248 lines
8.4 KiB
Idris
248 lines
8.4 KiB
Idris
module Quox.Typechecker
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import public Quox.Syntax
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import public Quox.Typing
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import public Quox.Equal
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import public Control.Monad.Either
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import Decidable.Decidable
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import Data.SnocVect
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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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SnocVect s q -> 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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private %inline
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tail : TyContext q d (S n) -> TyContext q d n
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tail = {tctx $= tail}
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private %inline
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weakI : IsQty q => InferResult q d n -> InferResult q d (S n)
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weakI = {type $= weakT, qout $= (:< zero)}
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private
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lookupBound : IsQty q => q -> Var n -> TyContext q d n -> InferResult q d n
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lookupBound pi VZ (MkTyContext {tctx = tctx :< ty, _}) =
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InfRes {type = weakT ty, qout = (zero <$ tctx) :< pi}
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lookupBound pi (VS i) ctx =
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weakI $ lookupBound pi i (tail ctx)
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private %inline
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lookupFree : CanTC' q g m => Name -> m (Definition' q g)
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lookupFree x = lookupFree' !ask x
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||| ``sg `subjMult` pi`` is zero if either argument is, otherwise it
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||| is equal to `sg`. (written as "σ ⨴ π" to emphasise its left bias.)
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|||
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||| only certain quantities can occur for a typing judgement to avoid losing
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||| subject reduction [@qtt, §2.3], which is why this is not just `sg*pi`.
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private %inline
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subjMult : IsQty q => SQty q -> q -> SQty q
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subjMult sg pi = if isYes $ isZero pi then szero else sg
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parameters {auto _ : IsQty q} {auto _ : CanTC q m}
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mutual
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-- [todo] it seems like the options here for dealing with substitutions are
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-- to either push them or parametrise the whole typechecker over ambient
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-- substitutions. both of them seem like the same amount of work for the
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-- computer but pushing is less work for the me
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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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export covering %inline
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check : 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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check ctx sg subj ty =
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let Element subj nc = pushSubsts subj in
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check' ctx sg subj nc ty
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||| `check0 ctx subj ty` checks a term 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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||| `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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export covering %inline
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infer : TyContext q d n -> SQty q -> Elim q d n -> m (InferResult q d n)
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infer ctx sg subj =
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let Element subj nc = pushSubsts subj in
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infer' ctx sg subj nc
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export 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 (TYPE k) _ ty = do
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-- if 𝓀 < ℓ then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type ℓ
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l <- expectTYPE !ask ty
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expectEqualQ zero sg.fst
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unless (k < l) $ throwError $ BadUniverse k l
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pure $ zeroFor ctx
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check' ctx sg (Pi qty _ arg res) _ ty = do
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l <- expectTYPE !ask ty
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expectEqualQ zero sg.fst
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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check0 ctx arg (TYPE l)
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-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
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case res of
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TUsed res => check0 (extendTy arg ctx) res (TYPE l)
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TUnused res => check0 ctx res (TYPE l)
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-- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ
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pure $ zeroFor ctx
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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 <- check (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 (Sig _ fst snd) _ ty = do
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l <- expectTYPE !ask ty
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expectEqualQ zero sg.fst
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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check0 ctx fst (TYPE l)
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-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
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case snd of
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TUsed snd => check0 (extendTy fst ctx) snd (TYPE l)
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TUnused snd => check0 ctx snd (TYPE l)
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-- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ
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pure $ zeroFor ctx
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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 <- check 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 <- check 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 (Eq i t l r) _ ty = do
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u <- expectTYPE !ask ty
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expectEqualQ zero sg.fst
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-- if Ψ, i | Γ ⊢₀ A ⇐ Type ℓ
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case t of
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DUsed t => check0 (extendDim ctx) t (TYPE u)
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DUnused t => check0 ctx t (TYPE 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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pure $ zeroFor ctx
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check' ctx sg (DLam i 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 <- check (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.dctx ctx.tctx ty.zero body.zero l
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-- if Ψ | Γ ⊢ t‹1› = r : A‹1›
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equal ctx.dctx ctx.tctx ty.one body.one r
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-- then Ψ | Γ ⊢ σ · (λᴰi ⇒ 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 <- infer ctx sg e
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-- if Ψ | Γ ⊢ A' <: A
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subtype ctx.dctx ctx.tctx 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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export 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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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
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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 <- infer 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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-- (σ ⨴ 0 = 0; σ ⨴ π = σ otherwise)
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argout <- check 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 ⊢ 1 · pair ⇒ (x : A) × B ⊳ Σ₁
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pairres <- infer ctx sone pair
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check0 (extendTy pairres.type ctx) ret.term (TYPE UAny)
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(tfst, tsnd) <- expectSig !ask pairres.type
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-- if Ψ | Γ, x : A, y : B ⊢ σ · body ⇐ ret[(x, y)] ⊳ Σ₂, ρ₁·x, ρ₂·y
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-- with ρ₁, ρ₂ ≤ π
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let bodyctx = extendTyN [< tfst, tsnd.term] ctx
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bodyty = substCasePairRet pairres.type ret
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bodyout <- check bodyctx sg body.term bodyty >>= popQs [< pi, pi]
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-- then Ψ | Γ ⊢ σ · case ⋯ ⇒ ret[pair] ⊳ 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 (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} <- infer ctx sg fun
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(ty, _, _) <- 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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check0 ctx type (TYPE UAny)
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-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ
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qout <- check 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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