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Implement proper inductive types

feature/hits
Amélia Liao 3 years ago
parent
commit
b42384125d
12 changed files with 321 additions and 138 deletions
  1. +23
    -20
      intro.tt
  2. +133
    -1
      src/Elab.hs
  3. +23
    -29
      src/Elab/Eval.hs
  4. +1
    -0
      src/Elab/Monad.hs
  5. +37
    -34
      src/Elab/WiredIn.hs
  6. +2
    -5
      src/Elab/WiredIn.hs-boot
  7. +2
    -0
      src/Presyntax/Lexer.x
  8. +27
    -1
      src/Presyntax/Parser.y
  9. +8
    -0
      src/Presyntax/Presyntax.hs
  10. +5
    -0
      src/Presyntax/Tokens.hs
  11. +49
    -31
      src/Syntax.hs
  12. +11
    -17
      src/Syntax/Pretty.hs

+ 23
- 20
intro.tt View File

@ -152,13 +152,7 @@ IsOne : I -> Pretype
-- The value itIs1 witnesses the fact that i1 = i1.
itIs1 : IsOne i1
-- Furthermore, if either of i or j are one, then so is (i or j).
isOneL : {i : I} {j : I} -> IsOne i -> IsOne (ior i j)
isOneR : {i : I} {j : I} -> IsOne j -> IsOne (ior i j)
{-# PRIMITIVE itIs1 #-}
{-# PRIMITIVE isOneL #-}
{-# PRIMITIVE isOneR #-}
-- Partial elements
-------------------
@ -579,24 +573,24 @@ involToIso {A} f inv = (f, inv, inv)
--
-- We define it here.
Bool : Type
{-# PRIMITIVE Bool #-}
data Bool : Type where
true : Bool
false : Bool
true, false : Bool
{-# PRIMITIVE true #-}
{-# PRIMITIVE false #-}
not : Bool -> Bool
not = \case
true -> false
false -> true
-- Pattern matching for booleans: If a proposition holds for true and
-- for false, then it holds for every bool.
elimBool : (P : Bool -> Type) -> P true -> P false -> (b : Bool) -> P b
{-# PRIMITIVE if elimBool #-}
elimBool P x y = \case
true -> x
false -> y
-- Non-dependent elimination of booleans
if : {A : Type} -> A -> A -> Bool -> A
if {A} = elimBool (\b -> A)
not : Bool -> Bool
not = if false true
if x y = \case
true -> x
false -> y
-- By pattern matching it suffices to prove (not (not true)) ≡ true and
-- not (not false) ≡ false. Since not (not true) computes to true (resp.
@ -686,4 +680,13 @@ pathIsHom {A} {B} {f} {g} =
let
theIso : Iso (Path f g) (Hom f g)
theIso = (happly {A} {B} {f} {g}, happlyIsIso {A} {B} {f} {g})
in univalence (IsoToEquiv theIso)
in univalence (IsoToEquiv theIso)
data List (A : Type) : Type where
nil : List A
cons : A -> List A -> List A
map : {A : Type} {B : Type} -> (A -> B) -> List A -> List B
map f = \case
nil -> nil
cons x xs -> cons (f x) (map f xs)

