make coercion computation type-directed like it should be
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@ -52,3 +52,8 @@ export %inline
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nchoose : (b : Bool) -> Either (So b) (No b)
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nchoose True = Left Oh
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nchoose False = Right Ah
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export
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0 notYesNo : {f : Dec p} -> Not p -> No (isYes f)
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notYesNo {f = Yes y} g = absurd $ g y
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notYesNo {f = No n} g = Ah
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@ -107,92 +107,84 @@ parameters {auto _ : CanWhnf Term Interface.isRedexT}
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(ST body.names $ body.term // (a' ::: shift 1)) loc
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||| pushes a coercion inside a whnf-ed term
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export covering
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pushCoe : BindName ->
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(ty : Term (S d) n) -> (0 tynf : No (isRedexT defs ty)) =>
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Dim d -> Dim d ->
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(s : Term d n) -> (0 snf : No (isRedexT defs s)) => Loc ->
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(ty : Term (S d) n) ->
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(p, q : Dim d) -> (0 npq : Not (p `Eqv` q)) =>
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(s : Term d n) -> (0 pc : So (canPushCoe ty s)) => Loc ->
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Eff Whnf (NonRedex Elim d n defs)
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pushCoe i ty p q s loc {snf} =
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if p == q then whnf defs ctx $ Ann s (ty // one q) loc else
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case s of
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-- (coe [_ ⇒ ★ᵢ] @_ @_ ty) ⇝ (ty ∷ ★ᵢ)
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TYPE {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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Pi {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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Sig {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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Enum {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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Eq {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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Nat {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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BOX {} => pure $ nred $ Ann s (TYPE !(unwrapTYPE ty) ty.loc) loc
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pushCoe i ty p q s loc =
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case ty of
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-- (coe ★ᵢ @_ @_ s) ⇝ (s ∷ ★ᵢ)
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TYPE l tyLoc =>
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whnf defs ctx $ Ann s (TYPE l tyLoc) loc
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-- just η expand it. then whnf for App will handle it later
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-- this is how @xtt does it
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-- η expand it so that whnf for App can deal with it
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--
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-- (coe [i ⇒ A] @p @q (λ x ⇒ s)) ⇝
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-- (λ y ⇒ (coe [i ⇒ A] @p @q (λ x ⇒ s)) y) ∷ A‹q/i› ⇝ ⋯
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lam@(Lam {body, _}) => do
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let lam' = CoeT i ty p q lam loc
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term' = LamY !(fresh body.name)
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(E $ App (weakE 1 lam') (BVT 0 noLoc) loc) loc
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type' = ty // one q
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whnf defs ctx $ Ann term' type' loc
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-- (coe (𝑖 ⇒ π.(x : A) → B) @p @q s)
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-- ⇝
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-- (λ y ⇒ (coe (𝑖 ⇒ π.(x : A) → B) @p @q s) y) ∷ (π.(x : A) → B)‹q/𝑖›
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Pi {} =>
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let inner = Coe (SY [< i] ty) p q s loc in
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whnf defs ctx $
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Ann (LamY !(mnb "y" loc)
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(E $ App (weakE 1 inner) (BVT 0 loc) loc) loc)
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(ty // one q) loc
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-- (coe [i ⇒ (x : A) × B] @p @q (s, t)) ⇝
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-- (coe [i ⇒ A] @p @q s,
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-- coe [i ⇒ B[(coe [j ⇒ A‹j/i›] @p @i s)/x]] @p @q t)
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-- ∷ (x : A‹q/i›) × B‹q/i›
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-- no η!!!
