grtt -> qtt
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@ -1,6 +1,4 @@
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#  quantitative observational extensional(ish) type theory
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hey what would happen if some idiot tried to weld qtt[^1] and xtt together?
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hey what would happen if some idiot tried to weld qtt and xtt together?
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let's find out together
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[^1]: actually grtt but wtf is a grox
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@ -43,10 +43,8 @@ parameters {auto _ : MonadThrow Error m}
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Sub => unless (k <= l) $ throw $ ClashU Sub k l
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compareTN' mode s@(TYPE _) t _ _ = clashT mode s t
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compareTN' mode (Pi qtm1 qty1 _ arg1 res1)
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(Pi qtm2 qty2 _ arg2 res2) _ _ = do
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-- [todo] these should probably always be ==, right..?
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unless (qtm1 == qtm2) $ throw $ ClashQ qtm1 qtm2
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compareTN' mode (Pi qty1 _ arg1 res1) (Pi qty2 _ arg2 res2) _ _ = do
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-- [todo] this should probably always be ==, right..?
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unless (qty1 == qty2) $ throw $ ClashQ qty1 qty2
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compareT0 mode arg2 arg1 -- reversed for contravariant Sub
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compareTS0 mode res1 res2
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@ -36,7 +36,7 @@ mutual
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TYPE : (l : Universe) -> Term d n
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||| function type
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Pi : (qtm, qty : Qty) -> (x : Name) ->
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Pi : (qty : Qty) -> (x : Name) ->
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(arg : Term d n) -> (res : ScopeTerm d n) -> Term d n
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||| function term
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Lam : (x : Name) -> (body : ScopeTerm d n) -> Term d n
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@ -91,7 +91,7 @@ mutual
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public export %inline
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Arr : Qty -> Term d n -> Term d n -> Term d n
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Arr pi a b = Pi {qtm = pi, qty = zero, x = "_", arg = a, res = TUnused b}
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Arr pi a b = Pi {qty = pi, x = "_", arg = a, res = TUnused b}
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||| same as `F` but as a term
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public export %inline
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@ -30,9 +30,9 @@ mutual
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PrettyHL (Term d n) where
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prettyM (TYPE l) =
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parensIfM App $ typeD <//> !(withPrec Arg $ prettyM l)
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prettyM (Pi qtm qty x s t) =
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prettyM (Pi qty x s t) =
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parensIfM Outer $ hang 2 $
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!(prettyBinder [qtm, qty] x s) <++> !arrowD
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!(prettyBinder [qty] x s) <++> !arrowD
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<//> !(under T x $ prettyM t)
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prettyM (Lam x t) =
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parensIfM Outer $
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@ -64,8 +64,8 @@ mutual
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Term dfrom from -> NotCloTerm dto to
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pushSubstsTWith th ph (TYPE l) =
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ncloT $ TYPE l
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pushSubstsTWith th ph (Pi qtm qty x a body) =
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ncloT $ Pi qtm qty x (subs a th ph) (subs body th ph)
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pushSubstsTWith th ph (Pi qty x a body) =
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ncloT $ Pi qty x (subs a th ph) (subs body th ph)
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pushSubstsTWith th ph (Lam x body) =
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ncloT $ Lam x $ subs body th ph
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pushSubstsTWith th ph (E e) =
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@ -120,9 +120,9 @@ mutual
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Tighten (Term d) where
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tighten p (TYPE l) =
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pure $ TYPE l
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tighten p (Pi qtm qty x arg res) =
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Pi qtm qty x <$> tighten p arg
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<*> tighten p res
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tighten p (Pi qty x arg res) =
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Pi qty x <$> tighten p arg
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<*> tighten p res
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tighten p (Lam x body) =
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Lam x <$> tighten p body
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tighten p (E e) =
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@ -160,4 +160,3 @@ weakT t = t //. shift 1
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public export %inline
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weakE : Elim d n -> Elim d (S n)
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weakE t = t //. shift 1
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@ -16,11 +16,11 @@ expectTYPE s =
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private covering %inline
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expectPi : MonadThrow Typing.Error m => Term d n ->
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m (Qty, Qty, Term d n, ScopeTerm d n)
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m (Qty, Term d n, ScopeTerm d n)
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expectPi ty =
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case (whnfT ty).fst of
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Pi qtm qty _ arg res => pure (qtm, qty, arg, res)
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_ => throw $ ExpectedPi ty