+ 133
- 1
src/Elab.hs View File

@ -2,13 +2,17 @@
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE DeriveAnyClass #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE DerivingStrategies #-}
module Elab where
import Control.Arrow (Arrow(first))
import Control.Monad.Reader
import Control.Exception
import qualified Data.Map.Strict as Map
import qualified Data.Sequence as Seq
import qualified Data.Set as Set
import qualified Data.Text as T
import Data.Traversable
import Data.Text (Text)
import Data.Map (Map)
@ -190,11 +194,79 @@ check (P.LamSystem bs) ty = do
mkB _ (Nothing, b) = b
pure (Lam P.Ex name (System (Map.fromList (map (\(_, (x, y)) -> (quote x, mkB name y)) eqns))))
check (P.LamCase pats) ty = do
porp <- isPiType P.Ex ty
case porp of
It'sProd dom rng wp -> do
name <- newName
liftIO . print $ show pats
cases <- for pats $ \(pat, rhs) -> do
checkPattern pat dom \pat wp -> do
pat_nf <- eval pat
rhs <- check rhs (rng pat_nf)
pure (pat, wp rhs)
pure (wp (Lam P.Ex name (Case (Ref name) cases)))
_ -> do
dom <- newMeta VTypeω
n <- newName' (Bound (T.singleton 'x') 0)
assume n dom \_ -> do
rng <- newMeta VTypeω
throwElab $ NotEqual (VPi P.Ex dom (Closure n (const rng))) ty
check exp ty = do
(tm, has) <- switch $ infer exp
wp <- isConvertibleTo has ty
pure (wp tm)
checkPattern :: P.Pattern -> NFSort -> (Term -> (Term -> Term) -> ElabM a) -> ElabM a
checkPattern (P.PCap var) dom cont = do
name <- asks (Map.lookup var . nameMap)
case name of
Just name@(ConName _ _ skip arity) -> do
unless (arity == 0) $ throwElab $ UnsaturatedCon name
ty <- instantiate =<< getNfType name
_ <- isConvertibleTo ty dom
wrap <- skipLams skip
cont (Con name) wrap
Just name -> throwElab $ NotACon name
Nothing -> assume (Bound var 0) dom \name -> cont (Ref name) (Lam P.Ex name)
checkPattern (P.PCon var args) dom cont =
do
name <- asks (Map.lookup var . nameMap)
case name of
Just name@(ConName _ _ nskip arity) -> do
unless (arity == length args) $ throwElab $ UnsaturatedCon name
ty <- instantiate =<< getNfType name
_ <- isConvertibleTo (skipBinders arity ty) dom
skip <- skipLams nskip
bindNames args ty $ \_ wrap ->
cont (Con name) (skip . wrap)
Just name -> throwElab $ NotACon name
_ -> throwElab $ NotInScope (Bound var 0)
where
skipBinders :: Int -> NFType -> NFType
skipBinders 0 t = t
skipBinders n (VPi _ _ (Closure v r)) = skipBinders (n - 1) (r (VVar v))
skipBinders _ _ = error $ "constructor type is wrong?"
bindNames (n:ns) (VPi p d (Closure _ r)) k =
assume (Bound n 0) d \n -> bindNames ns (r (VVar n)) \ns w ->
k (n:ns) (Lam p n . w)
bindNames [] _ k = k [] id
bindNames xs t _ = error $ show (xs, t)
instantiate :: NFType -> ElabM NFType
instantiate (VPi P.Im d (Closure _ k)) = do
t <- newMeta d
instantiate (k t)
instantiate x = pure x
skipLams :: Int -> ElabM (Term -> Term)
skipLams 0 = pure id
skipLams k = do
n <- newName
(Lam P.Im n . ) <$> skipLams (k - 1)
checkLetItems :: Map Text (Maybe NFType) -> [P.LetItem] -> ([(Name, Term, Term)] -> ElabM a) -> ElabM a
checkLetItems _ [] cont = cont []
checkLetItems map (P.LetDecl v t:xs) cont = do
@ -333,7 +405,7 @@ checkStatement (P.Defn name rhs) k = do
when t $ throwElab (Redefinition (Defined name 0))
rhs <- check rhs ty_nf
rhs_nf <- eval rhs
rhs_nf <- evalFix (Defined name 0) ty_nf rhs
makeLetDef (Defined name 0) ty_nf rhs_nf $ \name ->
local (\e -> e { definedNames = Set.insert name (definedNames e) }) k
@ -371,6 +443,58 @@ checkStatement (P.ReplTy e) k = do
liftIO (h ty)
k
checkStatement (P.Data name tele retk constrs) k =
do
checkTeleRetk True tele retk \kind tele -> do
kind_nf <- eval kind
defineInternal (Bound name 0) kind_nf (\name' -> VNe (HData name') mempty) \name' -> do
checkCons tele (VNe (HData name') (Seq.fromList (map makeProj tele))) constrs k
where
makeProj (x, p, _) = PApp p (VVar x)
checkTeleRetk allKan [] retk cont = do
t <- check retk VTypeω
t_nf <- eval t
when allKan $ unify t_nf VType
cont t []
checkTeleRetk allKan ((x, p, t):xs) retk cont = do
(t, ty) <- infer t
_ <- isConvertibleTo ty VTypeω
let
allKan' = case ty of
VType -> allKan
_ -> False
t_nf <- eval t
assume (Bound x 0) t_nf $ \nm -> checkTeleRetk allKan' xs retk \k xs -> cont (Pi p nm t k) ((nm, p, t_nf):xs)
checkCons _ _et [] k = k
checkCons n ret ((x, ty):xs) k = do
t <- check ty VTypeω
ty_nf <- eval t
let
(args, ret') = splitPi ty_nf
closed = close n t
n' = map (\(x, _, y) -> (x, P.Im, y)) n
unify ret' ret
closed_nf <- eval closed
defineInternal (ConName x 0 (length n') (length args)) closed_nf (makeCon closed_nf mempty n' args) \_ -> checkCons n ret xs k
close [] t = t
close ((x, _, y):xs) t = Pi P.Im x (quote y) (close xs t)
splitPi (VPi p y (Closure x k)) = first ((x, p, y):) $ splitPi (k (VVar x))
splitPi t = ([], t)
makeCon cty sp [] [] con = VNe (HCon cty con) sp
makeCon cty sp ((nm, p, _):xs) ys con = VLam p $ Closure nm \a -> makeCon cty (sp Seq.:|> PApp p a) xs ys con
makeCon cty sp [] ((nm, p, _):ys) con = VLam p $ Closure nm \a -> makeCon cty (sp Seq.:|> PApp p a) [] ys con
evalFix :: Name -> NFType -> Term -> ElabM Value
evalFix name nft term = do
env <- ask
pure . fix $ \val -> eval' env{ getEnv = Map.insert name (nft, val) (getEnv env) } term
checkProgram :: [P.Statement] -> ElabM a -> ElabM a
checkProgram [] k = k
checkProgram (st:sts) k = checkStatement st $ checkProgram sts k
@ -380,3 +504,11 @@ newtype Redefinition = Redefinition { getRedefName :: Name }
data WhenCheckingEndpoint = WhenCheckingEndpoint { leftEndp :: Value, rightEndp :: Value, whichIsWrong :: NFEndp, exc :: SomeException }
deriving (Show, Typeable, Exception)
data UnsaturatedCon = UnsaturatedCon { theConstr :: Name }
deriving (Show, Typeable)
deriving anyclass (Exception)
data NotACon = NotACon { theNotConstr :: Name }
deriving (Show, Typeable)
deriving anyclass (Exception)

