module Quox.Typechecker import public Quox.Typing import public Quox.Equal import Data.List import Data.SnocVect import Data.List1 import Quox.EffExtra %default total public export 0 TCEff : List (Type -> Type) TCEff = [ErrorEff, DefsReader] public export 0 TC : Type -> Type TC = Eff TCEff export runTC : Definitions -> TC a -> Either Error a runTC defs = extract . runExcept . runReaderAt DEFS defs export popQs : Has ErrorEff fs => QContext s -> QOutput (s + n) -> Eff fs (QOutput n) popQs [<] qout = pure qout popQs (pis :< pi) (qout :< rh) = do expectCompatQ rh pi; popQs pis qout export %inline popQ : Has ErrorEff fs => Qty -> QOutput (S n) -> Eff fs (QOutput n) popQ pi = popQs [< pi] export lubs1 : List1 (QOutput n) -> Maybe (QOutput n) lubs1 ([<] ::: _) = Just [<] lubs1 ((qs :< p) ::: pqs) = let (qss, ps) = unzip $ map unsnoc pqs in [|lubs1 (qs ::: qss) :< foldlM lub p ps|] export lubs : TyContext d n -> List (QOutput n) -> Maybe (QOutput n) lubs ctx [] = Just $ zeroFor ctx lubs ctx (x :: xs) = lubs1 $ x ::: xs ||| context extension with no names or quantities private CtxExtension0' : Nat -> Nat -> Nat -> Type CtxExtension0' s d n = Context (Term d . (+ n)) s private addNames0 : Context (Term d . (+ n)) s -> NContext s -> CtxExtension d n (s + n) addNames0 [<] [<] = [<] addNames0 (ts :< t) (xs :< x) = addNames0 ts xs :< (Zero, x, t) export typecaseTel : (k : TyConKind) -> Universe -> CtxExtension0' (arity k) d n typecaseTel k u = case k of KTYPE => [<] -- A : ★ᵤ, B : 0.A → ★ᵤ KPi => [< TYPE u, Arr Zero (BVT 0) (TYPE u)] KSig => [< TYPE u, Arr Zero (BVT 0) (TYPE u)] KEnum => [<] -- A₀ : ★ᵤ, A₁ : ★ᵤ, A : (A₀ ≡ A₁ : ★ᵤ), L : A₀, R : A₀ KEq => [< TYPE u, TYPE u, Eq0 (TYPE u) (BVT 1) (BVT 0), BVT 2, BVT 2] KNat => [<] -- A : ★ᵤ KBOX => [< TYPE u] mutual ||| "Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ" ||| ||| `check ctx sg subj ty` checks that in the context `ctx`, the term ||| `subj` has the type `ty`, with quantity `sg`. if so, returns the ||| quantities of all bound variables that it used. ||| ||| if the dimension context is inconsistent, then return `Nothing`, without ||| doing any further work. export covering %inline check : (ctx : TyContext d n) -> SQty -> Term d n -> Term d n -> TC (CheckResult ctx.dctx n) check ctx sg subj ty = ifConsistent ctx.dctx $ checkC ctx sg subj ty ||| "Ψ | Γ ⊢₀ s ⇐ A" ||| ||| `check0 ctx subj ty` checks a term (as `check`) in a zero context. export covering %inline check0 : TyContext d n -> Term d n -> Term d n -> TC () check0 ctx tm ty = ignore $ check ctx szero tm ty -- the output will always be 𝟎 because the subject quantity is 0 ||| `check`, assuming the dimension context is consistent export covering %inline checkC : (ctx : TyContext d n) -> SQty -> Term d n -> Term d n -> TC (CheckResult' n) checkC ctx sg subj ty = wrapErr (WhileChecking ctx sg.fst subj ty) $ let Element subj nc = pushSubsts subj in check' ctx sg subj ty ||| "Ψ | Γ ⊢₀ s ⇐ ★ᵢ" ||| ||| `checkType ctx subj ty` checks a type (in a zero context). sometimes the ||| universe doesn't matter, only that a term is _a_ type, so it is optional. export covering %inline checkType : TyContext d n -> Term d n -> Maybe Universe -> TC () checkType ctx subj l = ignore $ ifConsistent ctx.dctx $ checkTypeC ctx subj l export covering %inline checkTypeC : TyContext d