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Pi qty _ arg res => pure (qty, arg, res)
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_ => throw $ ExpectedPi ty
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private %inline
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expectEqualQ : MonadThrow Equal.Error m =>
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@ -40,14 +40,14 @@ tail = {tctx $= tail, qctx $= tail}
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private %inline
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weakI : InferResult d n -> InferResult d (S n)
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weakI = {type $= weakT, tmout $= (:< zero), tyout $= (:< zero)}
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weakI = {type $= weakT, qout $= (:< zero)}
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private
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lookupBound : {n : Nat} -> Var n -> TyContext d n -> InferResult d n
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lookupBound VZ (MkTyContext {tctx = _ :< ty, qctx = _ :< tyout, _}) =
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InfRes {type = weakT ty, tmout = zero :< one, tyout = tyout :< zero}
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lookupBound (VS i) ctx =
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weakI $ lookupBound i (tail ctx)
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lookupBound : {n : Nat} -> Qty -> Var n -> TyContext d n -> InferResult 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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mutual
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@ -55,88 +55,80 @@ mutual
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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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--
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-- [todo] probably need to check that pi is 1 or 0 like atkey said
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export covering %inline
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check : MonadThrows [Typing.Error, Equal.Error] m => {d, n : Nat} ->
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(ctx : TyContext d n) -> (subj : Term d n) -> (ty : Term d n) ->
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(ctx : TyContext d n) -> (pi : Qty) ->
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(subj : Term d n) -> (ty : Term d n) ->
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m (CheckResult n)
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check ctx subj ty = check' ctx (pushSubstsT subj) ty
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check ctx pi subj ty = check' ctx pi (pushSubstsT subj) ty
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export covering %inline
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infer : MonadThrows [Typing.Error, Equal.Error] m => {d, n : Nat} ->
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(ctx : TyContext d n) -> (subj : Elim d n) ->
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(ctx : TyContext d n) -> (pi : Qty) -> (subj : Elim d n) ->
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m (InferResult d n)
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infer ctx subj = infer' ctx (pushSubstsE subj)
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infer ctx pi subj = infer' ctx pi (pushSubstsE subj)
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export covering
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check' : MonadThrows [Typing.Error, Equal.Error] m => {d, n : Nat} ->
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(ctx : TyContext d n) ->
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(ctx : TyContext d n) -> (pi : Qty) ->
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(subj : NotCloTerm d n) -> (ty : Term d n) ->
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m (CheckResult n)
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check' ctx (Element (TYPE l) _) ty = do
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check' ctx pi (Element (TYPE l) _) ty = do
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l' <- expectTYPE ty
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expectEqualQ zero pi
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unless (l < l') $ throw $ BadUniverse l l'
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pure $ ChkRes {tmout = zero, tyout = zero}
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pure zero
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-- [todo] factor this stuff out
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check' ctx (Element (Pi qtm qty x arg (TUsed res)) _) ty = do
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check' ctx pi (Element (Pi qty x arg res) _) ty = do
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l <- expectTYPE ty
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argty <- check ctx arg (TYPE l)
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resty <- check (extendTy arg argty.tmout ctx) res (TYPE l)
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res'tmout <- popQ qty resty.tmout
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pure $ ChkRes {tmout = argty.tmout + res'tmout, tyout = zero}
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check' ctx (Element (Pi qtm qty x arg (TUnused res)) _) ty = do
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ignore $ expectTYPE ty
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argty <- check ctx arg ty
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resty <- check ctx res ty
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expectEqualQ qty zero
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pure $ ChkRes {tmout = argty.tmout + resty.tmout, tyout = zero}
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expectEqualQ zero pi
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ignore $ check ctx zero arg (TYPE l)
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case res of
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TUsed res => ignore $ check (extendTy arg zero ctx) zero res (TYPE l)
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TUnused res => ignore $ check ctx zero res (TYPE l)
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pure zero
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check' ctx (Element (Lam x body) _) ty = do
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(qtm, qty, arg, res) <- expectPi ty
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check' ctx pi (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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argres <- check ctx arg (TYPE UAny)
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let ctx' = extendTy arg argres.tmout ctx
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bodyres <- check ctx' body res
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tmout <- popQ qtm bodyres.tmout
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tyout <- popQ qty bodyres.tyout
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pure $ ChkRes {tmout, tyout = argres.tmout + tyout}