+ 23
- 29
src/Elab/Eval.hs View File

@ -6,6 +6,7 @@
{-# LANGUAGE TupleSections #-}
module Elab.Eval where
import Control.Arrow (Arrow(second))
import Control.Monad.Reader
import Control.Exception
@ -51,7 +52,7 @@ forceIO vl@(VSystem fs) =
Just x -> forceIO x
Nothing -> pure vl
forceIO (GluedVl _ _ vl) = forceIO vl
forceIO (VComp line phi u a0) = comp line <$> forceIO phi <*> pure u <*> pure a0
forceIO (VComp line phi u a0) = comp <$> forceIO line <*> forceIO phi <*> pure u <*> pure a0
forceIO x = pure x
applProj :: Value -> Projection -> Value
@ -99,8 +100,6 @@ zonkIO (VIOr x y) = ior <$> zonkIO x <*> zonkIO y
zonkIO (VINot x) = inot <$> zonkIO x
zonkIO (VIsOne x) = VIsOne <$> zonkIO x
zonkIO (VIsOne1 x) = VIsOne1 <$> zonkIO x
zonkIO (VIsOne2 x) = VIsOne2 <$> zonkIO x
zonkIO VItIsOne = pure VItIsOne
zonkIO (VPartial x y) = VPartial <$> zonkIO x <*> zonkIO y
@ -115,11 +114,7 @@ zonkIO (VComp a b c d) = comp <$> zonkIO a <*> zonkIO b <*> zonkIO c <*> zonkIO
zonkIO (VGlueTy a phi ty e) = glueType <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e
zonkIO (VGlue a phi ty e t x) = glueElem <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO t <*> zonkIO x
zonkIO (VUnglue a phi ty e x) = unglue <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO x
zonkIO VBool = pure VBool
zonkIO VTt = pure VTt
zonkIO VFf = pure VFf
zonkIO (VIf a b c d) = elimBool <$> zonkIO a <*> zonkIO b <*> zonkIO c <*> zonkIO d
zonkIO (VCase x xs) = VCase <$> zonkIO x <*> traverse (\(x, y) -> (x,) <$> zonkIO y) xs
zonkSp :: Projection -> IO Projection
zonkSp (PApp p x) = PApp p <$> zonkIO x
@ -143,6 +138,13 @@ eval' env (Ref x) =
case Map.lookup x (getEnv env) of
Just (_, vl) -> vl
_ -> VNe (HVar x) mempty
eval' env (Con x) =
case Map.lookup x (getEnv env) of
Just (ty, _) -> VNe (HCon ty x) mempty
Nothing -> error $ "constructor " ++ show x ++ " has no type in scope"
eval' _ (Data x) = VNe (HData x) mempty
eval' env (App p f x) = vApp p (eval' env f) (eval' env x)
eval' env (Lam p s t) =
@ -179,8 +181,6 @@ eval' e (IElim l x y f i) = ielim (eval' e l) (eval' e x) (eval' e y) (eval' e f
eval' e (PathIntro p x y f) = VLine (eval' e p) (eval' e x) (eval' e y) (eval' e f)
eval' e (IsOne i) = VIsOne (eval' e i)
eval' e (IsOne1 i) = VIsOne1 (eval' e i)
eval' e (IsOne2 i) = VIsOne2 (eval' e i)
eval' _ ItIsOne = VItIsOne
eval' e (Partial x y) = VPartial (eval' e x) (eval' e y)
@ -200,10 +200,15 @@ eval' e (Let ns x) =
let env' = foldl (\newe (n, ty, x) -> newe { getEnv = Map.insert n (eval' newe ty, eval' newe x) (getEnv newe) }) e ns
in eval' env' x
eval' e (If a b c d) = elimBool (eval' e a) (eval' e b) (eval' e c) (eval' e d)
eval' _ Bool = VBool
eval' _ Tt = VTt
eval' _ Ff = VFf
eval' e (Case sc xs) = evalCase e (eval' e sc) xs
evalCase :: ElabEnv -> Value -> [(Term, Term)] -> Value
evalCase _ sc [] = error $ "unmatched pattern for value: " ++ show (prettyTm (quote sc))
evalCase env sc ((Ref _, k):_) = eval' env k @@ sc
evalCase env (force -> val@(VNe (HCon _ x) sp)) ((Con x', k):xs)
| x == x' = foldl applProj (eval' env k) sp
| otherwise = evalCase env val xs
evalCase env sc xs = VCase sc (map (second (eval' env)) xs)
vApp :: HasCallStack => Plicity -> Value -> Value -> Value
vApp p (VLam p' k) arg
@ -291,10 +296,6 @@ unify' topa topb = join $ go <$> forceIO topa <*> forceIO topb where
-- IsOne is proof-irrelevant:
go VItIsOne _ = pure ()
go _ VItIsOne = pure ()
go VIsOne1{} _ = pure ()
go _ VIsOne1{} = pure ()
go VIsOne2{} _ = pure ()
go _ VIsOne2{} = pure ()
go (VPartial phi r) (VPartial phi' r') = unify' phi phi' *> unify' r r'
go (VPartialP phi r) (VPartialP phi' r') = unify' phi phi' *> unify' r r'
@ -317,10 +318,6 @@ unify' topa topb = join $ go <$> forceIO topa <*> forceIO topb where
go (VSystem sys) rhs = goSystem unify' sys rhs
go rhs (VSystem sys) = goSystem (flip unify') sys rhs
go VTt VTt = pure ()
go VFf VFf = pure ()
go VBool VBool = pure ()
go x y
| x == y = pure ()
| otherwise =
@ -356,7 +353,7 @@ unify' topa topb = join $ go <$> forceIO topa <*> forceIO topb where
| otherwise = fail
unify :: HasCallStack => Value -> Value -> ElabM ()
unify a b = unify' a b `catchElab` \(_ :: SomeException) -> liftIO $ throwIO (NotEqual a b)
unify a b = unify' a b -- `catchElab` \(_ :: SomeException) -> liftIO $ throwIO (NotEqual a b)
isConvertibleTo :: Value -> Value -> ElabM (Term -> Term)
isConvertibleTo a b = isConvertibleTo (force a) (force b) where
@ -436,7 +433,9 @@ checkScope scope (VNe h sp) =
unless (v `Set.member` scope) . throwElab $
NotInScope v
HVar{} -> pure ()
HCon{} -> pure ()
HMeta{} -> pure ()
HData{} -> pure ()
traverse_ checkProj sp
where
checkProj (PApp _ t) = checkScope scope t
@ -475,8 +474,6 @@ checkScope s (VPath line a b) = traverse_ (checkScope s) [line, a, b]
checkScope s (VLine _ _ _ line) = checkScope s line
checkScope s (VIsOne x) = checkScope s x
checkScope s (VIsOne1 x) = checkScope s x
checkScope s (VIsOne2 x) = checkScope s x
checkScope _ VItIsOne = pure ()
checkScope s (VPartial x y) = traverse_ (checkScope s) [x, y]
@ -492,10 +489,7 @@ checkScope s (VGlueTy a phi ty eq) = traverse_ (checkScope s) [a, phi, ty, eq]
checkScope s (VGlue a phi ty eq inv x) = traverse_ (checkScope s) [a, phi, ty, eq, inv, x]
checkScope s (VUnglue a phi ty eq vl) = traverse_ (checkScope s) [a, phi, ty, eq, vl]
checkScope s (VIf a b c d) = traverse_ (checkScope s) [a, b, c, d]
checkScope _ VBool = pure ()
checkScope _ VTt = pure ()
checkScope _ VFf = pure ()
checkScope s (VCase v xs) = checkScope s v *> traverse_ (checkScope s . snd) xs
checkSpine :: Set Name -> Seq Projection -> ElabM [Name]
checkSpine scope (PApp Ex (VVar n@Bound{}) Seq.:<| xs)


