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|
module Term.Syntax
import public Data.SnocList
import public Term
%prefix_record_projections off
-- Combinators
export
Id : Term (ty ~> ty) ctx
Id = Abs (Var Here)
export
Arb : {ty : Ty} -> Term ty ctx
Arb {ty = N} = Lit 0
Arb {ty = ty ~> ty'} = Const Arb
export
Zero : Term N ctx
Zero = Lit 0
-- HOAS
infixr 4 ~>*
public export
(~>*) : SnocList Ty -> Ty -> Ty
sty ~>* ty = foldr (~>) ty sty
export
Abs' : (Term ty (ctx :< ty) -> Term ty' (ctx :< ty)) -> Term (ty ~> ty') ctx
Abs' f = Abs (f $ Var Here)
export
App : {sty : SnocList Ty} -> Term (sty ~>* ty) ctx -> All (flip Term ctx) sty -> Term ty ctx
App t [<] = t
App t (us :< u) = App (App t us) u
export
AbsAll :
(sty : SnocList Ty) ->
(All (flip Term (ctx ++ sty)) sty -> Term ty (ctx ++ sty)) ->
Term (sty ~>* ty) ctx
AbsAll [<] f = f [<]
AbsAll (sty :< ty') f = AbsAll sty (\vars => Abs' (\x => f (mapProperty shift vars :< x)))
export
(.) : {ty, ty' : Ty} -> Term (ty' ~> ty'') ctx -> Term (ty ~> ty') ctx -> Term (ty ~> ty'') ctx
t . u = Abs (App (shift t) [<App (shift u) [<Var Here]])
export
(.:) :
{sty : SnocList Ty} ->
{ty : Ty} ->
Term (ty ~> ty') ctx ->
Term (sty ~>* ty) ctx ->
Term (sty ~>* ty') ctx
(t .: u) {sty = [<]} = App t u
(t .: u) {sty = sty :< ty''} = Abs' (\f => shift t . f) .: u
-- -- Incomplete Evaluation
-- data IsFunc : FullTerm (ty ~> ty') ctx -> Type where
-- ConstFunc : (t : FullTerm ty' ctx) -> IsFunc (Const t)
-- AbsFunc : (t : FullTerm ty' (ctx :< ty)) -> IsFunc (Abs t)
-- isFunc : (t : FullTerm (ty ~> ty') ctx) -> Maybe (IsFunc t)
-- isFunc Var = Nothing
-- isFunc (Const t) = Just (ConstFunc t)
-- isFunc (Abs t) = Just (AbsFunc t)
-- isFunc (App x) = Nothing
-- isFunc (Rec x) = Nothing
-- app :
-- (ratio : Double) ->
-- {ty : Ty} ->
-- (t : Term (ty ~> ty') ctx) ->
-- {auto 0 ok : IsFunc t.value} ->
-- Term ty ctx ->
-- Maybe (Term ty' ctx)
-- app ratio (Const t `Over` thin) u = Just (t `Over` thin)
-- app ratio (Abs t `Over` thin) u =
-- let uses = countUses (t `Over` Id) Here in
-- let sizeU = size u in
-- if cast (sizeU * uses) <= cast (S (sizeU + uses)) * ratio
-- then
-- Just (subst (t `Over` Keep thin) (Base Id :< u))
-- else
-- Nothing
-- App' :
-- {ty : Ty} ->
-- (ratio : Double) ->
-- Term (ty ~> ty') ctx ->
-- Term ty ctx ->
-- Maybe (Term ty' ctx)
-- App' ratio
-- (Rec (MakePair
-- t
-- (MakePair (u `Over` thin2) (Const v `Over` thin3) _ `Over` thin')
-- _) `Over` thin)
-- arg =
-- case (isFunc u, isFunc v) of
-- (Just ok1, Just ok2) =>
-- let thinA = thin . thin' . thin2 in
-- let thinB = thin . thin' . thin3 in
