module Quox.Typechecker import public Quox.Typing import public Quox.Equal %default total public export 0 CanTC' : (q : Type) -> (q -> Type) -> (Type -> Type) -> Type CanTC' q isGlobal m = (HasErr q m, MonadReader (Definitions' q isGlobal) m) public export 0 CanTC : (q : Type) -> IsQty q => (Type -> Type) -> Type CanTC q = CanTC' q IsGlobal private popQs : HasErr q m => IsQty q => QOutput q s -> QOutput q (s + n) -> m (QOutput q n) popQs [<] qout = pure qout popQs (pis :< pi) (qout :< rh) = do expectCompatQ rh pi; popQs pis qout private %inline popQ : HasErr q m => IsQty q => q -> QOutput q (S n) -> m (QOutput q n) popQ pi = popQs [< pi] parameters {auto _ : IsQty q} {auto _ : CanTC q m} 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 q d n) -> SQty q -> Term q d n -> Term q d n -> m (CheckResult ctx.dctx q 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 q d n -> Term q d n -> Term q d n -> m () 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 q d n) -> SQty q -> Term q d n -> Term q d n -> m (CheckResult' q 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 q d n -> Term q d n -> Maybe Universe -> m () checkType ctx subj l = ignore $ ifConsistent ctx.dctx $ checkTypeC ctx subj l export covering %inline checkTypeC : TyContext q d n -> Term q d n -> Maybe Universe -> m () checkTypeC ctx subj l = wrapErr (WhileCheckingTy ctx subj l) $ checkTypeNoWrap ctx subj l export covering %inline checkTypeNoWrap : TyContext q d n -> Term q d n -> Maybe Universe -> m () 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 q d n) -> SQty q -> Elim q d n -> m (InferResult ctx.dctx q 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 q d n) -> SQty q -> Elim q d n -> m (InferResult' q 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 q d n -> SQty q -> (subj : Term q d n) -> (0 nc : NotClo subj) => Term q d n -> m (CheckResult' q n) toCheckType ctx sg t ty = do u <- expectTYPE !ask ty expectEqualQ zero sg.fst checkTypeNoWrap ctx t (Just u) pure $ zeroFor ctx private covering check' : TyContext q d n -> SQty q -> (subj : Term q d n) -> (0 nc : NotClo subj) => Term q d n -> m (CheckResult' q 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 !ask ty -- if Ψ | Γ, x : A ⊢ σ · t ⇐ B ⊳ Σ, ρ·x -- with ρ ≤ σπ let qty' = sg.fst * qty qout <- checkC (extendTy 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 !ask 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 !ask ty -- if t ∈ ts unless (t `elem` tags) $ throwError $ 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 !ask ty -- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ qout <- checkC (extendDim ctx) sg body.term ty.term -- if Ψ | Γ ⊢ t‹0› = l : A‹0› equal ctx ty.zero body.zero l -- if Ψ | Γ ⊢ t‹1› = r : A‹1› equal ctx ty.one body.one r -- then Ψ | Γ ⊢ σ · (δ i ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ pure qout 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 q d n -> (subj : Term q d n) -> (0 nc : NotClo subj) => Maybe Universe -> m () 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) $ throwError $ 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 case res.body of Y res => checkTypeC (extendTy arg ctx) res u N res => checkTypeC ctx res u -- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ checkType' ctx t@(Lam {}) u = throwError $ NotType 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 case snd.body of Y snd => checkTypeC (extendTy fst ctx) snd u N snd => checkTypeC ctx snd u -- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ checkType' ctx t@(Pair {}) u = throwError $ NotType t checkType' ctx (Enum _) u = pure () -- Ψ | Γ ⊢₀ {ts} ⇐ Type ℓ checkType' ctx t@(Tag {}) u = throwError $ NotType 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 ctx) t u N t => checkTypeC ctx t u -- if Ψ | Γ ⊢₀ l ⇐ A‹0› check0 ctx t.zero l -- if Ψ | Γ ⊢₀ r ⇐ A‹1› check0 ctx t.one r -- then Ψ | Γ ⊢₀ Eq [i ⇒ A] l r ⇐ Type ℓ checkType' ctx t@(DLam {}) u = throwError $ NotType t checkType' ctx (E e) u = do -- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ infres <- inferC ctx szero e -- if Ψ | Γ ⊢ A' <: A case u of Just u => subtype ctx infres.type (TYPE u) Nothing => ignore $ expectTYPE !ask infres.type -- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ private covering infer' : TyContext q d n -> SQty q -> (subj : Elim q d n) -> (0 nc : NotClo subj) => m (InferResult' q d n) infer' ctx sg (F x) = do -- if π·x : A {≔ s} in global context g <- lookupFree x -- if σ ≤ π expectCompatQ sg.fst g.qty -- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ 𝟎 pure $ InfRes {type = g.type.get, qout = zeroFor ctx} where lookupFree : Name -> m (Definition q) lookupFree x = lookupFree' !ask x 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 : q -> Var n -> TContext q d n -> InferResult' q d n lookupBound pi VZ (ctx :< ty) = InfRes {type = weakT ty, qout = zeroFor ctx :< pi} lookupBound pi (VS i) (ctx :< _) = let InfRes {type, qout} = lookupBound pi i ctx in InfRes {type = weakT 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 !ask 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 + Σ₂ pure $ InfRes { type = sub1 res $ arg :# argty, qout = funres.qout + argout } infer' ctx sg (CasePair pi pair ret body) = do -- if 1 ≤ π expectCompatQ one pi -- 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 pairres.type ctx) ret.term Nothing (tfst, tsnd) <- expectSig !ask 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 bodyctx = extendTyN [< tfst, tsnd.term] ctx bodyty = substCasePairRet pairres.type ret pisg = pi * sg.fst bodyout <- popQs [< pisg, pisg] !(checkC bodyctx sg body.term bodyty) -- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[pair/p] ⊳ πΣ₁ + Σ₂ pure $ InfRes { type = sub1 ret pair, qout = pi * pairres.qout + bodyout } infer' ctx sg (CaseEnum pi t ret arms) {n} = do -- if 1 ≤ π expectCompatQ one pi -- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁ tres <- inferC ctx sg t -- if Ψ | Γ, x : {ts} ⊢₀ A ⇐ Type checkTypeC (extendTy tres.type ctx) ret.term Nothing -- if for each "a ⇒ s" in arms, -- Ψ | Γ ⊢ σ · s ⇐ A[a ∷ {ts}/x] ⊳ Σ₂ -- for fixed Σ₂ armres <- for (SortedMap.toList arms) $ \(a, s) => checkC ctx sg s (sub1 ret (Tag a :# tres.type)) armout <- allEqual armres -- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[t/x] ⊳ πΣ₁ + Σ₂ pure $ InfRes { type = sub1 ret t, qout = pi * tres.qout + armout } where allEqual : List (QOutput q n) -> m (QOutput q n) allEqual [] = pure $ zeroFor ctx allEqual lst@(x :: xs) = if all (== x) xs then pure x else throwError $ BadCaseQtys lst 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 type -- then Ψ | Γ ⊢ σ · f p ⇒ A‹p› ⊳ Σ pure $ InfRes {type = dsub1 ty dim, qout} 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}