+ 1
- 0
src/Elab/Monad.hs View File

@ -169,3 +169,4 @@ throwElab = liftIO . throwIO
incName :: Name -> Name -> Name
incName (Bound x _) n = Bound x (getNameNum n + 1)
incName (Defined x _) n = Defined x (getNameNum n + 1)
incName (ConName x _ s a) n = ConName x (getNameNum n + 1) s a

+ 37
- 34
src/Elab/WiredIn.hs View File

@ -17,13 +17,14 @@ import Data.Typeable
import Elab.Eval
import GHC.Stack (HasCallStack)
import qualified Presyntax.Presyntax as P
import Syntax.Pretty (prettyTm)
import Syntax
import System.IO.Unsafe
import Syntax.Pretty (prettyTm)
import GHC.Stack (HasCallStack)
wiType :: WiredIn -> NFType
wiType WiType = VType
@ -40,8 +41,6 @@ wiType WiPathP = dprod (VI ~> VType) \a -> a @@ VI0 ~> a @@ VI1 ~> VType
wiType WiIsOne = VI ~> VTypeω
wiType WiItIsOne = VIsOne VI1
wiType WiIsOne1 = forAll VI \i -> forAll VI \j -> VIsOne i ~> VIsOne (ior i j)
wiType WiIsOne2 = forAll VI \i -> forAll VI \j -> VIsOne j ~> VIsOne (ior i j)
wiType WiPartial = VI ~> VType ~> VTypeω
wiType WiPartialP = dprod VI \x -> VPartial x VType ~> VTypeω
@ -59,11 +58,6 @@ wiType WiGlueElem = forAll' "A" VType \a -> forAll' "phi" VI \phi -> forAll' "T"
-- {A : Type} {phi : I} {T : Partial phi Type} {e : PartialP phi (\o -> Equiv (T o) A)} -> Glue A phi T e -> A
wiType WiUnglue = forAll' "A" VType \a -> forAll' "phi" VI \phi -> forAll' "T" (VPartial phi VType) \ty -> forAll' "e" (VPartialP phi (fun \o -> equiv (ty @@ o) a)) \e -> VGlueTy a phi ty e ~> a
wiType WiBool = VType
wiType WiTrue = VBool
wiType WiFalse = VBool
wiType WiIf = dprod' "A" (VBool ~> VType) \a -> a @@ VTt ~> a @@ VFf ~> dprod' "b" VBool \b -> a @@ b
wiValue :: WiredIn -> Value
wiValue WiType = VType
wiValue WiPretype = VTypeω
@ -79,8 +73,6 @@ wiValue WiPathP = fun \a -> fun \x -> fun \y -> VPath a x y
wiValue WiIsOne = fun VIsOne
wiValue WiItIsOne = VItIsOne
wiValue WiIsOne1 = forallI \_ -> forallI \_ -> fun VIsOne1
wiValue WiIsOne2 = forallI \_ -> forallI \_ -> fun VIsOne2
wiValue WiPartial = fun \phi -> fun \r -> VPartial phi r
wiValue WiPartialP = fun \phi -> fun \r -> VPartialP phi r
@ -93,11 +85,6 @@ wiValue WiGlue = fun \a -> forallI \phi -> fun \t -> fun \e -> glueType a ph
wiValue WiGlueElem = forallI \a -> forallI \phi -> forallI \ty -> forallI \eqv -> fun \x -> fun \y -> glueElem a phi ty eqv x y
wiValue WiUnglue = forallI \a -> forallI \phi -> forallI \ty -> forallI \eqv -> fun \x -> unglue a phi ty eqv x
wiValue WiBool = VBool
wiValue WiTrue = VTt
wiValue WiFalse = VFf
wiValue WiIf = fun \a -> fun \b -> fun \c -> fun \d -> elimBool a b c d
(~>) :: Value -> Value -> Value
a ~> b = VPi P.Ex a (Closure (Bound "_" 0) (const b))
infixr 7 ~>
@ -142,8 +129,6 @@ wiredInNames = Map.fromList
, ("IsOne", WiIsOne)
, ("itIs1", WiItIsOne)
, ("isOneL", WiIsOne1)
, ("isOneR", WiIsOne2)
, ("Partial", WiPartial)
, ("PartialP", WiPartialP)
@ -155,11 +140,6 @@ wiredInNames = Map.fromList
, ("Glue", WiGlue)
, ("glue", WiGlueElem)
, ("unglue", WiUnglue)
, ("Bool", WiBool)
, ("true", WiTrue)
, ("false", WiFalse)
, ("if", WiIf)
]
newtype NoSuchPrimitive = NoSuchPrimitive { getUnknownPrim :: Text }
@ -215,6 +195,7 @@ ielim line left right fn i =
VNe n sp -> VNe n (sp Seq.:|> PIElim line left right i)
VSystem map -> VSystem (fmap (flip (ielim line left right) i) map)
VInc (VPath _ _ _) _ u -> ielim line left right u i
VCase x xs -> VCase x (fmap (fmap (flip (ielim line left right) i)) xs)
_ -> error $ "can't ielim " ++ show (prettyTm (quote fn))
outS :: NFSort -> NFEndp -> Value -> Value -> Value
@ -228,7 +209,7 @@ outS a phi u (VNe x sp) = VNe x (sp Seq.:|> POuc a phi u)
outS _ _ _ v = error $ "can't outS " ++ show (prettyTm (quote v))
-- Composition
comp :: HasCallStack => NFLine -> NFEndp -> Value -> Value -> Value
comp :: NFLine -> NFEndp -> Value -> Value -> Value
