git.iko.soy/Idris-dev
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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)
72data TT n = P NameType n (TT n) -- embed type
73 | V Int
74 | Bind n (Binder (TT n)) (TT n)
75 | App (TT n) (TT n) (TT n) -- function, function type, arg
76 | Set Int
77 deriving (Functor, Eq)
79type EnvTT n = [(n, Binder (TT n))]
81bindEnv :: EnvTT n -> TT n -> TT n
82bindEnv [] tm = tm
83bindEnv ((n, b):bs) tm = Bind n b (bindEnv bs tm)
85type Term = TT Name
86type Type = Term
88type Env = EnvTT Name
90-- an environment with de Bruijn indices 'normalised' so that they all refer to
91-- this environment
93newtype WkEnvTT n = Wk (EnvTT n)
94type WkEnv = WkEnvTT Name
96instance Show n => Show (TT n) where
97 show t = showEnv [] t
99showEnv env t = showEnv' env t False
100showEnvDbg env t = showEnv' env t True
102showEnv' env t dbg = se 10 env t where
103 se p env (P _ n _) = show n
104 se p env (V i) | i < length env = (show $ fst $ env!!i) ++
105 if dbg then "{" ++ show i ++ "}" else ""
106 | otherwise = "!!V " ++ show i ++ "!!"
107 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
108 se p env (App f t a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
109 se p env (Set i) = "Set" ++ show i
111 sb env n (Lam t) = showb env "\\ " " => " n t
112 sb env n (Hole t) = showb env "? " ". " n t
113 sb env n (Pi t) = showb env "forall " " -> " n t
114 sb env n (PVar t) = showb env "! " ". " n t
115 sb env n (Let t v) = showbv env "let " " in " n t v
116 sb env n (Guess t v) = showbv env "?? " " in " n t v
118 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
119 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
120 se 10 env v ++ sc
122 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
123 | otherwise = str
125-- Check whether a term has any holes in it - impure if so
127pureTerm :: TT n -> Bool
128pureTerm (App f t a) = pureTerm f && pureTerm t && pureTerm a
129pureTerm (Bind n b sc) = pureBinder b && pureTerm sc where
130 pureBinder (Hole _) = False
131 pureBinder (Guess _ _) = False
132 pureBinder (Let t v) = pureTerm t && pureTerm v
133 pureBinder t = pureTerm (binderTy t)
134pureTerm _ = True
136-- weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
138weakenTm :: Int -> TT n -> TT n
139weakenTm i t = wk i 0 t
140 where wk i min (V x) | x >= min = V (i + x)
141 wk i m (App f t a) = App (wk i m f) (wk i m t) (wk i m a)
142 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
143 wk i m t = t
144 wkb i m (Let t v) = Let (wk i m t) (wk i m v)
145 wkb i m (Guess t v) = Guess (wk i m t) (wk i m v)
146 wkb i m t = t { binderTy = wk i m (binderTy t) }
148-- weaken an environment so that all the de Bruijn indices are correct according
149-- to the latest bound variable
151weakenEnv :: Show n => EnvTT n -> EnvTT n
152weakenEnv env = wk (length env - 1) env
153 where wk i [] = []
154 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
155 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
156 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
157 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
159-- WELL TYPED TERMS AS HOAS -------------------------------------------------
161data HTT = HP NameType Name HTT
162 | HV Int
163 | HBind Name (Binder HTT) (HTT -> HTT)
164 | HApp HTT HTT HTT
165 | HSet Int
166 | HTmp Int
168instance Show HTT where
169 show h = "<<HOAS>>"
171hoas :: [HTT] -> TT Name -> HTT
172hoas env (P nt n ty) = HP nt n (hoas env ty)
173hoas env (V i) | i < length env = env!!i
174 | otherwise = HV i
175hoas env (Bind n b sc) = HBind n (hbind b) (\x -> hoas (x:env) sc)
176 where hbind (Lam t) = Lam (hoas env t)
177 hbind (Pi t) = Pi (hoas env t)
178 hbind (Hole t) = Hole (hoas env t)
179 hbind (PVar t) = PVar (hoas env t)
180 hbind (Let v t) = Let (hoas env v) (hoas env t)
181 hbind (Guess v t) = Guess (hoas env v) (hoas env t)
182hoas env (App f t a) = HApp (hoas env f) (hoas env t) (hoas env a)
183hoas env (Set i) = HSet i
185-- CONTEXTS -----------------------------------------------------------------
187data Fun = Fun Type HTT Term HTT
188 deriving Show
190data Def = Function Fun
191 | Constant NameType Type HTT
192 deriving Show
194type Context = [(Name, Def)]
196emptyContext = []
198addToCtxt :: Name -> Term -> Type -> Context -> Context
199addToCtxt n tm ty ctxt = (n, Function (Fun ty (hoas [] ty)
200 tm (hoas [] tm))) : ctxt
202lookupTy :: Name -> Context -> Maybe Type
203lookupTy n ctxt = do def <- lookup n ctxt
204 case def of
205 (Function (Fun ty _ _ _)) -> return ty
206 (Constant _ ty _) -> return ty
208lookupP :: Name -> Context -> Maybe Term
209lookupP n ctxt
210 = do def <- lookup n ctxt
211 case def of
212 (Function (Fun ty _ tm _)) -> return (P Ref n ty)
213 (Constant nt ty hty) -> return (P nt n ty)
215lookupVal :: Name -> Context -> Maybe HTT
216lookupVal n ctxt
217 = do def <- lookup n ctxt
218 case def of
219 (Function (Fun _ _ _ htm)) -> return htm
220 (Constant nt ty hty) -> return (HP nt n hty)
222lookupTyEnv :: Name -> Env -> Maybe (Int, Type)
223lookupTyEnv n env = li n 0 env where
224 li n i [] = Nothing
225 li n i ((x, b): xs)
226 | n == x = Just (i, binderTy b)
227 | otherwise = li n (i+1) xs
230x = UN ["x"]
231xt = UN ["X"]
232testtm = RBind xt (Lam (RSet 0)) (RBind x (Lam (Var xt)) (Var x))