566 lines
20 KiB
Idris
566 lines
20 KiB
Idris
module Quox.Typechecker
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import public Quox.Typing
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import public Quox.Equal
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import Quox.Displace
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import Quox.Pretty
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import Data.List
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import Data.SnocVect
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import Data.List1
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import Quox.EffExtra
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%default total
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public export
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0 TC : List (Type -> Type)
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TC = [ErrorEff, DefsReader, NameGen, Log]
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parameters (loc : Loc)
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export
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popQs : Has ErrorEff fs => QContext s -> QOutput (s + n) ->
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Eff fs (QOutput n)
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popQs [<] qout = pure qout
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popQs (pis :< pi) (qout :< rh) = do expectCompatQ loc rh pi; popQs pis qout
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export %inline
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popQ : Has ErrorEff fs => Qty -> QOutput (S n) -> Eff fs (QOutput n)
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popQ pi = popQs [< pi]
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export
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lubs1 : List1 (QOutput n) -> QOutput n
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lubs1 ([<] ::: _) = [<]
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lubs1 ((qs :< p) ::: pqs) =
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let (qss, ps) = unzip $ map unsnoc pqs in
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lubs1 (qs ::: qss) :< foldl lub p ps
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export
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lubs : TyContext d n -> List (QOutput n) -> QOutput n
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lubs ctx [] = zeroFor ctx
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lubs ctx (x :: xs) = lubs1 $ x ::: xs
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private
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prettyTermTC : {opts : LayoutOpts} ->
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TyContext d n -> Term d n -> Eff Pretty (Doc opts)
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prettyTermTC ctx s = prettyTerm ctx.dnames ctx.tnames s
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private
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checkLogs : String -> TyContext d n -> SQty ->
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Term d n -> Maybe (Term d n) -> Eff TC ()
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checkLogs fun ctx sg subj ty = do
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let tyDoc = delay $ maybe (text "none") (runPretty . prettyTermTC ctx) ty
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sayMany "check" subj.loc
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[10 :> text fun,
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95 :> hsep ["ctx =", runPretty $ prettyTyContext ctx],
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95 :> hsep ["sg =", runPretty $ prettyQty sg.qty],
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10 :> hsep ["subj =", runPretty $ prettyTermTC ctx subj],
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10 :> hsep ["ty =", tyDoc]]
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mutual
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||| "Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ"
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|||
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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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|||
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||| if the dimension context is inconsistent, then return `Nothing`, without
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||| doing any further work.
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export covering %inline
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check : (ctx : TyContext d n) -> SQty -> Term d n -> Term d n ->
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Eff TC (CheckResult ctx.dctx n)
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check ctx sg subj ty =
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ifConsistentElse ctx.dctx
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(do checkLogs "check" ctx sg subj (Just ty)
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checkC ctx sg subj ty)
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(say "check" 20 subj.loc "check: 0=1")
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||| "Ψ | Γ ⊢₀ s ⇐ A"
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|||
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||| `check0 ctx subj ty` checks a term (as `check`) in a zero context.
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export covering %inline
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check0 : TyContext d n -> Term d n -> Term d n -> Eff TC ()
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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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||| `check`, assuming the dimension context is consistent
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export covering %inline
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checkC : (ctx : TyContext d n) -> SQty -> Term d n -> Term d n ->
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Eff TC (CheckResult' n)
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checkC ctx sg subj ty =
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wrapErr (WhileChecking ctx sg subj ty) $
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checkCNoWrap ctx sg subj ty
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export covering %inline
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checkCNoWrap : (ctx : TyContext d n) -> SQty -> Term d n -> Term d n ->
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Eff TC (CheckResult' n)
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checkCNoWrap ctx sg subj ty =
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let Element subj nc = pushSubsts subj in
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check' ctx sg subj ty
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||| "Ψ | Γ ⊢₀ s ⇐ ★ᵢ"
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|||
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||| `checkType ctx subj ty` checks a type (in a zero context). sometimes the
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||| universe doesn't matter, only that a term is _a_ type, so it is optional.
