156 lines
4.6 KiB
Idris
156 lines
4.6 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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%default total
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private covering %inline
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expectTYPE : HasErr q m => Term q d n -> m Universe
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expectTYPE s =
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case (whnfT s).fst of
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TYPE l => pure l
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_ => throwError $ ExpectedTYPE s
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private covering %inline
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expectPi : HasErr q m => Term q d n ->
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m (q, Term q d n, ScopeTerm q d n)
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expectPi ty =
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case (whnfT ty).fst of
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Pi qty _ arg res => pure (qty, arg, res)
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_ => throwError $ ExpectedPi ty
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private %inline
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expectEqualQ : HasErr q m => Eq q =>
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(expect, actual : q) -> m ()
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expectEqualQ pi rh =
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unless (pi == rh) $ throwError $ ClashQ pi rh
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private %inline
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popQ : HasErr q m => Eq q => q -> QOutput q (S n) -> m (QOutput q n)
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popQ pi (qctx :< rh) = expectEqualQ pi rh $> qctx
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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, qctx $= 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 =>
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{n : Nat} -> q -> Var n -> TyContext q d n -> InferResult q d n
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lookupBound pi VZ (MkTyContext {tctx = _ :< ty, _}) =
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InfRes {type = weakT ty, qout = zero :< 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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subjMult : IsQty q => (sg : SQty q) -> q -> SQty q
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subjMult (Element sg subj) qty =
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if isYes (isZero sg) || isYes (isZero qty)
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then Element zero zeroIsSubj
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else Element sg subj
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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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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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export covering %inline
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check : {d, n : Nat} ->
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(ctx : TyContext q d n) -> (sg : SQty q) ->
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(subj : Term q d n) -> (ty : Term q d n) ->
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m (CheckResult q n)
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check ctx sg subj ty = check' ctx sg (pushSubstsT subj) ty
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export covering %inline
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infer : {d, n : Nat} ->
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(ctx : TyContext q d n) -> (sg : SQty q) ->
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(subj : Elim q d n) ->
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m (InferResult q d n)
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infer ctx sg subj = infer' ctx sg (pushSubstsE subj)
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export covering
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check' : {d, n : Nat} ->
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(ctx : TyContext q d n) -> (sg : SQty q) ->
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(subj : NotCloTerm q d n) -> (ty : Term q d n) ->
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m (CheckResult q n)
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check' ctx sg (Element (TYPE l) _) ty = do
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l' <- expectTYPE ty
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expectEqualQ zero sg.fst
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unless (l < l') $ throwError $ BadUniverse l l'
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pure zero
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check' ctx sg (Element (Pi qty x arg res) _) ty = do
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l <- expectTYPE ty
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expectEqualQ zero sg.fst
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ignore $ check ctx szero arg (TYPE l)
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case res of
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TUsed res =>
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ignore $ check (extendTy arg zero ctx) szero res (TYPE l)
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TUnused res =>
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ignore $ check ctx szero res (TYPE l)
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pure zero
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check' ctx sg (Element (Lam x body) _) ty = do
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(qty, arg, res) <- expectPi ty
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-- [todo] do this properly?
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let body = fromScopeTerm body; res = fromScopeTerm res
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qout <- check (extendTy arg (sg.fst * qty) ctx) sg body res
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popQ qty qout
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check' ctx sg (Element (E e) _) ty = do
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infres <- infer ctx sg e
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ignore $ check ctx szero ty (TYPE UAny)
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subT infres.type ty
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pure infres.qout
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export covering
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infer' : {d, n : Nat} ->
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(ctx : TyContext q d n) -> (sg : SQty q) ->
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(subj : NotCloElim q d n) ->
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m (InferResult q d n)
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infer' ctx sg (Element (F x) _) = do
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Just g <- asks $ lookup x | Nothing => throwError $ NotInScope x
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when (isZero g) $ expectEqualQ sg.fst zero
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pure $ InfRes {type = g.type.get, qout = zero}
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infer' ctx sg (Element (B i) _) =
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pure $ lookupBound sg.fst i ctx
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infer' ctx sg (Element (fun :@ arg) _) = do
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funres <- infer ctx sg fun
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(qty, argty, res) <- expectPi funres.type
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let sg' = subjMult sg qty
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argout <- check ctx sg' arg argty
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pure $ InfRes {type = fromScopeTerm res //. ((arg :# argty) ::: id),
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qout = funres.qout + argout}
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infer' ctx sg (Element (tm :# ty) _) = do
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ignore $ check ctx szero ty (TYPE UAny)
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qout <- check ctx sg tm ty
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pure $ InfRes {type = ty, qout}
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