Lam {body, _}) => do -- (λ y ⇒ (coe (𝑖 ⇒ π.(x : A) → B) @p @q s) y) ∷ (π.(x : A) → B)‹q/𝑖›
let lam' = CoeT i ty p q lam loc Pi {} =>
term' = LamY !(fresh body.name) let inner = Coe (SY [< i] ty) p q s loc in
(E $ App (weakE 1 lam') (BVT 0 noLoc) loc) loc whnf defs ctx $
type' = ty // one q Ann (LamY !(mnb "y" loc)
whnf defs ctx $ Ann term' type' loc (E $ App (weakE 1 inner) (BVT 0 loc) loc) loc)
(ty // one q) loc
-- (coe [i ⇒ (x : A) × B] @p @q (s, t)) ⇝ -- no η!!!
-- (coe [i ⇒ A] @p @q s, -- push into a pair constructor, otherwise still stuck
-- coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i s)/x]] @p @q t)
-- ∷ (x : A‹q/i›) × B‹q/i›
-- --
-- can't use η here because... it doesn't exist -- s̃‹𝑘› ≔ coe (𝑗 ⇒ A‹𝑗/𝑖›) @p @𝑘 s
Pair {fst, snd, loc = pairLoc} => do -- -----------------------------------------------
let Sig {fst = tfst, snd = tsnd, loc = sigLoc} = ty -- (coe (𝑖 ⇒ (x : A) × B) @p @q (s, t))
| _ => throw $ ExpectedSig ty.loc (extendDim i ctx.names) ty -- ⇝
let fst' = E $ CoeT i tfst p q fst fst.loc -- (s̃‹q›, coe (𝑖 ⇒ B[s̃‹𝑖›/x]) @p @q t)
tfst' = tfst // (B VZ noLoc ::: shift 2) -- ∷ ((x : A) × B)‹q/𝑖›
tsnd' = sub1 tsnd $ Sig tfst tsnd tyLoc => do
CoeT !(fresh i) tfst' (weakD 1 p) (B VZ noLoc) let Pair fst snd sLoc = s
(dweakT 1 fst) fst.loc fst' = CoeT i tfst p q fst fst.loc
snd' = E $ CoeT i tsnd' p q snd snd.loc fstInSnd =
pure $ CoeT !(fresh i)
Element (Ann (Pair fst' snd' pairLoc) (tfst // (BV 0 loc ::: shift 2))
(Sig (tfst // one q) (tsnd // one q) sigLoc) loc) Ah (weakD 1 p) (BV 0 loc) (dweakT 1 s) fst.loc
snd' = CoeT i (sub1 tsnd fstInSnd) p q snd snd.loc
whnf defs ctx $
Ann (Pair (E fst') (E snd') sLoc) (ty // one q) loc
-- η expand, like for Lam -- (coe {𝐚̄} @_ @_ s) ⇝ (s ∷ {𝐚̄})
Enum cases tyLoc =>
whnf defs ctx $ Ann s (Enum cases tyLoc) loc
-- η expand, same as for Π
-- --
-- (coe [i ⇒ A] @p @q (δ j ⇒ s)) ⇝ -- (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @q s)
-- (δ k ⇒ (coe [i ⇒ A] @p @q (δ j ⇒ s)) @k) ∷ A‹q/i› ⇝ ⋯ -- ⇝
dlam@(DLam {body, _}) => do -- (δ 𝑘 ⇒ (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @q s) @𝑘) ∷ (Eq (𝑗 ⇒ A) l r)‹q/𝑖›
let dlam' = CoeT i ty p q dlam loc Eq {} =>
term' = DLamY !(mnb "j") let inner = Coe (SY [< i] ty) p q s loc in
(E $ DApp (dweakE 1 dlam') (B VZ noLoc) loc) loc whnf defs ctx $
type' = ty // one q Ann (DLamY !(mnb "k" loc)
whnf defs ctx $ Ann term' type' loc (E $ DApp (dweakE 1 inner) (BV 0 loc) loc) loc)
(ty // one q) loc
-- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯}) -- (coe ℕ @_ @_ s) ⇝ (s ∷ ℕ)
Tag {tag, loc = tagLoc} => do Nat tyLoc =>
let Enum {cases, loc = enumLoc} = ty whnf defs ctx $ Ann s (Nat tyLoc) loc
| _ => throw $ ExpectedEnum ty.loc (extendDim i ctx.names) ty
pure $ Element (Ann (Tag tag tagLoc) (Enum cases enumLoc) loc) Ah
-- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ) -- η expand
Zero {loc = zeroLoc} => do --
pure $ Element (Ann (Zero zeroLoc) (Nat ty.loc) loc) Ah -- (coe (𝑖 ⇒ [π. A]) @p @q s)
Succ {p = pred, loc = succLoc} => do -- ⇝
pure $ Element (Ann (Succ pred succLoc) (Nat ty.loc) loc) Ah -- [case1 coe (𝑖 ⇒ [π. A]) @p @q s return A‹q/𝑖› of {[x] ⇒ x}]
-- ∷ [π. A]‹q/𝑖›
-- (coe [i ⇒ [π.A]] @p @q [s]) ⇝ BOX qty inner tyLoc =>
-- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›] let inner = CaseBox {