n -> Term d n -> Maybe Universe -> TC () checkTypeC ctx subj l = wrapErr (WhileCheckingTy ctx subj l) $ checkTypeNoWrap ctx subj l export covering %inline checkTypeNoWrap : TyContext d n -> Term d n -> Maybe Universe -> TC () checkTypeNoWrap ctx subj l = let Element subj nc = pushSubsts subj in checkType' ctx subj l ||| "Ψ | Γ ⊢ σ · e ⇒ A ⊳ Σ" ||| ||| `infer ctx sg subj` infers the type of `subj` in the context `ctx`, ||| and returns its type and the bound variables it used. ||| ||| if the dimension context is inconsistent, then return `Nothing`, without ||| doing any further work. export covering %inline infer : (ctx : TyContext d n) -> SQty -> Elim d n -> TC (InferResult ctx.dctx d n) infer ctx sg subj = ifConsistent ctx.dctx $ inferC ctx sg subj ||| `infer`, assuming the dimension context is consistent export covering %inline inferC : (ctx : TyContext d n) -> SQty -> Elim d n -> TC (InferResult' d n) inferC ctx sg subj = wrapErr (WhileInferring ctx sg.fst subj) $ let Element subj nc = pushSubsts subj in infer' ctx sg subj private covering toCheckType : TyContext d n -> SQty -> (subj : Term d n) -> (0 nc : NotClo subj) => Term d n -> TC (CheckResult' n) toCheckType ctx sg t ty = do u <- expectTYPE !defs ctx ty expectEqualQ Zero sg.fst checkTypeNoWrap ctx t (Just u) pure $ zeroFor ctx private covering check' : TyContext d n -> SQty -> (subj : Term d n) -> (0 nc : NotClo subj) => Term d n -> TC (CheckResult' n) check' ctx sg t@(TYPE _) ty = toCheckType ctx sg t ty check' ctx sg t@(Pi {}) ty = toCheckType ctx sg t ty check' ctx sg (Lam body) ty = do (qty, arg, res) <- expectPi !defs ctx ty -- if Ψ | Γ, x : A ⊢ σ · t ⇐ B ⊳ Σ, ρ·x -- with ρ ≤ σπ let qty' = sg.fst * qty qout <- checkC (extendTy qty' body.name arg ctx) sg body.term res.term -- then Ψ | Γ ⊢ σ · (λx ⇒ t) ⇐ (π·x : A) → B ⊳ Σ popQ qty' qout check' ctx sg t@(Sig {}) ty = toCheckType ctx sg t ty check' ctx sg (Pair fst snd) ty = do (tfst, tsnd) <- expectSig !defs ctx ty -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ₁ qfst <- checkC ctx sg fst tfst let tsnd = sub1 tsnd (fst :# tfst) -- if Ψ | Γ ⊢ σ · t ⇐ B[s] ⊳ Σ₂ qsnd <- checkC ctx sg snd tsnd -- then Ψ | Γ ⊢ σ · (s, t) ⇐ (x : A) × B ⊳ Σ₁ + Σ₂ pure $ qfst + qsnd check' ctx sg t@(Enum _) ty = toCheckType ctx sg t ty check' ctx sg (Tag t) ty = do tags <- expectEnum !defs ctx ty -- if t ∈ ts unless (t `elem` tags) $ throw $ TagNotIn t tags -- then Ψ | Γ ⊢ σ · t ⇐ {ts} ⊳ 𝟎 pure $ zeroFor ctx check' ctx sg t@(Eq {}) ty = toCheckType ctx sg t ty check' ctx sg (DLam body) ty = do (ty, l, r) <- expectEq !defs ctx ty let ctx' = extendDim body.name ctx ty = ty.term body = body.term -- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ qout <- checkC ctx' sg body ty -- if Ψ, i, i = 0 | Γ ⊢ t = l : A equal (eqDim (BV 0) (K Zero) ctx') ty body (dweakT 1 l) -- if Ψ, i, i = 1 | Γ ⊢ t = r : A equal (eqDim (BV 0) (K One) ctx') ty body (dweakT 1 r) -- then Ψ | Γ ⊢ σ · (δ i ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ pure qout check' ctx sg Nat ty = toCheckType ctx sg Nat ty check' ctx sg Zero ty = do expectNat !defs ctx ty pure $ zeroFor ctx check' ctx sg (Succ n) ty = do expectNat !defs ctx ty checkC ctx sg n Nat check' ctx sg t@(BOX {}) ty = toCheckType ctx sg t ty check' ctx sg (Box val) ty = do (q, ty) <- expectBOX !defs ctx ty -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ valout <- checkC ctx sg val ty -- then Ψ | Γ ⊢ σ · [s] ⇐ [π.A] ⊳ πΣ pure $ q * valout check' ctx sg (E e) ty = do -- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ infres <- inferC ctx sg e -- if Ψ | Γ ⊢ A' <: A subtype ctx infres.type ty -- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ pure infres.qout private covering checkType' : TyContext d n -> (subj : Term d n) -> (0 nc : NotClo subj) => Maybe Universe -> TC () checkType' ctx (TYPE k) u = do -- if 𝓀 < ℓ then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type ℓ case u of Just l => unless (k < l) $ throw $ BadUniverse k l Nothing => pure () checkType' ctx (Pi qty arg res) u = do -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ checkTypeC ctx arg u -- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ checkTypeScope ctx arg res u -- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ checkType' ctx t@(Lam {}) u = throw $ NotType ctx t checkType' ctx (Sig fst snd) u = do -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ checkTypeC ctx fst u -- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ checkTypeScope ctx fst snd u -- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ checkType' ctx t@(Pair {}) u = throw $ NotType ctx t checkType' ctx (Enum _) u = pure () -- Ψ | Γ ⊢₀ {ts} ⇐ Type ℓ checkType' ctx t@(Tag {}) u = throw $ NotType ctx t checkType' ctx (Eq t l r) u = do -- if Ψ, i | Γ ⊢₀ A ⇐ Type ℓ case t.body of Y t' => checkTypeC (extendDim t.name ctx) t' u N t' => checkTypeC ctx t' u -- if Ψ | Γ ⊢₀ l ⇐ A‹0› check0 ctx l t.zero -- if Ψ | Γ ⊢₀ r ⇐ A‹1› check0 ctx r t.one -- then Ψ | Γ ⊢₀ Eq [i ⇒ A] l r ⇐ Type ℓ checkType' ctx t@(DLam {}) u = throw $ NotType ctx t checkType' ctx Nat u = pure () checkType' ctx Zero u = throw $ NotType ctx Zero checkType' ctx t@(Succ _) u = throw $ NotType ctx t checkType' ctx (BOX q ty) u = checkType ctx ty u checkType' ctx t@(Box _) u = throw $ NotType ctx t checkType' ctx (E e) u = do -- if Ψ | Γ ⊢₀ E ⇒ Type ℓ infres <- inferC ctx szero e -- if Ψ | Γ ⊢ Type ℓ <: Type 𝓀 case u of Just u => subtype ctx infres.type (TYPE u) Nothing => ignore $ expectTYPE !defs ctx infres.type -- then Ψ | Γ ⊢₀ E ⇐ Type 𝓀 private covering check0ScopeN : {s : Nat} -> TyContext d n -> CtxExtension0' s d n -> ScopeTermN s d n -> Term d n -> TC () check0ScopeN ctx ext (S _ (N body)) ty = check0 ctx body ty check0ScopeN ctx ext (S names (Y body)) ty = check0 (extendTyN (addNames0 ext names) ctx) body (weakT s ty) private covering check0Scope : TyContext d n -> Term d n -> ScopeTerm d n -> Term d n -> TC () check0Scope ctx t = check0ScopeN ctx [< t] private covering checkTypeScopeN : TyContext d n -> CtxExtension0' s d n -> ScopeTermN s d n -> Maybe Universe -> TC () checkTypeScopeN ctx ext (S _ (N body)) u = checkType ctx body u checkTypeScopeN ctx ext (S names (Y body)) u = checkType (extendTyN (addNames0 ext names) ctx) body u private covering checkTypeScope : TyContext d n -> Term d n -> ScopeTerm d n -> Maybe Universe -> TC () checkTypeScope ctx s = checkTypeScopeN ctx [< s] private covering infer' : TyContext d n -> SQty -> (subj : Elim d n) -> (0 nc : NotClo subj) => TC (InferResult' d n) infer' ctx sg (F x) = do -- if π·x : A {≔ s} in global context g <- lookupFree x !defs -- if σ ≤ π expectCompatQ sg.fst g.qty.fst -- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ 𝟎 let Val d = ctx.dimLen; Val n = ctx.termLen pure $ InfRes {type = g.type, qout = zeroFor ctx} infer' ctx sg (B i) = -- if x : A ∈ Γ -- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ (𝟎, σ·x, 𝟎) pure $ lookupBound sg.fst i ctx.tctx where lookupBound : forall n. Qty -> Var n -> TContext d n -> InferResult' d n lookupBound pi VZ (ctx :< type) = InfRes {type = weakT 1 type, qout = zeroFor ctx :< pi} lookupBound pi (VS i) (ctx :< _) = let InfRes {type, qout} = lookupBound pi i ctx in InfRes {type = weakT 1 type, qout = qout :< Zero} infer' ctx sg (fun :@ arg) = do -- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁ funres <- inferC ctx sg fun (qty, argty, res) <- expectPi !defs ctx funres.type -- if Ψ | Γ ⊢ σ ⨴ π · s ⇐ A ⊳ Σ₂ argout <- checkC ctx (subjMult sg qty) arg argty -- then Ψ | Γ ⊢ σ · f s ⇒ B[s] ⊳ Σ₁ + πΣ₂ pure $ InfRes { type = sub1 res $ arg :# argty, qout = funres.qout + qty * argout } infer' ctx sg (CasePair pi pair ret body) = do -- no check for 1 ≤ π, since pairs have a single constructor. -- e.g. at 0 the components are also 0 in the body -- -- if Ψ | Γ ⊢ σ · pair ⇒ (x : A) × B ⊳ Σ₁ pairres <- inferC ctx sg pair -- if Ψ | Γ, p : (x : A) × B ⊢₀ ret ⇐ Type checkTypeC (extendTy Zero ret.name pairres.type ctx) ret.term Nothing (tfst, tsnd) <- expectSig !defs ctx pairres.type -- if Ψ | Γ, x : A, y : B ⊢ σ · body ⇐ -- ret[(x, y) ∷ (x : A) × B/p] ⊳ Σ₂, ρ₁·x, ρ₂·y -- with ρ₁, ρ₂ ≤ πσ let [< x, y] = body.names pisg = pi * sg.fst bodyctx = extendTyN [< (pisg, x, tfst), (pisg, y, tsnd.term)] ctx bodyty = substCasePairRet pairres.type ret bodyout <- checkC bodyctx sg body.term bodyty >>= popQs [< pisg, pisg] -- then Ψ | Γ ⊢ σ · caseπ ⋯ ⇒ ret[pair/p] ⊳ πΣ₁ + Σ₂ pure $ InfRes { type = sub1 ret pair, qout = pi * pairres.qout + bodyout } infer' ctx sg (CaseEnum pi t ret arms) {d, n} = do -- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁ tres <- inferC ctx sg t ttags <- expectEnum !defs ctx tres.type -- if 1 ≤ π, OR there is only zero or one option unless (length (SortedSet.toList ttags) <= 1) $ expectCompatQ One pi -- if Ψ | Γ, x : {ts} ⊢₀ A ⇐ Type checkTypeC (extendTy Zero ret.name tres.type ctx) ret.term Nothing -- if for each "a ⇒ s" in arms, -- Ψ | Γ ⊢ σ · s ⇐ A[a ∷ {ts}/x] ⊳ Σᵢ -- with Σ₂ = lubs Σᵢ let arms = SortedMap.toList arms let armTags = SortedSet.fromList $ map fst arms unless (ttags == armTags) $ throw $ BadCaseEnum ttags armTags armres <- for arms $ \(a, s) => checkC ctx sg s (sub1 ret (Tag a :# tres.type)) let Just armout = lubs ctx armres | _ => throw $ BadQtys "case arms" ctx $ zipWith (\qs, (t, rhs) => (qs, Tag t)) armres arms pure $ InfRes { type = sub1 ret t, qout = pi * tres.qout + armout } infer' ctx sg (CaseNat pi pi' n ret zer suc) = do -- if 1 ≤ π expectCompatQ One pi -- if Ψ | Γ ⊢ σ · n ⇒ ℕ ⊳ Σn nres <- inferC ctx sg n expectNat !defs ctx nres.type -- if Ψ | Γ, n : ℕ ⊢₀ A ⇐ Type checkTypeC (extendTy Zero ret.name Nat ctx) ret.term Nothing -- if Ψ | Γ ⊢ σ · zer ⇐ A[0 ∷ ℕ/n] ⊳ Σz zerout <- checkC ctx sg zer (sub1 ret (Zero :# Nat)) -- 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 !defs 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 !defs 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 !defs 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}