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Idris-dev/src/Core.hs
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1{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, DeriveFunctor #-}
3module Core where
5import Control.Monad.State
6import Debug.Trace
8{- The language has:
9 * Full dependent types
10 * A hierarchy of universes, with cumulativity: Set : Set1, Set1 : Set2, ...
11 * Pattern matching letrec binding
12 * (primitive types defined externally)
14 Some technical stuff:
15 * Typechecker is kept as simple as possible
16 - no unification, just a checker for incomplete terms.
17 * We have a simple collection of tactics which we use to elaborate source
18 programs with implicit syntax into fully explicit terms.
19-}
21data Option = SetInSet
22 | CheckConv
23 deriving Eq
25-- RAW TERMS ----------------------------------------------------------------
27-- Names are hierarchies of strings, describing scope (so no danger of
28-- duplicate names, but need to be careful on lookup).
29-- Also MN for machine chosen names
31data Name = UN [String]
32 | MN Int String
33 deriving Eq
35instance Show Name where
36 show (UN [n]) = n
37 show (UN (n:ns)) = show (UN [n]) ++ "." ++ show (UN ns)
38 show (MN i s) = "{" ++ s ++ show i ++ "}"
40data Raw = Var Name
41 | RBind Name (Binder Raw) Raw
42 | RApp Raw Raw
43 | RSet Int
44 deriving Show
46data Binder b = Lam { binderTy :: b }
47 | Pi { binderTy :: b }
48 | Let { binderTy :: b,
49 binderVal :: b }
50 | Hole { binderTy :: b}
51 | Guess { binderTy :: b,
52 binderVal :: b }
53 | PVar { binderTy :: b }
54 deriving (Show, Eq, Functor)
56data RawFun = RawFun { rtype :: Raw,
57 rval :: Raw
58 }
59 deriving Show
61data RDef = RFunction RawFun
62 | RConst Raw
63 deriving Show
65type RProgram = [(Name, RDef)]
67-- WELL TYPED TERMS ---------------------------------------------------------
69data NameType = Ref | DCon Int Int | TCon Int
70 deriving (Show, Eq)
72-- FIXME: Consider changing this to birectional, with type annotations.
74data TT n = P NameType n (TT n) -- embed type
75 | V Int
76 | Bind n (Binder (TT n)) (TT n)
77 | App (TT n) (TT n) -- function, function type, arg
78 | Set Int
79 deriving (Functor, Eq)
81type EnvTT n = [(n, Binder (TT n))]
83bindEnv :: EnvTT n -> TT n -> TT n
84bindEnv [] tm = tm
85bindEnv ((n, b):bs) tm = Bind n b (bindEnv bs tm)
87type Term = TT Name
88type Type = Term
90type Env = EnvTT Name
92-- an environment with de Bruijn indices 'normalised' so that they all refer to
93-- this environment
95newtype WkEnvTT n = Wk (EnvTT n)
96type WkEnv = WkEnvTT Name
98instance Show n => Show (TT n) where
99 show t = showEnv [] t
101showEnv env t = showEnv' env t False
102showEnvDbg env t = showEnv' env t True
104showEnv' env t dbg = se 10 env t where
105 se p env (P _ n _) = show n
106 se p env (V i) | i < length env = (show $ fst $ env!!i) ++
107 if dbg then "{" ++ show i ++ "}" else ""
108 | otherwise = "!!V " ++ show i ++ "!!"