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export covering %inline
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checkType : TyContext d n -> Term d n -> Maybe Universe -> Eff TC ()
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checkType ctx subj l = do
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let univ = TYPE <$> l <*> pure noLoc
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ignore $ ifConsistentElse ctx.dctx
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(do checkLogs "checkType" ctx SZero subj univ
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checkTypeC ctx subj l)
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(say "check" 20 subj.loc "checkType: 0=1")
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export covering %inline
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checkTypeC : TyContext d n -> Term d n -> Maybe Universe -> Eff TC ()
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checkTypeC ctx subj l =
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wrapErr (WhileCheckingTy ctx subj l) $ checkTypeNoWrap ctx subj l
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export covering %inline
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checkTypeNoWrap : TyContext d n -> Term d n -> Maybe Universe -> Eff TC ()
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checkTypeNoWrap ctx subj l =
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let Element subj nc = pushSubsts subj in
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checkType' ctx subj l
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||| "Ψ | Γ ⊢ σ · e ⇒ A ⊳ Σ"
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|||
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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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|||
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||| if the dimension context is inconsistent, then return `Nothing`, without
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||| doing any further work.
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export covering %inline
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infer : (ctx : TyContext d n) -> SQty -> Elim d n ->
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Eff TC (InferResult ctx.dctx d n)
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infer ctx sg subj = do
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ifConsistentElse ctx.dctx
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(do checkLogs "infer" ctx sg (E subj) Nothing
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inferC ctx sg subj)
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(say "check" 20 subj.loc "infer: 0=1")
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||| `infer`, assuming the dimension context is consistent
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export covering %inline
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inferC : (ctx : TyContext d n) -> SQty -> Elim d n ->
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Eff TC (InferResult' d n)
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inferC ctx sg subj =
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wrapErr (WhileInferring ctx sg subj) $
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let Element subj nc = pushSubsts subj in
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infer' ctx sg subj
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private covering
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toCheckType : TyContext d n -> SQty ->
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(subj : Term d n) -> (0 nc : NotClo subj) => Term d n ->
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Eff TC (CheckResult' n)
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toCheckType ctx sg t ty = do
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u <- expectTYPE !(askAt DEFS) ctx sg ty.loc ty
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expectEqualQ t.loc Zero sg.qty
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checkTypeNoWrap ctx t (Just u)
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pure $ zeroFor ctx
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private covering
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check' : TyContext d n -> SQty ->
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(subj : Term d n) -> (0 nc : NotClo subj) => Term d n ->