comp _ VI1 u _ = u @@ VI1 @@ VItIsOne
comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
case force $ a @@ VVar (Bound (T.pack "i") 0) of
@ -253,7 +234,7 @@ comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
w i = fill (fun dom) phi (system \i isone -> vProj1 (u @@ i @@ isone)) (VInc (dom VI0) phi (vProj1 a0)) i
c1 = comp (fun dom) phi (system \i isone -> vProj1 (u @@ i @@ isone)) (VInc (dom VI0) phi (vProj1 a0))
c2 = comp (fun \x -> rng x (w x)) phi (system \i isone -> vProj2 (u @@ i @@ isone)) (VInc (rng VI0 (w VI0)) phi (vProj2 a0))
in
in
VPair c1 c2
VPath{} ->
@ -312,11 +293,40 @@ comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
VType -> VGlueTy a0 phi (system \_ _ -> mkVSystem (Map.fromList [(phi, u @@ VI1 @@ VItIsOne)]))
(system \_ _ -> mkVSystem (Map.fromList [(phi, makeEquiv (\j -> (u @@ inot j)))]))
-- fibrancy structure of the booleans is trivial
VBool{} -> a0
VNe HData{} args ->
case force a0 of
VNe (HCon con_type con_name) con_args ->
VNe (HCon con_type con_name) $ compConArgs (length args) (a @@) con_type con_args phi u
_ -> VComp a phi u (VInc (a @@ VI0) phi a0)
_ -> VComp a phi u (VInc (a @@ VI0) phi a0)
compConArgs :: Int -> (NFEndp -> Value) -> Value -> Seq.Seq Projection -> NFEndp -> Value -> Seq.Seq Projection
compConArgs total_args fam = go total_args where
go _ _ Seq.Empty _ _ = Seq.Empty
go nargs (VPi p dom (Closure _ rng)) (PApp p' y Seq.:<| xs) phi u
| nargs > 0 = assert (p == p') $ go (nargs - 1) (rng (smuggle (fun (\i -> nthArg (total_args - nargs) (fam i))))) xs phi u
| otherwise = assert (p == p') $
let fill = makeFiller nargs dom phi u y
in PApp p' (fill @@ VI1) Seq.:<| go (nargs - 1) (rng fill) xs phi u
go _ _ _ _ _ = error $ "invalid constructor"
nthArg i (VNe hd s) =
case s Seq.!? i of
Just (PApp _ t) -> t
_ -> error $ "invalid " ++ show i ++ "th argument to data type " ++ show hd
nthArg i (VSystem vs) = VSystem (fmap (nthArg i) vs)
nthArg i xs = error $ "can't get " ++ show i ++ "th argument of " ++ show (prettyTm (quote xs))
makeFiller nth (VNe (HData (Bound _ (negate -> 10))) args) phi u a0 =
fun $ fill (makeDomain args) phi (system \i is1 -> nthArg nth (u @@ i @@ is1) ) a0
makeFiller _ _ _ _ a0 = fun (const a0)
makeDomain (PApp _ x Seq.:<| xs) = fun \i -> foldl (\t (~(PApp _ x)) -> t @@ (x @@ i)) (x @@ i) xs
makeDomain _ = error "somebody smuggled something that smells"
smuggle x = VNe (HData (Bound "__comp_con_tyarg" (negate 10))) (Seq.singleton (PApp P.Ex x))
compOutS :: NFSort -> NFEndp -> Value -> Value -> Value
compOutS a b c d = compOutS a b c (force d) where
compOutS _ _hi _0 vl@VComp{} = vl
@ -412,10 +422,3 @@ makeEquiv line = comp (fun \i -> equiv a (line i)) VI0 (system \_ _ -> VSystem m
ielim (fun (const a)) y y (vProj2 u) (iand i j)
id_fiber y = VPair y (VLine a y y (fun (const y)))
elimBool :: NFSort -> Value -> Value -> Value -> Value
elimBool prop x y bool =
case force bool of
VTt -> x
VFf -> y
_ -> VIf prop x y bool

+ 2
- 5
src/Elab/WiredIn.hs-boot View File

@ -1,7 +1,6 @@
module Elab.WiredIn where
import Syntax
import GHC.Stack
wiType :: WiredIn -> NFType
wiValue :: WiredIn -> NFType
@ -11,10 +10,8 @@ inot :: NFEndp -> NFEndp
ielim :: NFSort -> Value -> Value -> Value -> NFEndp -> Value
outS :: NFSort -> NFEndp -> Value -> Value -> Value
comp :: HasCallStack => NFLine -> NFEndp -> Value -> Value -> Value
comp :: NFLine -> NFEndp -> Value -> Value -> Value
glueType :: NFSort -> NFEndp -> NFPartial -> NFPartial -> Value
glueElem :: NFSort -> NFEndp -> NFPartial -> NFPartial -> NFPartial -> Value -> Value
unglue :: NFSort -> NFEndp -> NFPartial -> NFPartial -> Value -> Value
elimBool :: NFSort -> Value -> Value -> Value -> Value
unglue :: NFSort -> NFEndp -> NFPartial -> NFPartial -> Value -> Value