Box {val, loc = boxLoc} => do qty = One,
let BOX {qty, ty = a, loc = tyLoc} = ty box = Coe (SY [< i] ty) p q s loc,
| _ => throw $ ExpectedBOX ty.loc (extendDim i ctx.names) ty ret = SN $ ty // one q,
pure $ Element body = SY [< !(mnb "x" loc)] $ BVT 0 loc,
(Ann (Box (E $ CoeT i a p q val val.loc) boxLoc) loc
(BOX qty (a // one q) tyLoc) loc) }
Ah in
whnf defs ctx $ Ann (Box (E inner) loc) (ty // one q) loc
E e => pure $ Element (CoeT i ty p q (E e) e.loc) (snf `orNo` Ah)
where
unwrapTYPE : Term (S d) n -> Eff Whnf Universe
unwrapTYPE (TYPE {l, _}) = pure l
unwrapTYPE ty = throw $ ExpectedTYPE ty.loc (extendDim i ctx.names) ty

74
lib/Quox/Whnf/Interface.idr
View file

@ -147,25 +147,50 @@ isK (K {}) = True
isK _ = False isK _ = False
||| if `ty` is a type constructor, and `val` is a value of that type where a
||| coercion can be reduced. which is the case if any of:
||| - `ty` is an atomic type
||| - `ty` has η
||| - `val` is a constructor form
public export %inline
canPushCoe : (ty, val : Term {}) -> Bool
canPushCoe (TYPE {}) _ = True
canPushCoe (Pi {}) _ = True
canPushCoe (Lam {}) _ = False
canPushCoe (Sig {}) (Pair {}) = True
canPushCoe (Sig {}) _ = False
canPushCoe (Pair {}) _ = False
canPushCoe (Enum {}) _ = True
canPushCoe (Tag {}) _ = False
canPushCoe (Eq {}) _ = True
canPushCoe (DLam {}) _ = False
canPushCoe (Nat {}) _ = True
canPushCoe (Zero {}) _ = False
canPushCoe (Succ {}) _ = False
canPushCoe (BOX {}) _ = True
canPushCoe (Box {}) _ = False
canPushCoe (E {}) _ = False
canPushCoe (CloT {}) _ = False
canPushCoe (DCloT {}) _ = False
mutual mutual
||| a reducible elimination ||| a reducible elimination
||| |||
||| - a free variable, if its definition is known ||| 1. a free variable, if its definition is known
||| - an application whose head is an annotated lambda, ||| 2. an elimination whose head is reducible
||| a case expression whose head is an annotated constructor form, etc ||| 3. an "active" elimination:
||| - a redundant annotation, or one whose term or type is reducible ||| an application whose head is an annotated lambda,
||| - coercions `coe (𝑖 ⇒ A) @p @q s` where: ||| a case expression whose head is an annotated constructor form, etc
||| - `A` is in whnf, or ||| 4. a redundant annotation, or one whose term or type is reducible
||| - `𝑖` is not mentioned in `A`, or ||| 5. a coercion `coe (𝑖 ⇒ A) @p @q s` where:
||| - `p = q` ||| a. `A` is reducible or a type constructor, or
||| - [fixme] this is not true right now but that's because i wrote it ||| b. `𝑖` is not mentioned in `A`
||| wrong ||| ([fixme] should be A‹0/𝑖› = A‹1/𝑖›), or
||| - compositions `comp A @p @q s @r {⋯}` where: ||| c. `p = q`
||| - `A` is in whnf, or ||| 6. a composition `comp A @p @q s @r {⋯}`
||| - `p = q`, or ||| where `p = q`, `r = 0`, or `r = 1`
||| - `r = 0` or `r = 1` ||| 7. a closure
||| - [fixme] the p=q condition is also missing here
||| - closures
public export public export
isRedexE : RedexTest Elim isRedexE : RedexTest Elim
isRedexE defs (F {x, _}) {d, n} = isRedexE defs (F {x, _}) {d, n} =
@ -185,10 +210,11 @@ mutual
isRedexE defs fun || isDLamHead fun || isK arg isRedexE defs fun || isDLamHead fun || isK arg
isRedexE defs (Ann {tm, ty, _}) = isRedexE defs (Ann {tm, ty, _}) =
isE tm || isRedexT defs tm || isRedexT defs ty isE tm || isRedexT defs tm || isRedexT defs ty