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-- push into a pair constructor, otherwise still stuck
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--
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-- can't use η here because... it doesn't exist
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Pair {fst, snd, loc = pairLoc} => do
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let Sig {fst = tfst, snd = tsnd, loc = sigLoc} = ty
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| _ => throw $ ExpectedSig ty.loc (extendDim i ctx.names) ty
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let fst' = E $ CoeT i tfst p q fst fst.loc
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tfst' = tfst // (B VZ noLoc ::: shift 2)
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tsnd' = sub1 tsnd $
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CoeT !(fresh i) tfst' (weakD 1 p) (B VZ noLoc)
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(dweakT 1 fst) fst.loc
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snd' = E $ CoeT i tsnd' p q snd snd.loc
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pure $
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Element (Ann (Pair fst' snd' pairLoc)
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(Sig (tfst // one q) (tsnd // one q) sigLoc) loc) Ah
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-- s̃‹𝑘› ≔ coe (𝑗 ⇒ A‹𝑗/𝑖›) @p @𝑘 s
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-- -----------------------------------------------
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-- (coe (𝑖 ⇒ (x : A) × B) @p @q (s, t))
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-- ⇝
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-- (s̃‹q›, coe (𝑖 ⇒ B[s̃‹𝑖›/x]) @p @q t)
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-- ∷ ((x : A) × B)‹q/𝑖›
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Sig tfst tsnd tyLoc => do
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let Pair fst snd sLoc = s
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fst' = CoeT i tfst p q fst fst.loc
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fstInSnd =
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CoeT !(fresh i)
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(tfst // (BV 0 loc ::: shift 2))
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(weakD 1 p) (BV 0 loc) (dweakT 1 s) fst.loc
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snd' = CoeT i (sub1 tsnd fstInSnd) p q snd snd.loc
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whnf defs ctx $
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Ann (Pair (E fst') (E snd') sLoc) (ty // one q) loc
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-- η expand, like for Lam
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-- (coe {𝐚̄} @_ @_ s) ⇝ (s ∷ {𝐚̄})
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Enum cases tyLoc =>
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whnf defs ctx $ Ann s (Enum cases tyLoc) loc
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-- η expand, same as for Π
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--
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-- (coe [i ⇒ A] @p @q (δ j ⇒ s)) ⇝
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-- (δ k ⇒ (coe [i ⇒ A] @p @q (δ j ⇒ s)) @k) ∷ A‹q/i› ⇝ ⋯
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dlam@(DLam {body, _}) => do
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let dlam' = CoeT i ty p q dlam loc
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term' = DLamY !(mnb "j")
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(E $ DApp (dweakE 1 dlam') (B VZ noLoc) loc) loc
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type' = ty // one q
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whnf defs ctx $ Ann term' type' loc
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-- (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @q s)
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-- ⇝
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-- (δ 𝑘 ⇒ (coe (𝑖 ⇒ Eq (𝑗 ⇒ A) l r) @p @q s) @𝑘) ∷ (Eq (𝑗 ⇒ A) l r)‹q/𝑖›
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Eq {} =>
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let inner = Coe (SY [< i] ty) p q s loc in
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whnf defs ctx $
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Ann (DLamY !(mnb "k" loc)
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(E $ DApp (dweakE 1 inner) (BV 0 loc) loc) loc)
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(ty // one q) loc
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-- (coe [_ ⇒ {⋯}] @_ @_ t) ⇝ (t ∷ {⋯})
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Tag {tag, loc = tagLoc} => do
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let Enum {cases, loc = enumLoc} = ty
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| _ => throw $ ExpectedEnum ty.loc (extendDim i ctx.names) ty
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pure $ Element (Ann (Tag tag tagLoc) (Enum cases enumLoc) loc) Ah
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-- (coe ℕ @_ @_ s) ⇝ (s ∷ ℕ)
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Nat tyLoc =>
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whnf defs ctx $ Ann s (Nat tyLoc) loc
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-- (coe [_ ⇒ ℕ] @_ @_ n) ⇝ (n ∷ ℕ)
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Zero {loc = zeroLoc} => do
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pure $ Element (Ann (Zero zeroLoc) (Nat ty.loc) loc) Ah
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Succ {p = pred, loc = succLoc} => do
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pure $ Element (Ann (Succ pred succLoc) (Nat ty.loc) loc) Ah
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-- (coe [i ⇒ [π.A]] @p @q [s]) ⇝
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-- [coe [i ⇒ A] @p @q s] ∷ [π. A‹q/i›]
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Box {val, loc = boxLoc} => do
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let BOX {qty, ty = a, loc = tyLoc} = ty
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| _ => throw $ ExpectedBOX ty.loc (extendDim i ctx.names) ty
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pure $ Element
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(Ann (Box (E $ CoeT i a p q val val.loc) boxLoc)
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(BOX qty (a // one q) tyLoc) loc)
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Ah
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E e => pure $ Element (CoeT i ty p q (E e) e.loc) (snf `orNo` Ah)
