340 lines
11 KiB
Idris
340 lines
11 KiB
Idris
module Quox.Typechecker
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import public Quox.Typing
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import public Quox.Equal
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%default total
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public export
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0 CanTC' : (q : Type) -> (q -> Type) -> (Type -> Type) -> Type
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CanTC' q isGlobal m = (HasErr q m, MonadReader (Definitions' q isGlobal) m)
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public export
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0 CanTC : (q : Type) -> IsQty q => (Type -> Type) -> Type
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CanTC q = CanTC' q IsGlobal
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private
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popQs : HasErr q m => IsQty q =>
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QOutput q s -> QOutput q (s + n) -> m (QOutput q n)
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popQs [<] qout = pure qout
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popQs (pis :< pi) (qout :< rh) = do expectCompatQ rh pi; popQs pis qout
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private %inline
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popQ : HasErr q m => IsQty q => q -> QOutput q (S n) -> m (QOutput q n)
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popQ pi = popQs [< pi]
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parameters {auto _ : IsQty q} {auto _ : CanTC q m}
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mutual
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||| "Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ"
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|||
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||| `check ctx sg subj ty` checks that in the context `ctx`, the term
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||| `subj` has the type `ty`, with quantity `sg`. if so, returns the
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||| quantities of all bound variables that it used.
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|||
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||| if the dimension context is inconsistent, then return `Nothing`, without
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||| doing any further work.
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export covering %inline
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check : (ctx : TyContext q d n) -> SQty q -> Term q d n -> Term q d n ->
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m (CheckResult ctx.dctx q n)
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check ctx sg subj ty = ifConsistent ctx.dctx $ checkC ctx sg subj ty
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||| "Ψ | Γ ⊢₀ s ⇐ A"
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|||
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||| `check0 ctx subj ty` checks a term (as `check`) in a zero context.
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export covering %inline
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check0 : TyContext q d n -> Term q d n -> Term q d n -> m ()
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check0 ctx tm ty = ignore $ check ctx szero tm ty
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-- the output will always be 𝟎 because the subject quantity is 0
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||| `check`, assuming the dimension context is consistent
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export covering %inline
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checkC : (ctx : TyContext q d n) -> SQty q -> Term q d n -> Term q d n ->
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m (CheckResult' q n)
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checkC ctx sg subj ty =
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wrapErr (WhileChecking ctx sg.fst subj ty) $
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let Element subj nc = pushSubsts subj in
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check' ctx sg subj ty
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||| "Ψ | Γ ⊢₀ s ⇐ ★ᵢ"
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|||
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||| `checkType ctx subj ty` checks a type (in a zero context). sometimes the
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||| universe doesn't matter, only that a term is _a_ type, so it is optional.
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export covering %inline
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checkType : TyContext q d n -> Term q d n -> Maybe Universe -> m ()
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checkType ctx subj l = ignore $ ifConsistent ctx.dctx $ checkTypeC ctx subj l
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export covering %inline
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checkTypeC : TyContext q d n -> Term q d n -> Maybe Universe -> m ()
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checkTypeC ctx subj l =
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wrapErr (WhileCheckingTy ctx subj l) $ checkTypeNoWrap ctx subj l
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export covering %inline
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checkTypeNoWrap : TyContext q d n -> Term q d n -> Maybe Universe -> m ()
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checkTypeNoWrap ctx subj l =
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let Element subj nc = pushSubsts subj in
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checkType' ctx subj l
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||| "Ψ | Γ ⊢ σ · e ⇒ A ⊳ Σ"
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|||
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||| `infer ctx sg subj` infers the type of `subj` in the context `ctx`,
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||| and returns its type and the bound variables it used.
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|||
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||| if the dimension context is inconsistent, then return `Nothing`, without
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||| doing any further work.