+ 2
- 0
src/Presyntax/Lexer.x View File

@ -152,10 +152,12 @@ variableOrKeyword (AlexPn _ l c, _, s, _) size =
case T.unpack text of
"as" -> pure (Token TokAs l c)
"in" -> pure (Token TokIn l c)
"data" -> pure (Token TokData l c)
"postulate" -> laidOut TokPostulate l c
"let" -> laidOut TokLet l c
"where" -> laidOut TokWhere l c
"case" -> laidOut TokCase l c
_ -> pure (Token (TokVar text) l c)


+ 27
- 1
src/Presyntax/Parser.y View File

@ -59,6 +59,8 @@ import Debug.Trace
'let' { Token TokLet _ _ }
'in' { Token TokIn _ _ }
'data' { Token TokData _ _ }
'case' { Token TokCase _ _ }
'where' { Token TokWhere _ _ }
'&&' { Token TokAnd _ _ }
@ -79,6 +81,7 @@ Exp :: { Expr }
Exp
: '\\' LambdaList '->' Exp { span $1 $4 $ makeLams $2 $4 }
| '\\' MaybeLambdaList '[' System ']' { span $1 $5 $ makeLams $2 $ LamSystem $4 }
| '\\' 'case' START CaseList END { span $1 $5 $ LamCase $4 }
| '(' var ':' Exp ')' ProdTail { span $1 $6 $ Pi Ex (getVar $2) $4 $6 }
| '{' var ':' Exp '}' ProdTail { span $1 $6 $ Pi Im (getVar $2) $4 $6 }
| ExpApp '->' Exp { span $1 $3 $ Pi Ex (T.singleton '_') $1 $3 }
@ -142,11 +145,32 @@ LetList :: { [LetItem] }
| LetItem { [$1] }
| LetItem ';' LetList { $1:$3 }
CaseItem :: { (Pattern, Expr) }
: Pattern '->' Exp { ($1, $3) }
CaseList :: { [(Pattern, Expr)] }
: CaseItem { [$1] }
| CaseItem Semis CaseList { $1:$3 }
Pattern :: { Pattern }
: PatVarList { makePattern $1 }
PatVarList :: { (Posn, Posn, [Text]) }
: var { (startPosn $1, endPosn $1, [getVar $1]) }
| var PatVarList { case $2 of (_, end, xs) -> (startPosn $1, end, getVar $1:xs) }
Statement :: { Statement }
: VarList ':' Exp { spanSt $1 $3 $ Decl (thd $1) $3 }
| var LhsList '=' Rhs { spanSt $1 $4 $ Defn (getVar $1) (makeLams $2 $4) }
| '{-#' Pragma '#-}' { spanSt $1 $3 $ $2 }
| 'postulate' START Postulates END { spanSt $1 $4 $ Postulate $3 }
| 'data' var Parameters ':' Exp 'where' START Postulates END
{ spanSt $1 $9 $ Data (getVar $2) $3 $5 $8 }
Parameters :: { [(Text, Plicity, Expr)] }
: {- empty -} { [] }
| '(' var ':' Exp ')' Parameters { (getVar $2, Ex, $4):$6 }
| '{' var ':' Exp '}' Parameters { (getVar $2, Im, $4):$6 }
Rhs :: { Expr }
: Exp { $1 }
@ -242,10 +266,12 @@ instance HasPosn (Posn, Posn, a) where
thd :: (a, b, c) -> c
thd (x, y, z) = z
span s e ex = Span ex (startPosn s) (endPosn e)
spanSt s e ex = SpanSt ex (startPosn s) (endPosn e)
getVar (Token (TokVar s) _ _) = s
getVar _ = error "getVar non-var"
makePattern (_, _, [x]) = PCap x
makePattern (_, _, (x:xs)) = PCon x xs
}

+ 8
- 0
src/Presyntax/Presyntax.hs View File

@ -21,6 +21,7 @@ data Expr
| Proj2 Expr
| LamSystem [(Condition, Expr)]
| LamCase [(Pattern, Expr)]
| Let [LetItem] Expr
| Span Expr Posn Posn
@ -44,6 +45,11 @@ data Formula
| FBot
deriving (Eq, Show, Ord)
data Pattern
= PCon Text [Text]
| PCap Text
deriving (Eq, Show, Ord)
data Statement
= Decl [Text] Expr
| Defn Text Expr
@ -54,6 +60,8 @@ data Statement
| ReplNf Expr -- REPL eval
| ReplTy Expr -- REPL :t
| Data Text [(Text, Plicity, Expr)] Expr [(Text, Expr)]
| SpanSt Statement Posn Posn
deriving (Eq, Show, Ord)


+ 5
- 0
src/Presyntax/Tokens.hs View File

@ -44,7 +44,10 @@ data TokenClass
| TokAs
| TokWhere
| TokCase
| TokPostulate
| TokData
| TokSemi
deriving (Eq, Show, Ord)
@ -80,6 +83,8 @@ tokSize TokIn = 2
tokSize TokLStart = 0
tokSize TokLEnd = 0
tokSize TokWhere = length "where"
tokSize TokData = length "data"
tokSize TokCase = length "case"
tokSize TokPostulate = length "postulate"
data Token