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Eff TC (CheckResult' n)
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check' ctx sg t@(TYPE {}) ty = toCheckType ctx sg t ty
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check' ctx sg t@(IOState {}) ty = toCheckType ctx sg t ty
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check' ctx sg t@(Pi {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Lam body loc) ty = do
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(qty, arg, res) <- expectPi !(askAt DEFS) ctx SZero ty.loc 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.qty * qty
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qout <- checkC (extendTy qty' body.name 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 loc qty' qout
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check' ctx sg t@(Sig {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Pair fst snd loc) ty = do
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(tfst, tsnd) <- expectSig !(askAt DEFS) ctx SZero ty.loc ty
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-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ₁
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qfst <- checkC ctx sg fst tfst
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let tsnd = sub1 tsnd (Ann fst tfst fst.loc)
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-- if Ψ | Γ ⊢ σ · t ⇐ B[s] ⊳ Σ₂
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qsnd <- checkC 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 t@(Enum {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Tag t loc) ty = do
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tags <- expectEnum !(askAt DEFS) ctx SZero ty.loc ty
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-- if t ∈ ts
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unless (t `elem` tags) $ throw $ TagNotIn loc t tags
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-- then Ψ | Γ ⊢ σ · t ⇐ {ts} ⊳ 𝟎
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pure $ zeroFor ctx
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check' ctx sg t@(Eq {}) ty = toCheckType ctx sg t ty
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check' ctx sg (DLam body loc) ty = do
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(ty, l, r) <- expectEq !(askAt DEFS) ctx SZero ty.loc ty
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let ctx' = extendDim body.name ctx
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ty = ty.term
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body = body.term
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-- if Ψ, i | Γ ⊢ σ · t ⇐ A ⊳ Σ
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qout <- checkC ctx' sg body ty
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-- if Ψ, i, i = 0 | Γ ⊢ t = l : A
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let ctx0 = eqDim (B VZ loc) (K Zero loc) ctx'
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lift $ equal loc ctx0 sg ty body $ dweakT 1 l
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-- if Ψ, i, i = 1 | Γ ⊢ t = r : A
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let ctx1 = eqDim (B VZ loc) (K One loc) ctx'
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lift $ equal loc ctx1 sg ty body $ dweakT 1 r
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-- then Ψ | Γ ⊢ σ · (δ i ⇒ t) ⇐ Eq [i ⇒ A] l r ⊳ Σ
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pure qout
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check' ctx sg t@(NAT {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Nat {}) ty = do
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expectNAT !(askAt DEFS) ctx SZero ty.loc ty
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pure $ zeroFor ctx
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check' ctx sg (Succ n {}) ty = do
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expectNAT !(askAt DEFS) ctx SZero ty.loc ty
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checkC ctx sg n ty
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check' ctx sg t@(STRING {}) ty = toCheckType ctx sg t ty
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check' ctx sg t@(Str s {}) ty = do
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expectSTRING !(askAt DEFS) ctx SZero ty.loc ty
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pure $ zeroFor ctx
