add some needed ωs for w-types
i.o.u. linear trees. i'm still thinking
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3 changed files with 21 additions and 20 deletions
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@ -232,13 +232,13 @@ parameters (defs : Definitions)
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compare0' ctx ty@(W {shape, body, _}) s t =
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case (s, t) of
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-- Γ ⊢ s₁ = t₁ : A
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-- Γ ⊢ s₂ = t₂ : 1.B[s₁∷A/x] → (x : A) ⊲ B
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-- Γ ⊢ s₂ = t₂ : ω.B[s₁∷A/x] → (x : A) ⊲ B
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-- -----------------------------------------
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-- Γ ⊢ s₁⋄s₂ = t₁⋄t₂ : (x : A) ⊲ B
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(Sup sRoot sSub {}, Sup tRoot tSub {}) => do
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compare0 ctx shape sRoot tRoot
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let arg = sub1 body (Ann sRoot shape sRoot.loc)
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subTy = Arr One arg ty ty.loc
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subTy = Arr Any arg ty ty.loc
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compare0 ctx subTy sSub tSub
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(E e, E f) => Elim.compare0 ctx e f
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@ -481,7 +481,7 @@ parameters (defs : Definitions)
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-- Ψ | Γ ⊢ e = f ⇒ (x : A) ⊲ B
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-- Ψ | Γ, p : (x : A) ⊲ B ⊢ Q = R ⇐ Type
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-- Ψ | Γ, x : A, y : 1.B → (x : A) ⊲ B, ih : 1.(z : B) → Q[y z/p]
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-- Ψ | Γ, x : A, y : ω.B → (x : A) ⊲ B, ih : 1.(z : B) → Q[y z/p]
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-- ⊢ s = t ⇐ Q[(x⋄y ∷ (x : A) ⊲ B)/p]
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-- ----------------------------------------------------------------
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-- Ψ | Γ ⊢ caseπ e return Q of { x ⋄ y, ς.ih ⇒ s }
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@ -496,7 +496,7 @@ parameters (defs : Definitions)
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let [< x, y, ih] = ebody.names
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z <- mnb "z" ih.loc
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let xbind = (epi, x, shape)
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ybind = (epi, y, Arr One tbody.term (weakT 1 ety) y.loc)
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ybind = (epi, y, Arr Any tbody.term (weakT 1 ety) y.loc)
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ihbind = (epi', ih,
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PiY One z
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(sub1 (weakS 2 tbody) (BV 1 x.loc))
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@ -441,8 +441,8 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
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-- 𝒮‹𝑘› ≔ ((x : A) ⊲ B)‹𝑘/𝑖›
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-- 𝒶‹𝑘› ≔ coe [𝑖 ⇒ A] @p @𝑘 a
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-- : A‹𝑘/𝑖›
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-- 𝒷‹𝑘› ≔ coe [𝑖 ⇒ 1.B[𝒶‹𝑖›/x] → 𝒮‹𝑖›] @p @𝑘 b
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-- : 1.B‹𝑘/𝑖›[𝒶‹𝑘›/x] → 𝒮‹𝑘›
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-- 𝒷‹𝑘› ≔ coe [𝑖 ⇒ ω.B[𝒶‹𝑖›/x] → 𝒮‹𝑖›] @p @𝑘 b
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-- : ω.B‹𝑘/𝑖›[𝒶‹𝑘›/x] → 𝒮‹𝑘›
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-- 𝒾𝒽 ≔ coe [𝑖 ⇒ π.(z : B[𝒶‹𝑖›/x]) → C[𝒷‹𝑖› z/p]] @p @q ih
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-- : π.(z : B‹q/𝑖›[𝒶‹q›/x]) → C[𝒷‹q› z/p]
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-- --------------------------------------------------------------------
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@ -464,7 +464,7 @@ parameters {d, n : Nat} (defs : Definitions) (ctx : WhnfContext d n)
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// (a' (BV 0 bi.loc) ::: shift 3)
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ty' = ty // Shift (weak 1 by) // shift 3
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in
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CoeT bi (Arr One tbody' ty' b.loc) (p // by) k (BVT 1 b.loc) b.loc
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CoeT bi (Arr Any tbody' ty' b.loc) (p // by) k (BVT 1 b.loc) b.loc
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ih' : Elim d (3 + n) :=
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let tbody' = tbody.term // (a' (BV 0 ihi.loc) ::: shift 3)
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ret' = sub1 (weakS 4 $ dweakS 1 ret) $
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@ -636,17 +636,18 @@ pushCoe defs ctx i ty p q s loc =
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-- (coe [i ⇒ (x : A) ⊲ π.B] @p @q (s ⋄ t) ⇝
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-- (coe [i ⇒ A] @p @q s ⋄
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-- coe [i ⇒ 1.B[coe [j ⇒ A‹j/i›] @p @i s/x] → (x : A) ⊲ B] t)
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-- coe [i ⇒ ω.B[coe [j ⇒ A‹j/i›] @p @i s/x] → (x : A) ⊲ B] t)
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-- ∷ ((x : A) ⊲ B)‹q/i›
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Sup {root, sub, loc = supLoc} => do
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let W {shape, body, loc = wLoc} = ty
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| _ => throw $ ExpectedW ty.loc (extendDim i ctx.names) ty
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let root' = E $ CoeT i shape p q root root.loc
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tsub' = sub1 body $
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tsub0 = sub1 body $
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CoeT !(fresh i) (shape // (B VZ root.loc ::: shift 2))