+ 49
- 31
src/Syntax.hs View File

@ -3,6 +3,8 @@
{-# LANGUAGE DeriveDataTypeable #-}
module Syntax where
import Control.Arrow (Arrow(second))
import qualified Data.Map.Strict as Map
import qualified Data.Sequence as Seq
import qualified Data.Set as Set
@ -30,8 +32,6 @@ data WiredIn
| WiIsOne -- Proposition associated with an element of the interval
| WiItIsOne -- 1 = 1
| WiIsOne1 -- i j -> [i] -> [ior i j]
| WiIsOne2 -- i j -> [j] -> [ior i j]
| WiPartial -- (φ : I) -> Type -> Typeω
| WiPartialP -- (φ : I) -> Partial r Type -> Typeω
@ -47,15 +47,12 @@ data WiredIn
| WiGlue -- (A : Type) {phi : I} (T : Partial phi Type) (e : PartialP phi (\o -> Equiv (T o) A)) -> Type
| WiGlueElem -- {A : Type} {phi : I} {T : Partial phi Type} {e : PartialP phi (\o -> Equiv (T o) A)} -> (t : PartialP phi T) -> Sub A phi (\o -> e o (t o)) -> Glue A phi T e
| WiUnglue -- {A : Type} {phi : I} {T : Partial phi Type} {e : PartialP phi (\o -> Equiv (T o) A)} -> Glue A phi T e -> A
| WiBool
| WiTrue
| WiFalse
| WiIf
deriving (Eq, Show, Ord)
data Term
= Ref Name
| Con Name
| Data Name
| App Plicity Term Term
| Lam Plicity Name Term
| Pi Plicity Name Term Term
@ -84,8 +81,6 @@ data Term
-- ~~~~~~~~~ not printed at all
| IsOne Term
| IsOne1 Term
| IsOne2 Term
| ItIsOne
| Partial Term Term
@ -103,8 +98,7 @@ data Term
| Glue Term Term Term Term Term Term
| Unglue Term Term Term Term Term
-- ugly. TODO: proper inductive types
| Bool | Tt | Ff | If Term Term Term Term
| Case Term [(Term, Term)]
deriving (Eq, Show, Ord, Data)
data MV =
@ -130,7 +124,14 @@ instance Data MV where
data Name
= Bound {getNameText :: Text, getNameNum :: !Int}
| Defined {getNameText :: Text, getNameNum :: !Int}
deriving (Eq, Show, Ord, Data)
| ConName {getNameText :: Text, getNameNum :: !Int, conSkip :: !Int, conArity :: !Int}
deriving (Show, Data)
instance Eq Name where
x == y = getNameText x == getNameText y && getNameNum x == getNameNum y
instance Ord Name where
compare x y = getNameText x `compare` getNameText y <> getNameNum x `compare` getNameNum y
type NFType = Value
type NFEndp = Value
@ -160,8 +161,6 @@ data Value
| VIsOne NFEndp
| VItIsOne
| VIsOne1 NFEndp
| VIsOne2 NFEndp
| VPartial NFEndp Value
| VPartialP NFEndp Value
@ -176,10 +175,7 @@ data Value
| VGlue NFSort NFEndp NFPartial NFPartial NFPartial Value
| VUnglue NFSort NFEndp NFPartial NFPartial Value
| VBool
| VTt
| VFf
| VIf Value Value Value Value
| VCase Value [(Term, Value)]
deriving (Eq, Show, Ord)
pattern VVar :: Name -> Value
@ -187,8 +183,10 @@ pattern VVar x = VNe (HVar x) Seq.Empty
quoteWith :: Set Name -> Value -> Term
quoteWith names (VNe h sp) = foldl goSpine (goHead h) sp where
goHead (HVar v) = Ref v
goHead (HMeta m) = Meta m
goHead (HVar v) = Ref v
goHead (HMeta m) = Meta m
goHead (HCon _ v) = Con v
goHead (HData v) = Data v
goSpine t (PApp p v) = App p t (quoteWith names v)
goSpine t (PIElim l x y i) = IElim (quote l) (quote x) (quote y) t (quote i)
@ -232,8 +230,6 @@ quoteWith names (VPath line x y) = PathP (quoteWith names line) (quoteWith names
quoteWith names (VLine p x y f) = PathIntro (quoteWith names p) (quoteWith names x) (quoteWith names y) (quoteWith names f)
quoteWith names (VIsOne v) = IsOne (quoteWith names v)
quoteWith names (VIsOne1 v) = IsOne1 (quoteWith names v)
quoteWith names (VIsOne2 v) = IsOne2 (quoteWith names v)
quoteWith _ VItIsOne = ItIsOne
quoteWith names (VPartial x y) = Partial (quoteWith names x) (quoteWith names y)
@ -247,15 +243,10 @@ quoteWith names (VGlueTy a phi t e) = GlueTy (quoteWith names a) (quoteWith n
quoteWith names (VGlue a phi ty e t x) = Glue (quoteWith names a) (quoteWith names phi) (quoteWith names ty) (quoteWith names e) (quoteWith names t) (quoteWith names x)
quoteWith names (VUnglue a phi ty e x) = Unglue (quoteWith names a) (quoteWith names phi) (quoteWith names ty) (quoteWith names e) (quoteWith names x)
quoteWith _ames VBool = Bool
quoteWith _ames VTt = Tt
quoteWith _ames VFf = Ff
quoteWith names (VIf a b c d) = If (quoteWith names a) (quoteWith names b) (quoteWith names c) (quoteWith names d)
quoteWith names (VCase v xs) = Case (quoteWith names v) (map (second (quoteWith names)) xs)
alwaysShort :: Value -> Bool
alwaysShort VBool{} = True
alwaysShort VTt{} = True
alwaysShort VFf{} = True
alwaysShort (VNe HCon{} _) = True
alwaysShort VVar{} = True
alwaysShort _ = False
@ -288,8 +279,35 @@ instance Ord Closure where
data Head
= HVar Name
| HCon Value Name
| HMeta MV
deriving (Eq, Show, Ord)
| HData Name
deriving (Show)
instance Eq Head where
HVar x == HVar y = x == y
HCon _ x == HCon _ y = x == y
HMeta x == HMeta y = x == y
HData x == HData y = x == y
_ == _ = False
instance Ord Head where
compare x y =
case x of
HVar n -> case y of
HVar n' -> compare n n'
_ -> LT
HCon _ n -> case y of
HVar _ -> GT
HCon _ n' -> compare n n'
_ -> LT
HMeta n -> case y of
HMeta n' -> compare n n'
HData _ -> LT
_ -> GT
HData n -> case y of
HData n' -> compare n n'
_ -> GT
data Projection
= PApp Plicity Value
@ -297,4 +315,4 @@ data Projection
| PProj1
| PProj2
| POuc NFSort NFEndp Value
deriving (Eq, Show, Ord)
deriving (Eq, Show, Ord)

