512 lines
18 KiB
Idris
512 lines
18 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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import Data.List
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import Data.SnocVect
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import Data.List1
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import Quox.EffExtra
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%default total
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public export
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0 TCEff : List (Type -> Type)
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TCEff = [ErrorEff, DefsReader]
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public export
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0 TC : Type -> Type
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TC = Eff TCEff
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export
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runTC : Definitions -> TC a -> Either Error a
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runTC defs = extract . runExcept . runReader defs
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export
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popQs : Has ErrorEff fs => QOutput s -> QOutput (s + n) -> Eff fs (QOutput 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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export %inline
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popQ : Has ErrorEff fs => Qty -> QOutput (S n) -> Eff fs (QOutput n)
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popQ pi = popQs [< pi]
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export
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lubs1 : List1 (QOutput n) -> Maybe (QOutput n)
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lubs1 ([<] ::: _) = Just [<]
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lubs1 ((qs :< p) ::: pqs) =
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let (qss, ps) = unzip $ map unsnoc pqs in
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[|lubs1 (qs ::: qss) :< foldlM lub p ps|]
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export
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lubs : TyContext d n -> List (QOutput n) -> Maybe (QOutput n)
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lubs ctx [] = Just $ zeroFor ctx
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lubs ctx (x :: xs) = lubs1 $ x ::: xs
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||| context extension with no names or quantities
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private
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CtxExtension0' : Nat -> Nat -> Nat -> Type
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CtxExtension0' s d n = Context (Term d . (+ n)) s
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private
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addNames0 : Context (Term d . (+ n)) s -> NContext s -> CtxExtension d n (s + n)
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addNames0 [<] [<] = [<]
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addNames0 (ts :< t) (xs :< x) = addNames0 ts xs :< (Zero, x, t)
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export
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typecaseTel : (k : TyConKind) -> Universe -> CtxExtension0' (arity k) d n
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typecaseTel k u = case k of
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KTYPE => [<]
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-- A : ★ᵤ, B : 0.A → ★ᵤ
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KPi => [< TYPE u, Arr Zero (BVT 0) (TYPE u)]
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KSig => [< TYPE u, Arr Zero (BVT 0) (TYPE u)]
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KEnum => [<]
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-- A₀ : ★ᵤ, A₁ : ★ᵤ, A : (A₀ ≡ A₁ : ★ᵤ), L : A₀, R : A₀
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KEq => [< TYPE u, TYPE u, Eq0 (TYPE u) (BVT 1) (BVT 0), BVT 2, BVT 2]
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KNat => [<]
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-- A : ★ᵤ
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KBOX => [< TYPE u]
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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 d n) -> SQty -> Term d n -> Term d n ->
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TC (CheckResult ctx.dctx 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 d n -> Term d n -> Term d n -> TC ()
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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 d n) -> SQty -> Term d n -> Term d n ->
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TC (CheckResult' 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 d n -> Term d n -> Maybe Universe -> TC ()
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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 d n -> Term d n -> Maybe Universe -> TC ()
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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 d n -> Term d n -> Maybe Universe -> TC ()
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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 d n) -> SQty -> Elim d n ->
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TC (InferResult ctx.dctx 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 d n) -> SQty -> Elim d n ->
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TC (InferResult' 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 d n -> SQty ->
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(subj : Term d n) -> (0 nc : NotClo subj) => Term d n ->
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TC (CheckResult' n)
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toCheckType ctx sg t ty = do
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u <- expectTYPE !ask ctx 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 d n -> SQty ->
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(subj : Term d n) -> (0 nc : NotClo subj) => Term d n ->
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TC (CheckResult' 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 ctx 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 qty' body.name 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 ctx 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 ctx ty
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-- if t ∈ ts
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unless (t `elem` tags) $ throw $ 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 ctx ty
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-- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ
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qout <- checkC (extendDim body.name 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 Nat ty = toCheckType ctx sg Nat ty
