From 3649c9965e787c9cb0dc1cedc4400cdec4c5b8a2 Mon Sep 17 00:00:00 2001
From: Chloe Brown <chloe.brown.00@outlook.com>
Date: Sun, 26 Mar 2023 03:50:28 +0100
Subject: Add type checking.

Currently, there is Set in Set. Next step is to add universe levels.
---
 src/CC/Term/Elaborate.idr | 221 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 221 insertions(+)
 create mode 100644 src/CC/Term/Elaborate.idr

(limited to 'src/CC/Term/Elaborate.idr')

diff --git a/src/CC/Term/Elaborate.idr b/src/CC/Term/Elaborate.idr
new file mode 100644
index 0000000..458ec38
--- /dev/null
+++ b/src/CC/Term/Elaborate.idr
@@ -0,0 +1,221 @@
+module CC.Term.Elaborate
+
+import CC.Name
+import CC.Term
+import CC.Term.Eval
+import CC.Term.Raw
+import CC.Thinning
+
+import Data.DPair
+import Data.List1
+import Data.Singleton
+import Data.SnocList
+import Data.SnocList.Elem
+
+import Text.Bounded
+
+%prefix_record_projections off
+
+-- Elaboration Errors ----------------------------------------------------------
+
+export
+data ElabError : Type -> Type where
+  Ok : ty -> ElabError ty
+  Error : List1 (Either Name (String, Maybe Bounds)) -> ElabError ty
+
+Functor ElabError where
+  map f (Ok x) = Ok (f x)
+  map f (Error xs) = Error xs
+
+Applicative ElabError where
+  pure = Ok
+
+  Ok f <*> Ok v = Ok (f v)
+  Ok f <*> Error ys = Error ys
+  Error xs <*> Ok v = Error xs
+  Error xs <*> Error ys = Error (xs ++ ys)
+
+Monad ElabError where
+  join (Ok (Ok x)) = Ok x
+  join (Ok (Error xs)) = Error xs
+  join (Error xs) = Error xs
+
+export
+runElabError : ElabError ty -> Either (List1 (Either Name (String, Maybe Bounds))) ty
+runElabError (Ok x) = Right x
+runElabError (Error xs) = Left xs
+
+fromNameError : NameError ty -> ElabError ty
+fromNameError v =
+  case runNameError v of
+    Left errs => Error (map Left errs)
+    Right v => Ok v
+
+-- Elaboration Context ---------------------------------------------------------
+
+record ElabCtx (local, global : Context) where
+  constructor MkCtx
+  env : Env local global
+  types : (k : Nat) -> forall n. (0 prf : IsVar k n local) -> Lazy (Value global)
+  pos : Maybe Bounds
+
+%name ElabCtx ctx
+
+wknCtx :
+  {global : Context} ->
+  ElabCtx local global ->
+  (n : Name) ->
+  ElabCtx local (global :< n)
+wknCtx ctx n = { env $= flip wknEnv (drop id), types := types } ctx
+  where
+  types : (k : Nat) -> forall m. (0 _ : IsVar k m local) -> Lazy (Value (global :< n))
+  types k prf = wknVal (ctx.types k prf) (drop id)
+
+define :
+  ElabCtx local global ->
+  (n : Name) ->
+  (val : Lazy (Value global)) ->
+  (ty : Lazy (Value global)) ->
+  ElabCtx (local :< n) global
+define ctx n val ty = { env $= (:< (n, val)), types := types } ctx
+  where
+  types : (k : Nat) -> forall m. (0 _ : IsVar k m (local :< n)) -> Lazy (Value global)
+  types 0 (Here eq) = ty
+  types (S k) (There prf) = ctx.types k prf
+
+bind :
+  {global : Context} ->
+  ElabCtx local global ->
+  (n : Name) ->
+  (ty : Lazy (Value global)) ->
+  ElabCtx (local :< n) (global :< n)
+bind ctx n ty = define (wknCtx ctx n) n (Ntrl $ VVar 0 _ $ fromElem Here) (wknVal ty (drop id))
+
+updatePos : ElabCtx local global -> (irrel : Bool) -> Bounds -> ElabCtx local global
+updatePos ctx irrel bounds = { pos := if irrel then Nothing else Just bounds } ctx
+
+-- Checking and Inference ------------------------------------------------------
+
+record PiType (ctx : Context) where
+  constructor MkPi
+  {0 local : Context}
+  name : Name
+  dom : Lazy (Value ctx)
+  env : Env local ctx
+  cod : Term (local :< name)
+
+check :
+  {local, global : Context} ->
+  ElabCtx local global ->
+  RawTerm ->
+  Lazy (Value global) ->
+  ElabError (Term local)
+checkType :
+  {local, global : Context} ->
+  ElabCtx local global ->
+  RawTerm ->
+  ElabError (Term local)
+infer :