109 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
110 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
111 se p env (Set i) = "Set" ++ show i
113 sb env n (Lam t) = showb env "\\ " " => " n t
114 sb env n (Hole t) = showb env "? " ". " n t
115 sb env n (Pi t) = showb env "forall " " -> " n t
116 sb env n (PVar t) = showb env "! " ". " n t
117 sb env n (Let t v) = showbv env "let " " in " n t v
118 sb env n (Guess t v) = showbv env "?? " " in " n t v
120 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
121 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
122 se 10 env v ++ sc
124 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
125 | otherwise = str
127-- Check whether a term has any holes in it - impure if so
129pureTerm :: TT n -> Bool
130pureTerm (App f a) = pureTerm f && pureTerm a
131pureTerm (Bind n b sc) = pureBinder b && pureTerm sc where
132 pureBinder (Hole _) = False
133 pureBinder (Guess _ _) = False
134 pureBinder (Let t v) = pureTerm t && pureTerm v
135 pureBinder t = pureTerm (binderTy t)
136pureTerm _ = True
138-- weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
140weakenTm :: Int -> TT n -> TT n
141weakenTm i t = wk i 0 t
142 where wk i min (V x) | x >= min = V (i + x)
143 wk i m (App f a) = App (wk i m f) (wk i m a)
144 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
145 wk i m t = t
146 wkb i m (Let t v) = Let (wk i m t) (wk i m v)
147 wkb i m (Guess t v) = Guess (wk i m t) (wk i m v)
148 wkb i m t = t { binderTy = wk i m (binderTy t) }
150-- weaken an environment so that all the de Bruijn indices are correct according
151-- to the latest bound variable
153weakenEnv :: EnvTT n -> EnvTT n
154weakenEnv env = wk (length env - 1) env
155 where wk i [] = []
156 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
157 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
158 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
159 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
161weakenTmEnv :: Int -> EnvTT n -> EnvTT n
162weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
164-- WELL TYPED TERMS AS HOAS -------------------------------------------------
166data HTT = HP NameType Name HTT
167 | HV Int
168 | HBind Name (Binder HTT) (HTT -> HTT)
169 | HApp HTT HTT
170 | HSet Int
171 | HTmp Int
173instance Show HTT where
174 show h = "<<HOAS>>"
176hoas :: [HTT] -> TT Name -> HTT
177hoas env (P nt n ty) = HP nt n (hoas env ty)
178hoas env (V i) | i < length env = env!!i
179 | otherwise = HV i
180hoas env (Bind n b sc) = HBind n (hbind b) (\x -> hoas (x:env) sc)
181 where hbind (Lam t) = Lam (hoas env t)
182 hbind (Pi t) = Pi (hoas env t)
183 hbind (Hole t) = Hole (hoas env t)
184 hbind (PVar t) = PVar (hoas env t)
185 hbind (Let v t) = Let (hoas env v) (hoas env t)
186 hbind (Guess v t) = Guess (hoas env v) (hoas env t)
187hoas env (App f a) = HApp (hoas env f) (hoas env a)
188hoas env (Set i) = HSet i
190-- CONTEXTS -----------------------------------------------------------------
192data Fun = Fun Type HTT Term HTT
193 deriving Show
195data Def = Function Fun
196 | Constant NameType Type HTT
197 deriving Show
199type Context = [(Name, Def)]
201emptyContext = []
203addToCtxt :: Name -> Term -> Type -> Context -> Context
204addToCtxt n tm ty ctxt = (n, Function (Fun ty (hoas [] ty)
205 tm (hoas [] tm))) : ctxt
207lookupTy :: Name -> Context -> Maybe Type
208lookupTy n ctxt = do def <- lookup n ctxt
209 case def of
210 (Function (Fun ty _ _ _)) -> return ty
211 (Constant _ ty _) -> return ty
213lookupP :: Name -> Context -> Maybe Term
214lookupP n ctxt
215 = do def <- lookup n ctxt
216 case def of
217 (Function (Fun ty _ tm _)) -> return (P Ref n ty)
218 (Constant nt ty hty) -> return (P nt n ty)
220lookupVal :: Name -> Context -> Maybe HTT
221lookupVal n ctxt
222 = do def <- lookup n ctxt
223 case def of
224 (Function (Fun _ _ _ htm)) -> return htm
225 (Constant nt ty hty) -> return (HP nt n hty)
227lookupTyEnv :: Name -> Env -> Maybe (Int, Type)
228lookupTyEnv n env = li n 0 env where
229 li n i [] = Nothing
230 li n i ((x, b): xs)
231 | n == x = Just (i, binderTy b)
232 | otherwise = li n (i+1) xs
235x = UN ["x"]
236xt = UN ["X"]
237testtm = RBind xt (Lam (RSet 0)) (RBind x (Lam (Var xt)) (Var x))