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check' ctx sg Zero ty = do
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expectNat !ask ctx ty
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pure $ zeroFor ctx
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check' ctx sg (Succ n) ty = do
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expectNat !ask ctx ty
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checkC ctx sg n Nat
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check' ctx sg t@(BOX {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Box val) ty = do
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(q, ty) <- expectBOX !ask ctx ty
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-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ
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valout <- checkC ctx sg val ty
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-- then Ψ | Γ ⊢ σ · [s] ⇐ [π.A] ⊳ πΣ
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pure $ q * valout
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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 d n ->
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(subj : Term d n) -> (0 nc : NotClo subj) =>
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Maybe Universe -> TC ()
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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) $ throw $ 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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checkTypeScope ctx arg 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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throw $ NotType ctx 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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checkTypeScope ctx fst 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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throw $ NotType ctx 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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throw $ NotType ctx 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 t.name 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 l t.zero
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-- if Ψ | Γ ⊢₀ r ⇐ A‹1›
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check0 ctx r t.one
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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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throw $ NotType ctx t
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checkType' ctx Nat u = pure ()
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checkType' ctx Zero u = throw $ NotType ctx Zero
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checkType' ctx t@(Succ _) u = throw $ NotType ctx t
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checkType' ctx (BOX q ty) u = checkType ctx ty u
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checkType' ctx t@(Box _) u = throw $ NotType ctx t
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checkType' ctx (E e) u = do
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-- if Ψ | Γ ⊢₀ E ⇒ Type ℓ
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infres <- inferC ctx szero e
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-- if Ψ | Γ ⊢ Type ℓ <: Type 𝓀
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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 ctx infres.type
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-- then Ψ | Γ ⊢₀ E ⇐ Type 𝓀
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private covering
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check0ScopeN : {s : Nat} ->
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TyContext d n -> CtxExtension0' s d n ->
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ScopeTermN s d n -> Term d n -> TC ()
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check0ScopeN ctx ext (S _ (N body)) ty = check0 ctx body ty
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check0ScopeN ctx ext (S names (Y body)) ty =
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check0 (extendTyN (addNames0 ext names) ctx) body (weakT s ty)
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private covering
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check0Scope : TyContext d n -> Term d n ->
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ScopeTerm d n -> Term d n -> TC ()
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check0Scope ctx t = check0ScopeN ctx [< t]
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private covering
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checkTypeScopeN : TyContext d n -> CtxExtension0' s d n ->
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ScopeTermN s d n -> Maybe Universe -> TC ()
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checkTypeScopeN ctx ext (S _ (N body)) u = checkType ctx body u
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checkTypeScopeN ctx ext (S names (Y body)) u =
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checkType (extendTyN (addNames0 ext names) ctx) body u
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private covering
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checkTypeScope : TyContext d n -> Term d n ->
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ScopeTerm d n -> Maybe Universe -> TC ()
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checkTypeScope ctx s = checkTypeScopeN ctx [< s]
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private covering
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infer' : TyContext d n -> SQty ->
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(subj : Elim d n) -> (0 nc : NotClo subj) =>
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TC (InferResult' 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 !ask
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-- if σ ≤ π
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expectCompatQ sg.fst g.qty.fst
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-- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ 𝟎
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let Val d = ctx.dimLen; Val n = ctx.termLen
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pure $ InfRes {type = g.type, qout = zeroFor ctx}
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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 : forall n. Qty -> Var n -> TContext d n -> InferResult' d n
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lookupBound pi VZ (ctx :< type) =
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InfRes {type = weakT 1 type, 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 1 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 ctx 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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-- no check for 1 ≤ π, since pairs have a single constructor.