isRedexE defs (Coe {val, _}) = isRedexE defs (Coe {ty = S _ (N _), _}) = True
isRedexT defs val || not (isE val) isRedexE defs (Coe {ty = S _ (Y ty), p, q, val, _}) =
isRedexE defs (Comp {ty, r, _}) = isRedexT defs ty || canPushCoe ty val || isYes (p `decEqv` q)
isRedexT defs ty || isK r isRedexE defs (Comp {ty, r, p, q, _}) =
isYes (p `decEqv` q) || isK r
isRedexE defs (TypeCase {ty, ret, _}) = isRedexE defs (TypeCase {ty, ret, _}) =
isRedexE defs ty || isRedexT defs ret || isAnnTyCon ty isRedexE defs ty || isRedexT defs ret || isAnnTyCon ty
isRedexE _ (CloE {}) = True isRedexE _ (CloE {}) = True
@ -196,10 +222,10 @@ mutual
||| a reducible term ||| a reducible term
||| |||
||| - a reducible elimination, as `isRedexE` ||| 1. a reducible elimination, as `isRedexE`
||| - an annotated elimination ||| 2. an annotated elimination
||| (the annotation is redundant in a checkable context) ||| (the annotation is redundant in a checkable context)
||| - a closure ||| 3. a closure
public export public export
isRedexT : RedexTest Term isRedexT : RedexTest Term
isRedexT _ (CloT {}) = True isRedexT _ (CloT {}) = True

34
lib/Quox/Whnf/Main.idr
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@ -140,23 +140,31 @@ CanWhnf Elim Interface.isRedexE where
whnf defs ctx (Coe (S _ (N ty)) _ _ val coeLoc) = whnf defs ctx (Coe (S _ (N ty)) _ _ val coeLoc) =
whnf defs ctx $ Ann val ty coeLoc whnf defs ctx $ Ann val ty coeLoc
whnf defs ctx (Coe (S [< i] (Y ty)) p q val coeLoc) = do whnf defs ctx (Coe (S [< i] (Y ty)) p q val coeLoc) =
Element ty tynf <- whnf defs (extendDim i ctx) ty case p `decEqv` q of
Element val valnf <- whnf defs ctx val Yes y => whnf defs ctx $ Ann val (ty // one q) coeLoc
pushCoe defs ctx i ty p q val coeLoc No npq => do
Element ty tynf <- whnf defs (extendDim i ctx) ty
case nchoose $ canPushCoe ty val of
Left y =>
pushCoe defs ctx i ty p q val coeLoc
Right npc =>
-- [fixme] what about ty.zero = ty.one????
pure $ Element (Coe (SY [< i] ty) p q val coeLoc)
(tynf `orNo` npc `orNo` notYesNo npq)
whnf defs ctx (Comp ty p q val r zero one compLoc) = whnf defs ctx (Comp ty p q val r zero one compLoc) =
-- comp [A] @p @p s { ⋯ } ⇝ s ∷ A case p `decEqv` q of
if p == q then whnf defs ctx $ Ann val ty compLoc else -- comp [A] @p @p s @r { ⋯ } ⇝ s ∷ A
case nchoose (isK r) of Yes y => whnf defs ctx $ Ann val ty compLoc
-- comp [A] @p @q s @0 { 0 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A No npq => case r of
-- comp [A] @p @q s @1 { 1 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A -- comp [A] @p @q s @0 { 0 𝑗 ⇒ t₀; ⋯ } ⇝ t₀‹q/𝑗› ∷ A
Left y => case r of
K Zero _ => whnf defs ctx $ Ann (dsub1 zero q) ty compLoc K Zero _ => whnf defs ctx $ Ann (dsub1 zero q) ty compLoc
-- comp [A] @p @q s @1 { 1 𝑗 ⇒ t₁; ⋯ } ⇝ t₁‹q/𝑗› ∷ A
K One _ => whnf defs ctx $ Ann (dsub1 one q) ty compLoc K One _ => whnf defs ctx $ Ann (dsub1 one q) ty compLoc
Right nk => do B {} =>
Element ty tynf <- whnf defs ctx ty pure $ Element (Comp ty p q val r zero one compLoc)
pure $ Element (Comp ty p q val r zero one compLoc) $ tynf `orNo` nk (notYesNo npq `orNo` Ah)
whnf defs ctx (TypeCase ty ret arms def tcLoc) = do whnf defs ctx (TypeCase ty ret arms def tcLoc) = do
Element ty tynf <- whnf defs ctx ty Element ty tynf <- whnf defs ctx ty