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export covering %inline
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infer : (ctx : TyContext q d n) -> SQty q -> Elim q d n ->
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m (InferResult ctx.dctx q d n)
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infer ctx sg subj = ifConsistent ctx.dctx $ inferC ctx sg subj
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||| `infer`, assuming the dimension context is consistent
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export covering %inline
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inferC : (ctx : TyContext q d n) -> SQty q -> Elim q d n ->
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m (InferResult' q d n)
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inferC ctx sg subj =
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wrapErr (WhileInferring ctx sg.fst subj) $
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let Element subj nc = pushSubsts subj in
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infer' ctx sg subj
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private covering
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toCheckType : TyContext q d n -> SQty q ->
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(subj : Term q d n) -> (0 nc : NotClo subj) => Term q d n ->
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m (CheckResult' q n)
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toCheckType ctx sg t ty = do
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u <- expectTYPE !ask ty
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expectEqualQ zero sg.fst
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checkTypeNoWrap ctx t (Just u)
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pure $ zeroFor ctx
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private covering
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check' : TyContext q d n -> SQty q ->
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(subj : Term q d n) -> (0 nc : NotClo subj) => Term q d n ->
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m (CheckResult' q n)
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check' ctx sg t@(TYPE _) ty = toCheckType ctx sg t ty
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check' ctx sg t@(Pi {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Lam body) ty = do
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(qty, arg, res) <- expectPi !ask ty
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-- if Ψ | Γ, x : A ⊢ σ · t ⇐ B ⊳ Σ, ρ·x
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-- with ρ ≤ σπ
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let qty' = sg.fst * qty
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qout <- checkC (extendTy arg ctx) sg body.term res.term
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-- then Ψ | Γ ⊢ σ · (λx ⇒ t) ⇐ (π·x : A) → B ⊳ Σ
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popQ qty' qout
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check' ctx sg t@(Sig {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Pair fst snd) ty = do
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(tfst, tsnd) <- expectSig !ask ty
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-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ₁
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qfst <- checkC ctx sg fst tfst
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let tsnd = sub1 tsnd (fst :# tfst)
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-- if Ψ | Γ ⊢ σ · t ⇐ B[s] ⊳ Σ₂
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qsnd <- checkC ctx sg snd tsnd
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-- then Ψ | Γ ⊢ σ · (s, t) ⇐ (x : A) × B ⊳ Σ₁ + Σ₂
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pure $ qfst + qsnd
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check' ctx sg t@(Enum _) ty = toCheckType ctx sg t ty
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check' ctx sg (Tag t) ty = do
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tags <- expectEnum !ask ty
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-- if t ∈ ts
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unless (t `elem` tags) $ throwError $ TagNotIn t tags
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-- then Ψ | Γ ⊢ σ · t ⇐ {ts} ⊳ 𝟎
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pure $ zeroFor ctx
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check' ctx sg t@(Eq {}) ty = toCheckType ctx sg t ty
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check' ctx sg (DLam body) ty = do
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(ty, l, r) <- expectEq !ask ty
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-- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ
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qout <- checkC (extendDim ctx) sg body.term ty.term
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-- if Ψ | Γ ⊢ t‹0› = l : A‹0›
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equal ctx ty.zero body.zero l
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-- if Ψ | Γ ⊢ t‹1› = r : A‹1›
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equal ctx ty.one body.one r
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-- then Ψ | Γ ⊢ σ · (δ i ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ
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pure qout
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check' ctx sg (E e) ty = do
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-- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ
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infres <- inferC ctx sg e
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-- if Ψ | Γ ⊢ A' <: A
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subtype ctx infres.type ty
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-- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ
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pure infres.qout
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private covering
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checkType' : TyContext q d n ->
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(subj : Term q d n) -> (0 nc : NotClo subj) =>
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Maybe Universe -> m ()
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checkType' ctx (TYPE k) u = do
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-- if 𝓀 < ℓ then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type ℓ
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case u of
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Just l => unless (k < l) $ throwError $ BadUniverse k l
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Nothing => pure ()
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checkType' ctx (Pi qty arg res) u = do
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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checkTypeC ctx arg u
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-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
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case res.body of
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Y res => checkTypeC (extendTy arg ctx) res u
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N res => checkTypeC ctx res u
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-- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ
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checkType' ctx t@(Lam {}) u =
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throwError $ NotType t
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checkType' ctx (Sig fst snd) u = do
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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checkTypeC ctx fst u
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-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
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case snd.body of
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Y snd => checkTypeC (extendTy fst ctx) snd u
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N snd => checkTypeC ctx snd u
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-- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ
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checkType' ctx t@(Pair {}) u =
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throwError $ NotType t
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checkType' ctx (Enum _) u = pure ()
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-- Ψ | Γ ⊢₀ {ts} ⇐ Type ℓ
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checkType' ctx t@(Tag {}) u =
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throwError $ NotType t
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checkType' ctx (Eq t l r) u = do
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-- if Ψ, i | Γ ⊢₀ A ⇐ Type ℓ
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case t.body of
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Y t => checkTypeC (extendDim ctx) t u
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N t => checkTypeC ctx t u