+ 11
- 17
src/Syntax/Pretty.hs View File

@ -21,8 +21,7 @@ import Prettyprinter
import Syntax
instance Pretty Name where
pretty (Bound x _) = pretty x
pretty (Defined x _) = pretty x
pretty = pretty . getNameText
prettyTm :: Term -> Doc AnsiStyle
prettyTm = prettyTm . everywhere (mkT beautify) where
@ -30,6 +29,8 @@ prettyTm = prettyTm . everywhere (mkT beautify) where
case T.uncons (getNameText v) of
Just ('.', w) -> keyword (pretty w)
_ -> pretty v
prettyTm (Con v) = keyword (pretty v)
prettyTm (Data v) = operator (pretty v)
prettyTm (App Im f x) = parenFun f <+> braces (prettyTm x)
prettyTm (App Ex f x) = parenFun f <+> parenArg x
@ -75,21 +76,19 @@ prettyTm = prettyTm . everywhere (mkT beautify) where
prettyTm (System xs) = braces (mempty <+> hsep (punctuate comma (map go (Map.toList xs))) <+> mempty) where
go (f, t) = prettyTm f <+> operator (pretty "=>") <+> prettyTm t
prettyTm (Case x xs) = keyword (pretty "case") <+> prettyTm x <+> keyword (pretty "of") <+> braces (prettyCase xs)
prettyTm x = error (show x)
prettyCase = vsep . map go where
go (x, xs) = prettyTm x <+> operator (pretty "=>") <+> prettyTm xs
beautify (PathP l x y) = toFun "PathP" [l, x, y]
beautify (IElim _ _ _ f i) = App Ex f i
beautify (PathIntro _ _ _ f) = f
beautify (IsOne phi) = toFun "IsOne" [phi]
beautify ItIsOne = Ref (Bound (T.pack ".1=1") 0)
beautify (IsOne1 phi) = toFun "isOne1" [phi]
beautify (IsOne2 phi) = toFun "isOne2" [phi]
beautify Bool = Ref (Bound (T.pack ".Bool") 0)
beautify Tt = Ref (Bound (T.pack ".true") 0)
beautify Ff = Ref (Bound (T.pack ".false") 0)
beautify (If a b c d) = toFun "if" [a, b, c, d]
beautify (Lam Ex v (App Ex f (Ref v')))
| v == v', v `Set.notMember` freeVars f = f
@ -119,8 +118,6 @@ parenArg :: Term -> Doc AnsiStyle
parenArg x@App{} = parens (prettyTm x)
parenArg x@IElim{} = parens (prettyTm x)
parenArg x@IsOne{} = parens $ prettyTm x
parenArg x@IsOne1{} = parens $ prettyTm x
parenArg x@IsOne2{} = parens $ prettyTm x
parenArg x@Partial{} = parens $ prettyTm x
parenArg x@PartialP{} = parens $ prettyTm x
@ -161,6 +158,8 @@ freeVars (Let ns x) = Set.union (freeVars x `Set.difference` bound) freed where
bound = Set.fromList (map (\(x, _, _) -> x) ns)
freed = foldr (\(_, x, y) -> Set.union (Set.union (freeVars x) (freeVars y))) mempty ns
freeVars Meta{} = mempty
freeVars Con{} = mempty
freeVars Data{} = mempty
freeVars Type{} = mempty
freeVars Typeω{} = mempty
freeVars I{} = mempty
@ -177,8 +176,6 @@ freeVars (PathP x y z) = Set.unions $ map freeVars [x, y, z]
freeVars (IElim x y z a b) = Set.unions $ map freeVars [x, y, z, a, b]
freeVars (PathIntro x y z a) = Set.unions $ map freeVars [x, y, z, a]
freeVars (IsOne a) = Set.unions $ map freeVars [a]
freeVars (IsOne1 a) = Set.unions $ map freeVars [a]
freeVars (IsOne2 a) = Set.unions $ map freeVars [a]
freeVars ItIsOne{} = mempty
freeVars (Partial x y) = Set.unions $ map freeVars [x, y]
freeVars (PartialP x y) = Set.unions $ map freeVars [x, y]
@ -191,7 +188,4 @@ freeVars (Comp x y z a) = Set.unions $ map freeVars [x, y, z, a]
freeVars (GlueTy x y z a) = Set.unions $ map freeVars [x, y, z, a]
freeVars (Glue x y z a b c) = Set.unions $ map freeVars [x, y, z, a, b, c]
freeVars (Unglue x y z a c) = Set.unions $ map freeVars [x, y, z, a, c]
freeVars Bool{} = mempty
freeVars Tt{} = mempty
freeVars Ff{} = mempty
freeVars (If x y z a) = Set.unions $ map freeVars [x, y, z, a]
freeVars (Case x y) = freeVars x <> foldMap (freeVars . snd) y

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