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check' ctx sg t@(BOX {}) ty = toCheckType ctx sg t ty
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check' ctx sg (Box val loc) ty = do
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(q, ty) <- expectBOX !(askAt DEFS) ctx SZero ty.loc ty
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-- if Ψ | Γ ⊢ σ ⨴ π · s ⇐ A ⊳ Σ
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valout <- checkC ctx (subjMult sg q) val ty
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-- then Ψ | Γ ⊢ σ · [s] ⇐ [π.A] ⊳ πΣ
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pure $ q * valout
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check' ctx sg (Let qty rhs body loc) ty = do
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eres <- inferC ctx (subjMult sg qty) rhs
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let sqty = sg.qty * qty
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qout <- checkC (extendTyLet sqty body.name eres.type (E rhs) ctx)
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sg body.term (weakT 1 ty)
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>>= popQ loc sqty
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pure $ qty * eres.qout + 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 <- inferC ctx sg e
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-- if Ψ | Γ ⊢ A' <: A
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lift $ subtype e.loc ctx 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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private covering
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checkType' : TyContext d n ->
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(subj : Term d n) -> (0 nc : NotClo subj) =>
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Maybe Universe -> Eff TC ()
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checkType' ctx (TYPE k loc) u = do
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-- if 𝓀 < ℓ then Ψ | Γ ⊢₀ Type 𝓀 ⇐ Type ℓ
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case u of
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Just l => unless (k < l) $ throw $ BadUniverse loc k l
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Nothing => pure ()
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checkType' ctx (IOState loc) u = pure ()
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-- Ψ | Γ ⊢₀ IOState ⇒ Type ℓ
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checkType' ctx (Pi qty arg res _) u = do
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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checkTypeC ctx arg u
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-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
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checkTypeScope ctx arg res u
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-- then Ψ | Γ ⊢₀ (π·x : A) → B ⇐ Type ℓ
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checkType' ctx t@(Lam {}) u =
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throw $ NotType t.loc ctx t
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checkType' ctx (Sig fst snd _) u = do
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-- if Ψ | Γ ⊢₀ A ⇐ Type ℓ
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checkTypeC ctx fst u
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-- if Ψ | Γ, x : A ⊢₀ B ⇐ Type ℓ
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checkTypeScope ctx fst snd u
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-- then Ψ | Γ ⊢₀ (x : A) × B ⇐ Type ℓ
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checkType' ctx t@(Pair {}) u =
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throw $ NotType t.loc ctx t
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checkType' ctx (Enum {}) u = pure ()
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-- Ψ | Γ ⊢₀ {ts} ⇐ Type ℓ
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checkType' ctx t@(Tag {}) u =
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throw $ NotType t.loc ctx t
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checkType' ctx (Eq t l r _) u = do
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-- if Ψ, i | Γ ⊢₀ A ⇐ Type ℓ
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case t.body of
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Y t' => checkTypeC (extendDim t.name ctx) t' u
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N t' => checkTypeC ctx t' u
