module Quox.Typechecker import public Quox.Syntax import public Quox.Typing import public Quox.Equal import public Control.Monad.Either import Decidable.Decidable import Data.SnocVect %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 => SnocVect s q -> 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] private %inline tail : TyContext q d (S n) -> TyContext q d n tail = {tctx $= tail} private %inline weakI : IsQty q => InferResult q d n -> InferResult q d (S n) weakI = {type $= weakT, qout $= (:< zero)} private lookupBound : IsQty q => q -> Var n -> TyContext q d n -> InferResult q d n lookupBound pi VZ (MkTyContext {tctx = tctx :< ty, _}) = InfRes {type = weakT ty, qout = (zero <$ tctx) :< pi} lookupBound pi (VS i) ctx = weakI $ lookupBound pi i (tail ctx) private %inline lookupFree : CanTC' q g m => Name -> m (Definition' q g) lookupFree x = lookupFree' !ask x parameters {auto _ : IsQty q} {auto _ : CanTC q m} mutual -- [todo] it seems like the options here for dealing with substitutions are -- to either push them or parametrise the whole typechecker over ambient -- substitutions. both of them seem like the same amount of work for the -- computer but pushing is less work for the me ||| "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. export covering %inline check : TyContext q d n -> SQty q -> Term q d n -> Term q d n -> m (CheckResult q n) check ctx sg subj ty = let Element subj nc = pushSubsts subj in check' ctx sg subj nc 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 ||| "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. export covering %inline infer : TyContext q d n -> SQty q -> Elim q d n -> m (InferResult q d n) infer ctx sg subj = let Element subj nc = pushSubsts subj in infer' ctx sg subj nc export 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 (TYPE k) _ ty = do -- if 𝓀 < ℓ then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type ℓ l <- expectTYPE !ask ty expectEqualQ zero sg.fst unless (k < l) $ throwError $ BadUniverse k l pure $ zeroFor ctx check' ctx sg (Pi qty _ arg res) _ ty = do l <- expectTYPE !ask ty expectEqualQ zero sg.fst -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ check0 ctx arg (TYPE l) -- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ case res of TUsed res => check0 (extendTy arg ctx) res (TYPE l) TUnused res => check0 ctx res (TYPE l) -- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ pure $ zeroFor ctx 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 <- check (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 (Sig _ fst snd) _ ty = do l <- expectTYPE !ask ty expectEqualQ zero sg.fst -- if Ψ | Γ ⊢₀ A ⇐ Type ℓ check0 ctx fst (TYPE l) -- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ case snd of TUsed snd => check0 (extendTy fst ctx) snd (TYPE l) TUnused snd => check0 ctx snd (TYPE l) -- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ pure $ zeroFor ctx check' ctx sg (Pair fst snd) _ ty = do (tfst, tsnd) <- expectSig !ask ty -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ₁ qfst <- check ctx sg fst tfst let tsnd = sub1 tsnd (fst :# tfst) -- if Ψ | Γ ⊢ σ · t ⇐ B[s] ⊳ Σ₂ qsnd <- check ctx sg snd tsnd -- then Ψ | Γ ⊢ σ · (s, t) ⇐ (x : A) × B ⊳ Σ₁ + Σ₂ pure $ qfst + qsnd check' ctx sg (Eq i t l r) _ ty = do u <- expectTYPE !ask ty expectEqualQ zero sg.fst -- if Ψ, i | Γ ⊢₀ A ⇐ Type ℓ case t of DUsed t => check0 (extendDim ctx) t (TYPE u) DUnused t => check0 ctx t (TYPE 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 pure $ zeroFor ctx check' ctx sg (DLam i body) _ ty = do (ty, l, r) <- expectEq !ask ty -- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ qout <- check (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 · (λᴰi ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ pure qout check' ctx sg (E e) _ ty = do -- if Ψ | Γ ⊢ σ · e ⇒ A' ⊳ Σ infres <- infer ctx sg e -- if Ψ | Γ ⊢ A' <: A subtype ctx infres.type ty -- then Ψ | Γ ⊢ σ · e ⇐ A ⊳ Σ pure infres.qout export 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} 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 infer' ctx sg (fun :@ arg) _ = do -- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁ funres <- infer ctx sg fun (qty, argty, res) <- expectPi !ask funres.type -- if Ψ | Γ ⊢ σ ⨴ π · s ⇐ A ⊳ Σ₂ argout <- check 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 ⊢ 1 · pair ⇒ (x : A) × B ⊳ Σ₁ pairres <- infer ctx sone pair check0 (extendTy pairres.type ctx) ret.term (TYPE UAny) (tfst, tsnd) <- expectSig !ask pairres.type -- if Ψ | Γ, x : A, y : B ⊢ σ · body ⇐ ret[(x, y)] ⊳ Σ₂, ρ₁·x, ρ₂·y -- with ρ₁, ρ₂ ≤ π let bodyctx = extendTyN [< tfst, tsnd.term] ctx bodyty = substCasePairRet pairres.type ret bodyout <- check bodyctx sg body.term bodyty >>= popQs [< pi, pi] -- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[pair] ⊳ πΣ₁ + Σ₂ pure $ InfRes { type = sub1 ret pair, qout = pi * pairres.qout + bodyout } infer' ctx sg (fun :% dim) _ = do -- if Ψ | Γ ⊢ σ · f ⇒ Eq [i ⇒ A] l r ⊳ Σ InfRes {type, qout} <- infer ctx sg fun (ty, _, _) <- 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 check0 ctx type (TYPE UAny) -- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ qout <- check ctx sg term type -- then Ψ | Γ ⊢ σ · (s ∷ A) ⇒ A ⊳ Σ pure $ InfRes {type, qout}