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-- e.g. at 0 the components are also 0 in the body
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--
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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 Zero ret.name pairres.type ctx) ret.term Nothing
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(tfst, tsnd) <- expectSig !ask ctx 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 [< x, y] = body.names
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pisg = pi * sg.fst
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bodyctx = extendTyN [< (pisg, x, tfst), (pisg, y, tsnd.term)] ctx
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bodyty = substCasePairRet pairres.type ret
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bodyout <- checkC bodyctx sg body.term bodyty >>= popQs [< pisg, pisg]
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-- then Ψ | Γ ⊢ σ · caseπ ⋯ ⇒ 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 + bodyout
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}
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infer' ctx sg (CaseEnum pi t ret arms) {d, n} = do
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-- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁
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tres <- inferC ctx sg t
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ttags <- expectEnum !ask ctx tres.type
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-- if 1 ≤ π, OR there is only zero or one option
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unless (length (SortedSet.toList ttags) <= 1) $ expectCompatQ One pi
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-- if Ψ | Γ, x : {ts} ⊢₀ A ⇐ Type
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checkTypeC (extendTy Zero ret.name 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] ⊳ Σᵢ
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-- with Σ₂ = lubs Σᵢ
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let arms = SortedMap.toList arms
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let armTags = SortedSet.fromList $ map fst arms
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unless (ttags == armTags) $ throw $ BadCaseEnum ttags armTags
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armres <- for arms $ \(a, s) =>
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checkC ctx sg s (sub1 ret (Tag a :# tres.type))
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let Just armout = lubs ctx armres
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| _ => throw $ BadQtys "case arms" ctx $
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zipWith (\qs, (t, rhs) => (qs, Tag t)) armres arms
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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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infer' ctx sg (CaseNat pi pi' n ret zer suc) = do
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-- if 1 ≤ π
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expectCompatQ One pi
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-- if Ψ | Γ ⊢ σ · n ⇒ ℕ ⊳ Σn
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nres <- inferC ctx sg n
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expectNat !ask ctx nres.type
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-- if Ψ | Γ, n : ℕ ⊢₀ A ⇐ Type
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checkTypeC (extendTy Zero ret.name Nat ctx) ret.term Nothing
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-- if Ψ | Γ ⊢ σ · zer ⇐ A[0 ∷ ℕ/n] ⊳ Σz