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-- if Ψ | Γ ⊢₀ l ⇐ A‹0›
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check0 ctx l t.zero
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-- if Ψ | Γ ⊢₀ r ⇐ A‹1›
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check0 ctx r t.one
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-- then Ψ | Γ ⊢₀ Eq [i ⇒ A] l r ⇐ Type ℓ
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checkType' ctx t@(DLam {}) u =
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throw $ NotType t.loc ctx t
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checkType' ctx (NAT {}) u = pure ()
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checkType' ctx t@(Nat {}) u = throw $ NotType t.loc ctx t
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checkType' ctx t@(Succ {}) u = throw $ NotType t.loc ctx t
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checkType' ctx (STRING loc) u = pure ()
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-- Ψ | Γ ⊢₀ STRING ⇒ Type ℓ
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checkType' ctx t@(Str {}) u = throw $ NotType t.loc ctx t
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checkType' ctx (BOX q ty _) u = checkType ctx ty u
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checkType' ctx t@(Box {}) u = throw $ NotType t.loc ctx t
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checkType' ctx (Let qty rhs body loc) u = do
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expectEqualQ loc qty Zero
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ety <- inferC ctx SZero rhs
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checkType (extendTy Zero body.name ety.type ctx) body.term u
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checkType' ctx (E e) u = do
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-- if Ψ | Γ ⊢₀ E ⇒ Type ℓ
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infres <- inferC ctx SZero e
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-- if Ψ | Γ ⊢ Type ℓ <: Type 𝓀
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case u of
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Just u => lift $ subtype e.loc ctx infres.type (TYPE u e.loc)
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Nothing => ignore $ expectTYPE !(askAt DEFS) ctx SZero e.loc infres.type
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-- then Ψ | Γ ⊢₀ E ⇐ Type 𝓀
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private covering
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checkTypeScope : TyContext d n -> Term d n ->
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ScopeTerm d n -> Maybe Universe -> Eff TC ()
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checkTypeScope ctx s (S _ (N body)) u = checkType ctx body u
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checkTypeScope ctx s (S [< x] (Y body)) u =
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checkType (extendTy Zero x s ctx) body u
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private covering
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infer' : TyContext d n -> SQty ->
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(subj : Elim d n) -> (0 nc : NotClo subj) =>
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Eff TC (InferResult' d n)
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infer' ctx sg (F x u loc) = do
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-- if π·x : A {≔ s} in global context
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g <- lookupFree x loc !(askAt DEFS)
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-- if σ ≤ π
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expectCompatQ loc sg.qty g.qty.qty
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-- then Ψ | Γ ⊢ σ · x ⇒ A ⊳ 𝟎
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pure $ InfRes {
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type = g.typeWithAt ctx.dimLen ctx.termLen u,
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qout = zeroFor ctx
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}
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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.qty i ctx.tctx
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where
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lookupBound : forall n. Qty -> Var n -> TContext d n -> InferResult' d n