-- case (app ratio (u `Over` thinA) arg , app ratio (v `Over` thinB) arg)
-- of
-- (Just u, Just v) => Just (Rec (wkn t thin) u (Const v))
-- (Just u, Nothing) => Just (Rec (wkn t thin) u (Const $ App (v `Over` thinB) arg))
-- (Nothing, Just v) => Just (Rec (wkn t thin) (App (u `Over` thinA) arg) (Const v))
-- (Nothing, Nothing) =>
-- Just (Rec (wkn t thin) (App (u `Over` thinA) arg) (Const $ App (v `Over` thinB) arg))
-- _ => Nothing
-- App' ratio t arg =
-- case isFunc t.value of
-- Just _ => app ratio t arg
-- Nothing => Nothing
-- Rec' :
-- {ty : Ty} ->
-- FullTerm N ctx' ->
-- ctx' `Thins` ctx ->
-- Term ty ctx ->
-- Term (ty ~> ty) ctx ->
-- Maybe (Term ty ctx)
-- Rec' (Lit 0) thin u v = Just u
-- Rec' (Lit (S n)) thin u v = Just u
-- Rec' (Suc t) thin u v =
-- let rec = maybe (Rec (t `Over` thin) u v) id (Rec' t thin u v) in
-- Just $ maybe (App v rec) id $ (App' 1 v rec)
-- Rec' t thin (Zero `Over` thin1) (Const Zero `Over` thin2) =
-- Just (Zero `Over` Empty)
-- Rec' t thin u v = Nothing
-- eval' : {ty : Ty} -> (fuel : Nat) -> (ratio : Double) -> Term ty ctx -> (Nat, Term ty ctx)
-- fullEval' : {ty : Ty} -> (fuel : Nat) -> (ratio : Double) -> FullTerm ty ctx -> (Nat, Term ty ctx)
-- eval' fuel r (t `Over` thin) = mapSnd (flip wkn thin) (fullEval' fuel r t)
-- fullEval' 0 r t = (0, t `Over` Id)
-- fullEval' fuel@(S f) r Var = (fuel, Var `Over` Id)
-- fullEval' fuel@(S f) r (Const t) = mapSnd Const (fullEval' fuel r t)
-- fullEval' fuel@(S f) r (Abs t) = mapSnd Abs (fullEval' fuel r t)
-- fullEval' fuel@(S f) r (App (MakePair t u _)) =
-- case App' r t u of
-- Just t => (f, t)
-- Nothing =>
-- let (fuel', t) = eval' f r t in
-- let (fuel', u) = eval' (assert_smaller fuel fuel') r u in
-- (fuel', App t u)
-- fullEval' fuel@(S f) r (Lit n) = (fuel, Lit n `Over` Id)
-- fullEval' fuel@(S f) r (Suc t) = mapSnd Suc (fullEval' fuel r t)
-- fullEval' fuel@(S f) r (Rec (MakePair t (MakePair u v _ `Over` thin) _)) =
-- case Rec' t.value t.thin (wkn u thin) (wkn v thin) of
-- Just t => (f, t)
-- Nothing =>
-- let (fuel', t) = eval' f r t in
-- let (fuel', u) = eval' (assert_smaller fuel fuel') r u in
-- let (fuel', v) = eval' (assert_smaller fuel fuel') r v in
-- (fuel', Rec t (wkn u thin) (wkn v thin))
-- export
-- eval :
-- {ty : Ty} ->
-- {default 1.5 ratio : Double} ->
-- {default 20000 fuel : Nat} ->
-- Term ty ctx ->
-- Term ty ctx
-- eval t = loop fuel t
-- where
-- loop : Nat -> Term ty ctx -> Term ty ctx
-- loop fuel t =
-- case eval' fuel ratio t of
-- (0, t) => t
-- (S f, t) => loop (assert_smaller fuel f) t
|
