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87 lines
2.2 KiB
87 lines
2.2 KiB
{-# LANGUAGE TupleSections, OverloadedStrings #-}
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module Elab where
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import Elab.Monad
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import qualified Presyntax.Presyntax as P
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import Syntax
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import Elab.Eval
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infer :: P.Expr -> ElabM (Term, NFType)
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infer (P.Var t) = (Ref (Bound t),) <$> getNfType (Bound t)
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infer (P.App p f x) = do
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(f, f_ty) <- infer f
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(d, r, w) <- isPiType p f_ty
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x <- check x d
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x_nf <- eval x
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pure (App p (w f) x, r x_nf)
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infer (P.Pi p s d r) = do
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d <- check d VType
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d_nf <- eval d
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assume (Bound s) d_nf $ do
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r <- check r VType
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pure (Pi p s d r, VType)
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infer (P.Sigma s d r) = do
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d <- check d VType
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d_nf <- eval d
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assume (Bound s) d_nf $ do
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r <- check r VType
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pure (Sigma s d r, VType)
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infer exp = do
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t <- newMeta VType
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tm <- check exp t
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pure (tm, t)
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check :: P.Expr -> NFType -> ElabM Term
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check (P.Lam p var body) (VPi p' dom (Closure _ rng)) | p == p' =
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assume (Bound var) dom $
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Lam p var <$> check body (rng (VVar (Bound var)))
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check tm (VPi P.Im dom (Closure var rng)) =
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assume (Bound var) dom $
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Lam P.Im var <$> check tm (rng (VVar (Bound var)))
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check (P.Lam p v b) ty = do
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(d, r, wp) <- isPiType p ty
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assume (Bound v) d $
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wp . Lam P.Im v <$> check b (r (VVar (Bound v)))
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check (P.Pair a b) ty = do
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(d, r, wp) <- isSigmaType ty
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a <- check a d
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a_nf <- eval a
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b <- check b (r a_nf)
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pure (wp (Pair a b))
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check exp ty = do
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(tm, has) <- infer exp
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unify has ty
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pure tm
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isPiType :: P.Plicity -> NFType -> ElabM (Value, NFType -> NFType, Term -> Term)
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isPiType p (VPi p' d (Closure _ k)) | p == p' = pure (d, k, id)
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isPiType p t = do
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dom <- newMeta VType
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name <- newName
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assume (Bound name) dom $ do
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rng <- newMeta VType
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wp <- isConvertibleTo t (VPi p dom (Closure name (const rng)))
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pure (dom, const rng, wp)
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isSigmaType :: NFType -> ElabM (Value, NFType -> NFType, Term -> Term)
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isSigmaType (VSigma d (Closure _ k)) = pure (d, k, id)
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isSigmaType t = do
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dom <- newMeta VType
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name <- newName
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assume (Bound name) dom $ do
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rng <- newMeta VType
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wp <- isConvertibleTo t (VSigma dom (Closure name (const rng)))
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pure (dom, const rng, wp)
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identityTy :: NFType
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identityTy = VPi P.Im VType (Closure "A" $ \t -> VPi P.Ex t (Closure "_" (const t)))
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