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zerout <- checkC ctx sg zer (sub1 ret (Zero :# Nat))
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-- if Ψ | Γ, n : ℕ, ih : A ⊢ σ · suc ⇐ A[succ p ∷ ℕ/n] ⊳ Σs, ρ₁.p, ρ₂.ih
|
||
-- with ρ₂ ≤ π'σ, (ρ₁ + ρ₂) ≤ πσ
|
||
let [< p, ih] = suc.names
|
||
pisg = pi * sg.fst
|
||
sucCtx = extendTyN [< (pisg, p, Nat), (pi', ih, ret.term)] ctx
|
||
sucType = substCaseSuccRet ret
|
||
sucout :< qp :< qih <- checkC sucCtx sg suc.term sucType
|
||
expectCompatQ qih (pi' * sg.fst)
|
||
-- [fixme] better error here
|
||
expectCompatQ (qp + qih) pisg
|
||
-- then Ψ | Γ ⊢ caseπ ⋯ ⇒ A[n] ⊳ πΣn + Σz + ωΣs
|
||
pure $ InfRes {
|
||
type = sub1 ret n,
|
||
qout = pi * nres.qout + zerout + Any * sucout
|
||
}
|
||
|
||
infer' ctx sg (CaseBox pi box ret body) = do
|
||
-- if Ψ | Γ ⊢ σ · b ⇒ [ρ.A] ⊳ Σ₁
|
||
boxres <- inferC ctx sg box
|
||
(q, ty) <- expectBOX !ask ctx boxres.type
|
||
-- if Ψ | Γ, x : [ρ.A] ⊢₀ R ⇐ Type
|
||
checkTypeC (extendTy Zero ret.name boxres.type ctx) ret.term Nothing
|
||
-- if Ψ | Γ, x : A ⊢ t ⇐ R[[x] ∷ [ρ.A/x]] ⊳ Σ₂, ς·x
|
||
-- with ς ≤ ρπσ
|
||
let qpisg = q * pi * sg.fst
|
||
bodyCtx = extendTy qpisg body.name ty ctx
|
||
bodyType = substCaseBoxRet ty ret
|
||
bodyout <- checkC bodyCtx sg body.term bodyType >>= popQ qpisg
|
||
-- then Ψ | Γ ⊢ caseπ ⋯ ⇒ R[b/x] ⊳ Σ₁ + Σ₂
|
||
pure $ InfRes {
|
||
type = sub1 ret box,
|
||
qout = boxres.qout + bodyout
|
||
}
|
||
|
||
infer' ctx sg (fun :% dim) = do
|
||
-- if Ψ | Γ ⊢ σ · f ⇒ Eq [𝑖 ⇒ A] l r ⊳ Σ
|
||
InfRes {type, qout} <- inferC ctx sg fun
|
||
ty <- fst <$> expectEq !ask ctx type
|
||
-- then Ψ | Γ ⊢ σ · f p ⇒ A‹p/𝑖› ⊳ Σ
|
||
pure $ InfRes {type = dsub1 ty dim, qout}
|
||
|
||
infer' ctx sg (Coe (S [< i] ty) p q val) = do
|
||
let ty = ty.term
|
||
checkType (extendDim i ctx) ty Nothing
|
||
qout <- checkC ctx sg val (ty // one p)
|
||
pure $ InfRes {type = ty // one q, qout}
|
||
|
||
infer' ctx sg (Comp ty p q val r (S [< j0] val0) (S [< j1] val1)) = do
|
||
checkType ctx ty Nothing
|
||
qout <- checkC ctx sg val ty
|
||
let ty' = dweakT 1 ty; val' = dweakT 1 val; p' = weakD 1 p
|
||
ctx0 = extendDim j0 $ eqDim r (K Zero) ctx
|
||
val0 = val0.term
|
||
qout0 <- check ctx0 sg val0 ty'
|
||
equal (eqDim (BV 0) p' ctx0) ty' val0 val'
|
||
let ctx1 = extendDim j0 $ eqDim r (K One) ctx
|
||
val1 = val1.term
|
||
qout1 <- check ctx1 sg val1 ty'
|
||
equal (eqDim (BV 0) p' ctx1) ty' val1 val'
|
||
let qout0' = toMaybe $ map (, val0 // one p) qout0
|
||
qout1' = toMaybe $ map (, val1 // one p) qout1
|
||
qouts = (qout, val) :: catMaybes [qout0', qout1']
|
||
let Just qout = lubs ctx $ map fst qouts
|
||
| Nothing => throw $ BadQtys "composition" ctx qouts
|
||
pure $ InfRes {type = ty, qout}
|
||
|
||
infer' ctx sg (TypeCase ty ret arms def) = do
|
||
-- if σ = 0
|
||
expectEqualQ Zero sg.fst
|
||
-- if Ψ, Γ ⊢₀ e ⇒ Type u
|
||
u <- expectTYPE !ask ctx . type =<< inferC ctx szero ty
|
||
-- if Ψ, Γ ⊢₀ C ⇐ Type (non-dependent return type)
|
||
checkTypeC ctx ret Nothing
|
||
-- if Ψ, Γ' ⊢₀ A ⇐ C for each rhs A
|
||
for_ allKinds $ \k =>
|
||
for_ (lookupPrecise k arms) $ \(S names t) =>
|
||
check0 (extendTyN (addNames0 (typecaseTel k u) names) ctx)
|
||
t.term (weakT (arity k) ret)
|
||
-- then Ψ, Γ ⊢₀ type-case ⋯ ⇒ C
|
||
pure $ InfRes {type = ret, qout = zeroFor ctx}
|
||
|
||
infer' ctx sg (term :# type) = do
|
||
-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
|
||
checkTypeC ctx type Nothing
|
||
-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ
|
||
qout <- checkC ctx sg term type
|
||
-- then Ψ | Γ ⊢ σ · (s ∷ A) ⇒ A ⊳ Σ
|
||
pure $ InfRes {type, qout}
|