quox/lib/Quox/Typechecker.idr

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module Quox.Typechecker
import public Quox.Syntax
import public Quox.Typing
import public Quox.Equal
import public Control.Monad.Either
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%default total
private covering %inline
expectTYPE : MonadError Error m => Term d n -> m Universe
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expectTYPE s =
case (whnfT s).fst of
TYPE l => pure l
_ => throwError $ ExpectedTYPE s
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private covering %inline
expectPi : MonadError Error m => Term d n ->
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m (Qty, Term d n, ScopeTerm d n)
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expectPi ty =
case (whnfT ty).fst of
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Pi qty _ arg res => pure (qty, arg, res)
_ => throwError $ ExpectedPi ty
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private %inline
expectEqualQ : MonadError Error m =>
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(expect, actual : Qty) -> m ()
expectEqualQ pi rh =
unless (pi == rh) $ throwError $ ClashQ pi rh
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private %inline
popQ : MonadError Error m => Qty -> QOutput (S n) -> m (QOutput n)
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popQ pi (qctx :< rh) = expectEqualQ pi rh $> qctx
private %inline
tail : TyContext d (S n) -> TyContext d n
tail = {tctx $= tail, qctx $= tail}
private %inline
weakI : InferResult d n -> InferResult d (S n)
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weakI = {type $= weakT, qout $= (:< zero)}
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private
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lookupBound : {n : Nat} -> Qty -> Var n -> TyContext d n -> InferResult d n
lookupBound pi VZ (MkTyContext {tctx = _ :< ty, _}) =
InfRes {type = weakT ty, qout = zero :< pi}
lookupBound pi (VS i) ctx =
weakI $ lookupBound pi i (tail ctx)
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private %inline
subjMult : Qty -> Qty -> Subset Qty IsSubj
subjMult sg qty =
if sg == Zero || qty == Zero
then Element Zero %search
else Element One %search
public export
CanTC : (Type -> Type) -> Type
CanTC m = (MonadError Error m, MonadReader Definitions m)
parameters {auto _ : CanTC m}
mutual
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-- [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
export covering %inline
check : {d, n : Nat} ->
(ctx : TyContext d n) -> (sg : Qty) -> (0 _ : IsSubj sg) =>
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(subj : Term d n) -> (ty : Term d n) ->
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m (CheckResult n)
check ctx sg subj ty = check' ctx sg (pushSubstsT subj) ty
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export covering %inline
infer : {d, n : Nat} ->
(ctx : TyContext d n) -> (sg : Qty) -> (0 _ : IsSubj sg) =>
(subj : Elim d n) ->
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m (InferResult d n)
infer ctx sg subj = infer' ctx sg (pushSubstsE subj)
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export covering
check' : {d, n : Nat} ->
(ctx : TyContext d n) -> (sg : Qty) -> (0 _ : IsSubj sg) =>
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(subj : NotCloTerm d n) -> (ty : Term d n) ->
m (CheckResult n)
check' ctx sg (Element (TYPE l) _) ty = do
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l' <- expectTYPE ty
expectEqualQ zero sg
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
expectEqualQ zero sg
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ignore $ check ctx zero arg (TYPE l)
case res of
TUsed res => ignore $ check (extendTy arg zero ctx) zero res (TYPE l)
TUnused res => ignore $ check ctx zero res (TYPE l)
pure zero
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?
let body = fromScopeTerm body; res = fromScopeTerm res
qout <- check (extendTy arg (sg * qty) ctx) sg body res
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popQ qty qout
check' ctx sg (Element (E e) _) ty = do
infres <- infer ctx sg e
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ignore $ check ctx zero ty (TYPE UAny)
subT infres.type ty
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pure infres.qout
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export covering
infer' : {d, n : Nat} ->
(ctx : TyContext d n) -> (sg : Qty) -> (0 _ : IsSubj sg) =>
(subj : NotCloElim d n) ->
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m (InferResult d n)
infer' ctx sg (Element (F x) _) = do
Just g <- asks $ lookup x | Nothing => throwError $ NotInScope x
when (isZero g) $ expectEqualQ sg Zero
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pure $ InfRes {type = g.type.get, qout = zero}
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infer' ctx sg (Element (B i) _) =
pure $ lookupBound sg i ctx
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infer' ctx sg (Element (fun :@ arg) _) = do
funres <- infer ctx sg fun
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(qty, argty, res) <- expectPi funres.type
let Element sg' _ = subjMult sg qty
argout <- check ctx sg' arg argty
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pure $ InfRes {type = fromScopeTerm res //. ((arg :# argty) ::: id),
qout = funres.qout + argout}
infer' ctx sg (Element (tm :# ty) _) = do
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ignore $ check ctx zero ty (TYPE UAny)
qout <- check ctx sg tm ty
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pure $ InfRes {type = ty, qout}