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-- if Ψ | Γ ⊢₀ l ⇐ A‹0›
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check0 ctx t.zero l
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-- if Ψ | Γ ⊢₀ r ⇐ A‹1›
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check0 ctx t.one r
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-- then Ψ | Γ ⊢₀ Eq [i ⇒ A] l r ⇐ Type ℓ
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checkType' ctx t@(DLam {}) u =
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throwError $ NotType t
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checkType' ctx (E e) u = do
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-- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ
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infres <- inferC ctx szero e
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-- if Ψ | Γ ⊢ A' <: A
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case u of
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Just u => subtype ctx infres.type (TYPE u)
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Nothing => ignore $ expectTYPE !ask infres.type
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-- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ
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private covering
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infer' : TyContext q d n -> SQty q ->
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(subj : Elim q d n) -> (0 nc : NotClo subj) =>
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m (InferResult' q d n)
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infer' ctx sg (F x) = do
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-- if π·x : A {≔ s} in global context
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g <- lookupFree x
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-- if σ ≤ π
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expectCompatQ sg.fst g.qty
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-- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ 𝟎
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pure $ InfRes {type = g.type.get, qout = zeroFor ctx}
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where
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lookupFree : Name -> m (Definition q)
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lookupFree x = lookupFree' !ask x
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infer' ctx sg (B i) =
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-- if x : A ∈ Γ
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-- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ (𝟎, σ·x, 𝟎)
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pure $ lookupBound sg.fst i ctx.tctx
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where
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lookupBound : q -> Var n -> TContext q d n -> InferResult' q d n
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lookupBound pi VZ (ctx :< ty) =
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InfRes {type = weakT ty, qout = zeroFor ctx :< pi}
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lookupBound pi (VS i) (ctx :< _) =
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let InfRes {type, qout} = lookupBound pi i ctx in
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InfRes {type = weakT type, qout = qout :< zero}
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infer' ctx sg (fun :@ arg) = do
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-- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁
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funres <- inferC ctx sg fun
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(qty, argty, res) <- expectPi !ask funres.type
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-- if Ψ | Γ ⊢ σ ⨴ π · s ⇐ A ⊳ Σ₂
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argout <- checkC ctx (subjMult sg qty) arg argty
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-- then Ψ | Γ ⊢ σ · f s ⇒ B[s] ⊳ Σ₁ + Σ₂
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pure $ InfRes {
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type = sub1 res $ arg :# argty,
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qout = funres.qout + argout
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}
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infer' ctx sg (CasePair pi pair ret body) = do
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-- if 1 ≤ π
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expectCompatQ one pi
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-- if Ψ | Γ ⊢ σ · pair ⇒ (x : A) × B ⊳ Σ₁
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pairres <- inferC ctx sg pair
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-- if Ψ | Γ, p : (x : A) × B ⊢₀ ret ⇐ Type
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checkTypeC (extendTy pairres.type ctx) ret.term Nothing
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(tfst, tsnd) <- expectSig !ask pairres.type
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-- if Ψ | Γ, x : A, y : B ⊢ σ · body ⇐
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-- ret[(x, y) ∷ (x : A) × B/p] ⊳ Σ₂, ρ₁·x, ρ₂·y
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-- with ρ₁, ρ₂ ≤ πσ
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let bodyctx = extendTyN [< tfst, tsnd.term] ctx
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bodyty = substCasePairRet pairres.type ret
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pisg = pi * sg.fst
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bodyout <- checkC bodyctx sg body.term bodyty
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-- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[pair/p] ⊳ πΣ₁ + Σ₂
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pure $ InfRes {
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type = sub1 ret pair,
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qout = pi * pairres.qout + !(popQs [< pisg, pisg] bodyout)
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}
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infer' ctx sg (CaseEnum pi t ret arms) {n} = do
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-- if 1 ≤ π
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expectCompatQ one pi
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-- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁
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tres <- inferC ctx sg t
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-- if Ψ | Γ, x : {ts} ⊢₀ A ⇐ Type
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checkTypeC (extendTy tres.type ctx) ret.term Nothing
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-- if for each "a ⇒ s" in arms,
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-- Ψ | Γ ⊢ σ · s ⇐ A[a ∷ {ts}/x] ⊳ Σ₂
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-- for fixed Σ₂
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armres <- for (SortedMap.toList arms) $ \(a, s) =>
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checkC ctx sg s (sub1 ret (Tag a :# tres.type))
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armout <- allEqual armres
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-- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[t/x] ⊳ πΣ₁ + Σ₂
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pure $ InfRes {
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type = sub1 ret t,
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qout = pi * tres.qout + armout
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}
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where
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allEqual : List (QOutput q n) -> m (QOutput q n)
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allEqual [] = pure $ zeroFor ctx
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allEqual lst@(x :: xs) =
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if all (== x) xs then pure x
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else throwError $ BadCaseQtys lst
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infer' ctx sg (fun :% dim) = do
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-- if Ψ | Γ ⊢ σ · f ⇒ Eq [i ⇒ A] l r ⊳ Σ
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InfRes {type, qout} <- inferC ctx sg fun
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ty <- fst <$> expectEq !ask type
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-- then Ψ | Γ ⊢ σ · f p ⇒ A‹p› ⊳ Σ
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pure $ InfRes {type = dsub1 ty dim, qout}
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infer' ctx sg (term :# type) = do
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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checkTypeC ctx type Nothing
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-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ
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qout <- checkC ctx sg term type
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-- then Ψ | Γ ⊢ σ · (s ∷ A) ⇒ A ⊳ Σ
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pure $ InfRes {type, qout}
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