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where
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unwrapTYPE : Term (S d) n -> Eff Whnf Universe
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unwrapTYPE (TYPE {l, _}) = pure l
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unwrapTYPE ty = throw $ ExpectedTYPE ty.loc (extendDim i ctx.names) ty
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-- η expand
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--
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-- (coe (𝑖 ⇒ [π. A]) @p @q s)
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-- ⇝
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-- [case1 coe (𝑖 ⇒ [π. A]) @p @q s return A‹q/𝑖› of {[x] ⇒ x}]
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-- ∷ [π. A]‹q/𝑖›
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BOX qty inner tyLoc =>
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let inner = CaseBox {
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qty = One,
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box = Coe (SY [< i] ty) p q s loc,
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ret = SN $ ty // one q,
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body = SY [< !(mnb "x" loc)] $ BVT 0 loc,
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loc
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}
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in
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whnf defs ctx $ Ann (Box (E inner) loc) (ty // one q) loc
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@ -147,25 +147,50 @@ isK (K {}) = True
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isK _ = False
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||| if `ty` is a type constructor, and `val` is a value of that type where a
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||| coercion can be reduced. which is the case if any of:
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||| - `ty` is an atomic type
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||| - `ty` has η
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||| - `val` is a constructor form
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public export %inline
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canPushCoe : (ty, val : Term {}) -> Bool
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canPushCoe (TYPE {}) _ = True
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canPushCoe (Pi {}) _ = True
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canPushCoe (Lam {}) _ = False
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canPushCoe (Sig {}) (Pair {}) = True
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canPushCoe (Sig {}) _ = False
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canPushCoe (Pair {}) _ = False
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canPushCoe (Enum {}) _ = True
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canPushCoe (Tag {}) _ = False
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canPushCoe (Eq {}) _ = True
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canPushCoe (DLam {}) _ = False
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canPushCoe (Nat {}) _ = True
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canPushCoe (Zero {}) _ = False
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canPushCoe (Succ {}) _ = False
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canPushCoe (BOX {}) _ = True
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canPushCoe (Box {}) _ = False
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canPushCoe (E {}) _ = False
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canPushCoe (CloT {}) _ = False
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canPushCoe (DCloT {}) _ = False
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mutual
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||| a reducible elimination
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||| - a free variable, if its definition is known
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||| - an application whose head is an annotated lambda,
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||| a case expression whose head is an annotated constructor form, etc
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||| - a redundant annotation, or one whose term or type is reducible
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||| - coercions `coe (𝑖 ⇒ A) @p @q s` where:
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||| - `A` is in whnf, or
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||| - `𝑖` is not mentioned in `A`, or
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||| - `p = q`
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||| - [fixme] this is not true right now but that's because i wrote it
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||| wrong
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||| - compositions `comp A @p @q s @r {⋯}` where:
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||| - `A` is in whnf, or
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||| - `p = q`, or
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||| - `r = 0` or `r = 1`
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||| - [fixme] the p=q condition is also missing here
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||| - closures
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||| 1. a free variable, if its definition is known
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||| 2. an elimination whose head is reducible
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||| 3. an "active" elimination:
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||| an application whose head is an annotated lambda,
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||| a case expression whose head is an annotated constructor form, etc
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||| 4. a redundant annotation, or one whose term or type is reducible
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||| 5. a coercion `coe (𝑖 ⇒ A) @p @q s` where:
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||| a. `A` is reducible or a type constructor, or
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||| b. `𝑖` is not mentioned in `A`
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||| ([fixme] should be A‹0/𝑖› = A‹1/𝑖›), or
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||| c. `p = q`
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||| 6. a composition `comp A @p @q s @r {⋯}`
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||| where `p = q`, `r = 0`, or `r = 1`
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||| 7. a closure