+  {local, global : Context} ->
+  ElabCtx local global ->
+  RawTerm ->
+  ElabError (Term local, Lazy (Value global))
+inferPi :
+  {local, global : Context} ->
+  ElabCtx local global ->
+  RawTerm ->
+  ElabError (Term local, PiType global)
+inferType :
+  {local, global : Context} ->
+  ElabCtx local global ->
+  RawTerm ->
+  ElabError (Term local)
+
+check ctx (Bounded (MkBounded t irrel bounds)) ty = check (updatePos ctx irrel bounds) t ty
+
+check ctx (Let n Nothing val t) ty = do
+  (val, ty') <- infer ctx val
+  t <- check (define ctx n (eval ctx.env val) ty') t ty
+  pure $ Let {n, ty = Nothing, val, t}
+check ctx (Let n (Just ty') val t) ty = do
+  ty' <- checkType ctx ty'
+  let vty : Lazy (Value global) = eval ctx.env ty'
+  val <- check ctx val vty
+  t <- check (define ctx n (eval ctx.env val) vty) t ty
+  pure $ Let {n, ty = Just ty', val, t}
+
+check ctx Set VSet = pure $ Set
+
+check ctx (Abs Nothing t) (VFunc env dom cod) = do
+  t <- check ctx t (eval env cod)
+  pure $ Abs (fresh local) (wknTerm t (drop id))
+check ctx (Abs (Just n) t) (VFunc env dom cod) = do
+  t <- check (bind ctx n (eval env dom)) t (eval (wknEnv env (drop id)) cod)
+  pure $ Abs n t
+check ctx (Abs Nothing t) (VPi m dom env cod) = do
+  t <- check (wknCtx ctx m) t (eval (liftEnv [<m] env) cod)
+  pure $ Abs m (wknTerm t (drop id))
+check ctx (Abs (Just n) t) (VPi m dom env cod) = do
+  t <- check (bind ctx n dom) t (eval (liftEnv [<n] env) $ renTerm Refl cod)
+  pure $ Abs n t
+
+check ctx t ty = do
+  (t, ty') <- infer ctx t
+  let True = convert ty ty'
+    | False => Error $ singleton $ Right ("conversion failed", ctx.pos)
+  pure t
+
+checkType ctx t = check ctx t VSet
+
+infer ctx (Bounded (MkBounded t irrel bounds)) = infer (updatePos ctx irrel bounds) t
+infer ctx (Var n) = do
+  Element k prf <- fromNameError $ lookup local n
+  pure (Var k n prf, ctx.types k prf)
+infer ctx (Let n Nothing val t) = do
+  (val, ty') <- infer ctx val
+  (t, ty) <- infer (define ctx n (eval ctx.env val) ty') t
+  pure $ (Let {n, ty = Nothing, val, t}, ty)
+infer ctx (Let n (Just ty) val t) = do
+  ty' <- checkType ctx ty
+  let vty : Lazy (Value global) = eval ctx.env ty'
+  val <- check ctx val vty
+  (t, ty) <- infer (define ctx n (eval ctx.env val) vty) t
+  pure $ (Let {n, ty = Just ty', val, t}, ty)
+infer ctx Set = pure (Set, delay VSet)
+infer ctx (Pi (Nothing `Of` dom) cod) = do
+  (dom, cod) <- [| MkPair (inferType ctx dom) (inferType ctx cod) |]
+  pure $ (Pi Nothing dom cod, delay VSet)
+infer ctx (Pi (Just n `Of` dom) cod) = do
+  dom <- inferType ctx dom
+  let vdom : Lazy (Value global) = eval ctx.env dom
+  cod <- inferType (bind ctx n vdom) cod
+  pure $ (Pi (Just n) dom cod, delay VSet)
+infer ctx (App t u) = do
+  (t, ty) <- inferPi ctx t
+  u <- check ctx u ty.dom
+  let vu : Lazy (Value global) = eval ctx.env u
+  pure $ (App t u, delay $ eval (ty.env :< (ty.name, vu)) ty.cod)
+infer ctx t = Error $ singleton $ Right ("cannot infer type", ctx.pos)
+
+inferPi ctx t = do
+  (t, ty) <- infer ctx t
+  case force ty of
+    VPi n dom env cod =>
+      pure $ (t, MkPi n dom env cod)
+    VFunc env dom cod =>
+      let local' = recomputeLocal env in
+      pure $ (t, MkPi (fresh' local') (eval env dom) env (wknTerm cod (drop $ id' local')))
+    ty => Error $ singleton $ Right ("expected pi type", ctx.pos)
+
+inferType ctx t = do
+  (t, ty) <- infer ctx t
+  case force ty of
+    VSet => pure t
+    ty => Error $ singleton $ Right ("expected set type", ctx.pos)
+
+export
+inferTerm : RawTerm -> ElabError (Term [<], Lazy (Value [<]))
+inferTerm = infer (MkCtx [<] types Nothing)
+  where
+  types : (k : Nat) -> forall n. (0 _ : IsVar k n [<]) -> Lazy (Value [<])
+  types k prf impossible
-- 
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