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(weakD 1 p) (BV 0 sub.loc)
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(dweakT 1 sub) sub.loc
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sub' = E $ CoeT i tsub' p q sub sub.loc
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tsub' = Arr Any tsub0 ty sub.loc
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sub' = E $ CoeT i tsub' p q sub sub.loc
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pure $
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Element (Ann (Sup root' sub' supLoc)
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(W (shape // one q) (body // one q) wLoc) loc) Ah
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@ -731,7 +732,7 @@ CanWhnf Elim Reduce.isRedexE where
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pure $ Element (CasePair pi pair ret body caseLoc) $ pairnf `orNo` np
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-- s' ≔ s ∷ A
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-- t' ≔ t ∷ 1.B[s'/x] → (x : A) ⊲ B
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-- t' ≔ t ∷ ω.B[s'/x] → (x : A) ⊲ B
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-- ih' ≔ (λ x ⇒ caseπ t x return p ⇒ C of { (a ⋄ b), ς.ih ⇒ u }) ∷
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-- π.(y : B[s'/x]) → C[t' y/p]
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-- st' ≔ s ⋄ t ∷ (x : A) ⊲ B
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@ -748,7 +749,7 @@ CanWhnf Elim Reduce.isRedexE where
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w@(W {shape, body = wbody, _}) treeLoc =>
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let root = Ann root shape root.loc
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wbody' = sub1 wbody root
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tsub = Arr One wbody' w sub.loc
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tsub = Arr Any wbody' w sub.loc
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sub = Ann sub tsub sub.loc
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ih' = LamY !(mnb "y" caseLoc) -- [todo] better name
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(E $ CaseW qty qtyIH
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@ -85,12 +85,12 @@ where
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(Zero, r, BVT 2 r.loc)]
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||| if a ⋄ b : (x : A) ⊲ B, then b : `supSubTy a A B _`
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||| i.e. 1.B[a∷A/x] → ((x : A) ⊲ B)
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||| i.e. ω.B[a∷A/x] → ((x : A) ⊲ B)
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export
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supSubTy : (root, rootTy : Term d n) ->
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(body : ScopeTerm d n) -> Loc -> Term d n
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supSubTy root rootTy body loc =
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Arr One (sub1 body (Ann root rootTy root.loc)) (W rootTy body loc) loc
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Arr Any (sub1 body (Ann root rootTy root.loc)) (W rootTy body loc) loc
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mutual
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@ -207,10 +207,10 @@ mutual
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(shape, body) <- expectW !(askAt DEFS) ctx ty.loc ty
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-- if Ψ | Γ ⊢ σ · a ⇐ A ⊳ Σ₁
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qroot <- checkC ctx sg root shape
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-- if Ψ | Γ ⊢ σ · b ⇐ 1.B[a∷A/x] → ((x : A) ⊲ B) ⊳ Σ₂
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-- if Ψ | Γ ⊢ σ · b ⇐ ω.B[a∷A/x] → ((x : A) ⊲ B) ⊳ Σ₂
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qsub <- checkC ctx sg sub (supSubTy root shape body sub.loc)
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-- then Ψ | Γ ⊢ σ · (a ⋄ b) ⇐ ((x : A) ⊲ B) ⊳ Σ₁+Σ₂
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pure $ qroot + qsub
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-- then Ψ | Γ ⊢ σ · (a ⋄ b) ⇐ ((x : A) ⊲ B) ⊳ Σ₁+ωΣ₂
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pure $ qroot + Any * qsub
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check' ctx sg (Pair fst snd loc) ty = do
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(tfst, tsnd) <- expectSig !(askAt DEFS) ctx ty.loc ty
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@ -430,14 +430,14 @@ mutual
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-- if Ψ | Γ, p : (x : A) ⊲ B ⊢₀ C ⇐ Type
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checkTypeC (extendTy Zero ret.name w ctx) ret.term Nothing
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(shape, tbody) <- expectW !(askAt DEFS) ctx tree.loc w
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-- if Ψ | Γ, x : A, y : 1.B → (x : A) ⊲ B,
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-- if Ψ | Γ, x : A, y : ω.B → (x : A) ⊲ B,
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-- ih : π.(z : B) → C[y z/p]
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-- ⊢ σ · u ⇐ C[((x ⋄ y) ∷ (x : A) ⊲ B)/p]
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-- ⊳ Σ₂, π'.x, ς₁.y, ς₂.ih
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-- with π' ≤ σπ, ς₂ ≤ σς, ς₁+ς₂ ≤ σπ
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let [< x, y, ih] = body.names
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-- 1.B → (x : A) ⊲ B
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tsub = Arr One tbody.term (weakT 1 w) y.loc
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-- ω.B → (x : A) ⊲ B
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tsub = Arr Any tbody.term (weakT 1 w) y.loc
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-- y z
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ihret = App (BV 1 y.loc) (BVT 0 ih.loc) y.loc
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-- π.(z : B) → C[y z/p]
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