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qout <- check (extendTy arg (pi * qty) ctx) pi body res
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popQ qty qout
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check' ctx (Element (E e) _) ty = do
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infres <- infer ctx e
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tyres <- check ctx ty (TYPE UAny)
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check' ctx pi (Element (E e) _) ty = do
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infres <- infer ctx pi e
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ignore $ check ctx zero ty (TYPE UAny)
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infres.type `subT` ty
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pure $ ChkRes {tmout = infres.tmout, tyout = tyres.tmout}
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pure infres.qout
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export covering
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infer' : MonadThrows [Typing.Error, Equal.Error] m => {d, n : Nat} ->
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(ctx : TyContext d n) -> (subj : NotCloElim d n) ->
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(ctx : TyContext d n) -> (pi : Qty) -> (subj : NotCloElim d n) ->
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m (InferResult d n)
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infer' ctx (Element (F x) _) =
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infer' ctx pi (Element (F x) _) =
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-- [todo] check that global is erased ==> pi = zero
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case lookup x ctx.globals of
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Just g => pure $ InfRes {type = g.type, tmout = zero, tyout = zero}
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Just g => pure $ InfRes {type = g.type, qout = zero}
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Nothing => throw $ NotInScope x
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infer' ctx (Element (B i) _) = pure $ lookupBound i ctx
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infer' ctx pi (Element (B i) _) =
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pure $ lookupBound pi i ctx
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infer' ctx (Element (fun :@ arg) _) = do
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funres <- infer ctx fun
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(qtm, qty, argty, resty) <- expectPi funres.type
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let resty = fromScopeTerm resty
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argres <- check ctx arg argty
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let ctx' = extendTy argty argres.tyout ctx
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resres <- check ctx' resty (TYPE UAny)
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res'tyout <- popQ qty resres.tmout
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let type = resty //. (arg :# argty ::: id)
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pure $ InfRes {type,
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tmout = funres.tmout + qtm * argres.tmout,
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tyout = res'tyout + qty * argres.tmout}
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infer' ctx pi (Element (fun :@ arg) _) = do
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funres <- infer ctx pi fun
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(qty, argty, res) <- expectPi funres.type
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argout <- check ctx (pi * qty) 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 (Element (tm :# ty) _) = do
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ignore $ check ctx ty (TYPE UAny)
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res <- check ctx tm ty
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pure $ InfRes {type = ty, tmout = res.tmout, tyout = res.tyout}
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infer' ctx pi (Element (tm :# ty) _) = do
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ignore $ check ctx zero ty (TYPE UAny)
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qout <- check ctx pi tm ty
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pure $ InfRes {type = ty, qout}
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@ -24,11 +24,11 @@ TContext d = Context (Term d)
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public export
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QContext : Nat -> Type
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QContext = Triangle' Qty
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QContext = Context' Qty
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public export
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QOutput : Nat -> Type
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QOutput = Context' Qty
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QOutput = QContext
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public export
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@ -60,8 +60,8 @@ namespace TContext
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namespace TyContext
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export
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extendTy : Term d n -> QOutput n -> TyContext d n -> TyContext d (S n)
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extendTy s rhos = {tctx $= (:< s), qctx $= (:< rhos)}
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extendTy : Term d n -> Qty -> TyContext d n -> TyContext d (S n)
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extendTy s rho = {tctx $= (:< s), qctx $= (:< rho)}
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export
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extendDim : TyContext d n -> TyContext (S d) n
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@ -87,15 +87,14 @@ namespace QOutput
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public export
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record CheckResult n where
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constructor ChkRes
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tmout, tyout : QOutput n
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CheckResult : Nat -> Type
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CheckResult = QOutput
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public export
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record InferResult d n where
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constructor InfRes
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type : Term d n
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tmout, tyout : QOutput n
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qout : QOutput n
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public export
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