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lookupBound pi VZ (ctx :< var) =
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InfRes {type = weakT 1 var.type, qout = zeroFor ctx :< pi}
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lookupBound pi (VS i) (ctx :< _) =
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let InfRes {type, qout} = lookupBound pi i ctx in
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InfRes {type = weakT 1 type, qout = qout :< Zero}
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|
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infer' ctx sg (App fun arg loc) = do
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-- if Ψ | Γ ⊢ σ · f ⇒ (π·x : A) → B ⊳ Σ₁
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funres <- inferC ctx sg fun
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(qty, argty, res) <- expectPi !(askAt DEFS) ctx SZero fun.loc funres.type
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-- if Ψ | Γ ⊢ σ ⨴ π · s ⇐ A ⊳ Σ₂
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argout <- checkC ctx (subjMult sg qty) arg argty
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-- then Ψ | Γ ⊢ σ · f s ⇒ B[s] ⊳ Σ₁ + πΣ₂
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pure $ InfRes {
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type = sub1 res $ Ann arg argty arg.loc,
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qout = funres.qout + qty * argout
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}
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infer' ctx sg (CasePair pi pair ret body loc) = do
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-- no check for 1 ≤ π, since pairs have a single constructor.
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-- e.g. at 0 the components are also 0 in the body
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--
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-- if Ψ | Γ ⊢ σ · pair ⇒ (x : A) × B ⊳ Σ₁
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pairres <- inferC ctx sg pair
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-- if Ψ | Γ, p : (x : A) × B ⊢₀ ret ⇐ Type
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checkTypeC (extendTy Zero ret.name pairres.type ctx) ret.term Nothing
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(tfst, tsnd) <- expectSig !(askAt DEFS) ctx SZero pair.loc pairres.type
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-- if Ψ | Γ, x : A, y : B ⊢ σ · body ⇐
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-- ret[(x, y) ∷ (x : A) × B/p] ⊳ Σ₂, ρ₁·x, ρ₂·y
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-- with ρ₁, ρ₂ ≤ πσ
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let [< x, y] = body.names
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pisg = pi * sg.qty
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bodyctx = extendTyN [< (pisg, x, tfst), (pisg, y, tsnd.term)] ctx
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bodyty = substCasePairRet body.names pairres.type ret
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bodyout <- checkC bodyctx sg body.term bodyty >>=
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popQs loc [< pisg, pisg]
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-- then Ψ | Γ ⊢ σ · caseπ ⋯ ⇒ ret[pair/p] ⊳ 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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|
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infer' ctx sg (Fst pair loc) = do
|
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-- if Ψ | Γ ⊢ σ · e ⇒ (x : A) × B ⊳ Σ
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pairres <- inferC ctx sg pair
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(tfst, _) <- expectSig !(askAt DEFS) ctx SZero pair.loc pairres.type
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-- then Ψ | Γ ⊢ σ · fst e ⇒ A ⊳ ωΣ
|
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pure $ InfRes {
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type = tfst,
|
||
qout = Any * pairres.qout
|
||
}
|
||
|
||
infer' ctx sg (Snd pair loc) = do
|
||
-- if Ψ | Γ ⊢ σ · e ⇒ (x : A) × B ⊳ Σ
|
||
pairres <- inferC ctx sg pair
|
||
(_, tsnd) <- expectSig !(askAt DEFS) ctx SZero pair.loc pairres.type
|
||
-- then Ψ | Γ ⊢ σ · snd e ⇒ B[fst e/x] ⊳ ωΣ
|
||
pure $ InfRes {
|
||
type = sub1 tsnd (Fst pair loc),
|
||
qout = Any * pairres.qout
|
||
}
|
||
|
||
infer' ctx sg (CaseEnum pi t ret arms loc) {d, n} = do