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public export
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isRedexE : RedexTest Elim
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isRedexE defs (F {x, _}) {d, n} =
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@ -185,10 +210,11 @@ mutual
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isRedexE defs fun || isDLamHead fun || isK arg
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isRedexE defs (Ann {tm, ty, _}) =
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isE tm || isRedexT defs tm || isRedexT defs ty
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isRedexE defs (Coe {val, _}) =
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isRedexT defs val || not (isE val)
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isRedexE defs (Comp {ty, r, _}) =
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isRedexT defs ty || isK r
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isRedexE defs (Coe {ty = S _ (N _), _}) = True
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isRedexE defs (Coe {ty = S _ (Y ty), p, q, val, _}) =
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isRedexT defs ty || canPushCoe ty val || isYes (p `decEqv` q)
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isRedexE defs (Comp {ty, r, p, q, _}) =
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isYes (p `decEqv` q) || isK r
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isRedexE defs (TypeCase {ty, ret, _}) =
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isRedexE defs ty || isRedexT defs ret || isAnnTyCon ty
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isRedexE _ (CloE {}) = True
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@ -196,10 +222,10 @@ mutual
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||| a reducible term
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||| - a reducible elimination, as `isRedexE`
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||| - an annotated elimination
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||| (the annotation is redundant in a checkable context)
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||| - a closure
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||| 1. a reducible elimination, as `isRedexE`
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||| 2. an annotated elimination
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||| (the annotation is redundant in a checkable context)
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||| 3. a closure
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public export
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isRedexT : RedexTest Term
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isRedexT _ (CloT {}) = True
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@ -140,23 +140,31 @@ CanWhnf Elim Interface.isRedexE where
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whnf defs ctx (Coe (S _ (N ty)) _ _ val coeLoc) =
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whnf defs ctx $ Ann val ty coeLoc
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whnf defs ctx (Coe (S [< i] (Y ty)) p q val coeLoc) = do
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Element ty tynf <- whnf defs (extendDim i ctx) ty
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Element val valnf <- whnf defs ctx val
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pushCoe defs ctx i ty p q val coeLoc
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whnf defs ctx (Coe (S [< i] (Y ty)) p q val coeLoc) =
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case p `decEqv` q of
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Yes y => whnf defs ctx $ Ann val (ty // one q) coeLoc
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No npq => do
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Element ty tynf <- whnf defs (extendDim i ctx) ty
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case nchoose $ canPushCoe ty val of
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Left y =>
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pushCoe defs ctx i ty p q val coeLoc
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Right npc =>
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-- [fixme] what about ty.zero = ty.one????
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pure $ Element (Coe (SY [< i] ty) p q val coeLoc)
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(tynf `orNo` npc `orNo` notYesNo npq)
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whnf defs ctx (Comp ty p q val r zero one compLoc) =
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-- comp [A] @p @p s { ⋯ } ⇝ s ∷ A
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if p == q then whnf defs ctx $ Ann val ty compLoc else
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case nchoose (isK r) of
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-- comp [A] @p @q s @0 { 0 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
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-- comp [A] @p @q s @1 { 1 j ⇒ t; ⋯ } ⇝ t‹q/j› ∷ A
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Left y => case r of
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case p `decEqv` q of
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-- comp [A] @p @p s @r { ⋯ } ⇝ s ∷ A
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Yes y => whnf defs ctx $ Ann val ty compLoc
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No npq => case r of
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-- comp [A] @p @q s @0 { 0 𝑗 ⇒ t₀; ⋯ } ⇝ t₀‹q/𝑗› ∷ A
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K Zero _ => whnf defs ctx $ Ann (dsub1 zero q) ty compLoc
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-- comp [A] @p @q s @1 { 1 𝑗 ⇒ t₁; ⋯ } ⇝ t₁‹q/𝑗› ∷ A
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K One _ => whnf defs ctx $ Ann (dsub1 one q) ty compLoc
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Right nk => do
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Element ty tynf <- whnf defs ctx ty
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pure $ Element (Comp ty p q val r zero one compLoc) $ tynf `orNo` nk
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B {} =>
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pure $ Element (Comp ty p q val r zero one compLoc)
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(notYesNo npq `orNo` Ah)
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whnf defs ctx (TypeCase ty ret arms def tcLoc) = do
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Element ty tynf <- whnf defs ctx ty
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