quox/lib/Quox/Typechecker.idr

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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 ⊢ t0 = l : A0
equal ctx ty.zero body.zero l
-- if Ψ | Γ ⊢ t1 = r : A1
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 < then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type
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
checkTypeC ctx arg u
-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type
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
checkType' ctx t@(Lam {}) u =
throwError $ NotType t
checkType' ctx (Sig fst snd) u = do
-- if Ψ | Γ ⊢₀ A ⇐ Type
checkTypeC ctx fst u
-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type
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
checkType' ctx t@(Pair {}) u =
throwError $ NotType t
checkType' ctx (Enum _) u = pure ()
-- Ψ | Γ ⊢₀ {ts} ⇐ Type
checkType' ctx t@(Tag {}) u =
throwError $ NotType t
checkType' ctx (Eq t l r) u = do
-- if Ψ, i | Γ ⊢₀ A ⇐ Type
case t.body of
Y t => checkTypeC (extendDim ctx) t u
N t => checkTypeC ctx t u
-- if Ψ | Γ ⊢₀ l ⇐ A0
check0 ctx t.zero l
-- if Ψ | Γ ⊢₀ r ⇐ A1
check0 ctx t.one r
-- then Ψ | Γ ⊢₀ Eq [i ⇒ A] l r ⇐ Type
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 ⇒ Ap ⊳ Σ
pure $ InfRes {type = dsub1 ty dim, qout}
infer' ctx sg (term :# type) = do
-- if Ψ | Γ ⊢₀ A ⇐ Type
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}