|
||
-- if Ψ | Γ ⊢ σ · t ⇒ {ts} ⊳ Σ₁
|
||
tres <- inferC ctx sg t
|
||
ttags <- expectEnum !(askAt DEFS) ctx SZero t.loc tres.type
|
||
-- if 1 ≤ π, OR there is only zero or one option
|
||
unless (length (SortedSet.toList ttags) <= 1) $ expectCompatQ loc 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 loc ttags armTags
|
||
armres <- for arms $ \(a, s) =>
|
||
checkC ctx sg s $ sub1 ret $ Ann (Tag a s.loc) tres.type s.loc
|
||
pure $ InfRes {
|
||
type = sub1 ret t,
|
||
qout = pi * tres.qout + lubs ctx armres
|
||
}
|
||
|
||
infer' ctx sg (CaseNat pi pi' n ret zer suc loc) = do
|
||
-- if 1 ≤ π
|
||
expectCompatQ loc One pi
|
||
-- if Ψ | Γ ⊢ σ · n ⇒ ℕ ⊳ Σn
|
||
nres <- inferC ctx sg n
|
||
let nat = nres.type
|
||
expectNAT !(askAt DEFS) ctx SZero n.loc nat
|
||
-- 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 $ Ann (Zero zer.loc) nat zer.loc
|
||
-- if Ψ | Γ, n : ℕ, ih : A ⊢ σ · suc ⇐ A[succ p ∷ ℕ/n] ⊳ Σs, ρ.p, ς.ih
|
||
-- with ς ≤ π'σ, (ρ + ς) ≤ πσ
|
||
let [< p, ih] = suc.names
|
||
pisg = pi * sg.qty
|
||
sucCtx = extendTyN [< (pisg, p, NAT p.loc), (pi', ih, ret.term)] ctx
|
||
sucType = substCaseSuccRet suc.names ret
|
||
sucout :< qp :< qih <- checkC sucCtx sg suc.term sucType
|
||
expectCompatQ loc qih (pi' * sg.qty)
|
||
-- [fixme] better error here
|
||
expectCompatQ loc (qp + qih) pisg
|
||
-- if ς = 0, then Σb = lubs(Σz, Σs), otherwise Σb = Σz + ωςΣs
|
||
let bodyout = case qih of
|
||
Zero => lubs ctx [zerout, sucout]
|
||
_ => zerout + Any * sucout
|
||
-- then Ψ | Γ ⊢ caseπ ⋯ ⇒ A[n] ⊳ πΣn + Σb
|
||
pure $ InfRes {
|
||
type = sub1 ret n,
|
||
qout = pi * nres.qout + bodyout
|
||
}
|
||
|
||
infer' ctx sg (CaseBox pi box ret body loc) = do
|
||
-- if Ψ | Γ ⊢ σ · b ⇒ [ρ.A] ⊳ Σ₁
|
||
boxres <- inferC ctx sg box
|
||
(rh, ty) <- expectBOX !(askAt DEFS) ctx SZero box.loc 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 ⊢ σ · t ⇐ R[[x] ∷ [ρ.A/x]] ⊳ Σ₂, ς·x
|
||
-- with ς ≤ ρπσ
|
||
let rhpisg = rh * pi * sg.qty
|
||
bodyCtx = extendTy rhpisg body.name ty ctx
|
||
bodyType = substCaseBoxRet body.name ty ret
|
||
bodyout <- checkC bodyCtx sg body.term bodyType >>= popQ loc rhpisg
|
||
-- then Ψ | Γ ⊢ caseπ ⋯ ⇒ R[b/x] ⊳ Σ₁ + Σ₂
|
||
pure $ InfRes {
|
||
type = sub1 ret box,
|
||
qout = boxres.qout + bodyout
|
||
}
|
||
|
||
infer' ctx sg (DApp fun dim loc) = do
|
||
-- if Ψ | Γ ⊢ σ · f ⇒ Eq [𝑖 ⇒ A] l r ⊳ Σ
|
||
InfRes {type, qout} <- inferC ctx sg fun
|
||
ty <- fst <$> expectEq !(askAt DEFS) ctx SZero fun.loc type
|
||
-- then Ψ | Γ ⊢ σ · f p ⇒ A‹p/𝑖› ⊳ Σ
|
||
pure $ InfRes {type = dsub1 ty dim, qout}
|
||
|
||
infer' ctx sg (Coe ty p q val loc) = do
|
||
-- if Ψ, 𝑖 | Γ ⊢₀ A ⇐ Type _
|
||
checkType (extendDim ty.name ctx) ty.term Nothing
|
||
-- if Ψ | Γ ⊢ σ · s ⇐ A‹p/𝑖› ⊳ Σ
|
||
qout <- checkC ctx sg val $ dsub1 ty p
|
||
-- then Ψ | Γ ⊢ σ · coe (𝑖 ⇒ A) @p @q s ⇒ A‹q/𝑖› ⊳ Σ
|
||
pure $ InfRes {type = dsub1 ty q, qout}
|
||
|
||
infer' ctx sg (Comp ty p q val r (S [< j0] val0) (S [< j1] val1) loc) = do
|
||
-- if Ψ | Γ ⊢₀ A ⇐ Type _
|
||
checkType ctx ty Nothing
|
||
-- if Ψ | Γ ⊢ σ · s ⇐ A ⊳ Σ
|
||
qout <- checkC ctx sg val ty
|
||
-- if Ψ, 𝑗, 𝑖=0 | Γ ⊢ σ · t₀ ⇐ A ⊳ Σ₀
|
||
-- Ψ, 𝑗, 𝑖=0, 𝑗=p | Γ ⊢ t₀ = s ⇐ A
|
||
let ty' = dweakT 1 ty; val' = dweakT 1 val; p' = weakD 1 p
|
||
ctx0 = extendDim j0 $ eqDim r (K Zero j0.loc) ctx
|
||
val0 = getTerm val0
|
||
qout0 <- check ctx0 sg val0 ty'
|
||
lift $ equal loc (eqDim (B VZ p.loc) p' ctx0) sg ty' val0 val'
|
||
-- if Ψ, 𝑗, 𝑖=1 | Γ ⊢ σ · t₁ ⇐ A ⊳ Σ₁
|
||
-- Ψ, 𝑗, 𝑖=1, 𝑗=p | Γ ⊢ t₁ = s ⇐ A
|
||
let ctx1 = extendDim j1 $ eqDim r (K One j1.loc) ctx
|
||
val1 = getTerm val1
|
||
qout1 <- check ctx1 sg val1 ty'
|
||
-- if Σ = Σ₀ = Σ₁
|
||
lift $ equal loc (eqDim (B VZ p.loc) p' ctx1) sg ty' val1 val'
|
||
let qouts = qout :: catMaybes [toMaybe qout0, toMaybe qout1]
|
||
-- then Ψ | Γ ⊢ comp A @p @q s @r {0 𝑗 ⇒ t₀; 1 𝑗 ⇒ t₁} ⇒ A ⊳ Σ
|
||
pure $ InfRes {type = ty, qout = lubs ctx qouts}
|
||
|
||
infer' ctx sg (TypeCase ty ret arms def loc) = do
|
||
-- if σ = 0
|
||
expectEqualQ loc Zero sg.qty
|
||
-- if Ψ, Γ ⊢₀ e ⇒ Type u
|
||
u <- inferC ctx SZero ty >>=
|
||
expectTYPE !(askAt DEFS) ctx SZero ty.loc . type
|
||
-- 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 (typecaseTel k names u) ctx)
|
||
(getTerm t) (weakT (arity k) ret)
|
||
-- then Ψ, Γ ⊢₀ type-case ⋯ ⇒ C
|
||
pure $ InfRes {type = ret, qout = zeroFor ctx}
|
||
|
||
infer' ctx sg (Ann term type loc) = 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}
|