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Idris-dev/src/Core/TT.hs
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1{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, DeriveFunctor #-}
3module Core.TT where
5import Control.Monad.State
6import Debug.Trace
7import qualified Data.Map as Map
8import Data.Char
10{- The language has:
11 * Full dependent types
12 * A hierarchy of universes, with cumulativity: Set : Set1, Set1 : Set2, ...
13 * Pattern matching letrec binding
14 * (primitive types defined externally)
16 Some technical stuff:
17 * Typechecker is kept as simple as possible
18 - no unification, just a checker for incomplete terms.
19 * We have a simple collection of tactics which we use to elaborate source
20 programs with implicit syntax into fully explicit terms.
21-}
23data Option = SetInSet
24 | CheckConv
25 deriving Eq
27data FC = FC { fc_fname :: String,
28 fc_line :: Int }
29 deriving Eq
31instance Show FC where
32 show (FC f l) = f ++ ":" ++ show l
34data Err = Msg String
35 | CantUnify Term Term Err
36 | At FC Err
37 deriving Eq
39instance Show Err where
40 show (Msg s) = s
42data TC a = OK a
43 | Error Err
44 deriving (Eq, Functor)
46instance Show a => Show (TC a) where
47 show (OK x) = show x
48 show (Error str) = "Error: " ++ show str
50-- at some point, this instance should also carry type checking options
51-- (e.g. Set:Set)
53instance Monad TC where
54 return = OK
55 x >>= k = case x of
56 OK v -> k v
57 Error e -> Error e
58 fail e = Error (Msg e)
60tfail :: Err -> TC a
61tfail e = Error e
63trun :: FC -> TC a -> TC a
64trun fc (OK a) = OK a
65trun fc (Error e) = Error (At fc e)
67instance MonadPlus TC where
68 mzero = fail "Unknown error"
69 (OK x) `mplus` _ = OK x
70 _ `mplus` (OK y) = OK y
71 err `mplus` _ = err
73discard :: Monad m => m a -> m ()
74discard f = f >> return ()
76showSep :: String -> [String] -> String
77showSep sep [] = ""
78showSep sep [x] = x
79showSep sep (x:xs) = x ++ sep ++ showSep sep xs
81traceWhen True msg a = trace msg a
82traceWhen False _ a = a
84-- RAW TERMS ----------------------------------------------------------------
86-- Names are hierarchies of strings, describing scope (so no danger of
87-- duplicate names, but need to be careful on lookup).
88-- Also MN for machine chosen names
90data Name = UN [String]
91 | MN Int String
92 deriving (Eq, Ord)
94instance Show Name where
95 show (UN [n]) = n
96 show (UN (n:ns)) = show (UN [n]) ++ "." ++ show (UN ns)
97 show (MN i s) = "{" ++ s ++ show i ++ "}"
100-- Contexts allow us to map names to things
101-- TODO: Namespaces and ambiguous names
103type Ctxt a = Map.Map Name a
104emptyContext = Map.empty
106addDef :: Name -> a -> Ctxt a -> Ctxt a
107addDef = Map.insert
109lookupCtxt :: Name -> Ctxt a -> Maybe a
110lookupCtxt = Map.lookup
112toAlist :: Ctxt a -> [(Name, a)]
113toAlist = Map.toList
115addAlist :: [(Name, a)] -> Ctxt a -> Ctxt a
116addAlist [] ctxt = ctxt
117addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
119data Const = I Int | Fl Double | Ch Char | Str String
120 | IType | FlType | ChType | StrType | PtrType
121 deriving Eq
123data Raw = Var Name
124 | RBind Name (Binder Raw) Raw
125 | RApp Raw Raw
126 | RSet Int
127 | RConstant Const
128 deriving (Show, Eq)
130data Binder b = Lam { binderTy :: b }
131 | Pi { binderTy :: b }
132 | Let { binderTy :: b,
133 binderVal :: b }
134 | NLet { binderTy :: b,
135 binderVal :: b }
136 | Hole { binderTy :: b}
137 | GHole { binderTy :: b}
138 | Guess { binderTy :: b,
139 binderVal :: b }
140 | PVar { binderTy :: b }
141 | PVTy { binderTy :: b }
142 deriving (Show, Eq, Functor)
144fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
145fmapMB f (Let t v) = liftM2 Let (f t) (f v)
146fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
147fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
148fmapMB f (Lam t) = liftM Lam (f t)
149fmapMB f (Pi t) = liftM Pi (f t)
150fmapMB f (Hole t) = liftM Hole (f t)
151fmapMB f (GHole t) = liftM GHole (f t)
152fmapMB f (PVar t) = liftM PVar (f t)
153fmapMB f (PVTy t) = liftM PVTy (f t)
155raw_apply :: Raw -> [Raw] -> Raw
156raw_apply f [] = f
157raw_apply f (a : as) = raw_apply (RApp f a) as
159data RawFun = RawFun { rtype :: Raw,
160 rval :: Raw
161 }
162 deriving Show
164data RawDatatype = RDatatype Name Raw [(Name, Raw)]
165 deriving Show
167data RDef = RFunction RawFun
168 | RConst Raw
169 | RData RawDatatype
170 deriving Show
172type RProgram = [(Name, RDef)]
174-- WELL TYPED TERMS ---------------------------------------------------------
176data NameType = Bound | Ref | DCon Int Int | TCon Int Int
177 deriving (Show, Eq)
179data TT n = P NameType n (TT n) -- embed type
180 | V Int
181 | Bind n (Binder (TT n)) (TT n)
182 | App (TT n) (TT n) -- function, function type, arg
183 | Constant Const
184 | Set Int
185 deriving Functor
187type EnvTT n = [(n, Binder (TT n))]
189data Datatype n = Data { d_typename :: n,
190 d_typetag :: Int,
191 d_type :: (TT n),
192 d_cons :: [(n, TT n)] }
193 deriving (Show, Functor, Eq)
195instance Eq n => Eq (TT n) where
196 (==) (P xt x _) (P yt y _) = xt == yt && x == y
197 (==) (V x) (V y) = x == y
198 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
199 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
200 (==) (Set x) (Set y) = x == y
201 (==) (Constant x) (Constant y) = x == y
202 (==) _ _ = False
204-- A few handy operations on well typed terms:
206instantiate :: TT n -> TT n -> TT n
207instantiate e = subst 0 where
208 subst i (V x) | i == x = e
209 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
210 subst i (App f a) = App (subst i f) (subst i a)
211 subst i t = t
213pToV :: Eq n => n -> TT n -> TT n
214pToV n = pToV' n 0
215pToV' n i (P _ x _) | n == x = V i
216pToV' n i (Bind x b sc)
217 | n == x = Bind x (fmap (pToV' n i) b) sc
218 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
219pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
220pToV' n i t = t
222-- Convert several names. First in the list comes out as V 0
223pToVs :: Eq n => [n] -> TT n -> TT n
224pToVs ns tm = pToVs' ns tm 0 where
225 pToVs' [] tm i = tm
226 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
228vToP :: TT n -> TT n
229vToP = vToP' [] where
230 vToP' env (V i) = let (n, b) = (env !! i) in
231 P Bound n (binderTy b)
232 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
233 Bind n b' (vToP' ((n, b'):env) sc)
234 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
235 vToP' env t = t
237finalise :: Eq n => TT n -> TT n
238finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
239finalise (App f a) = App (finalise f) (finalise a)
240finalise t = t
242subst :: Eq n => n -> TT n -> TT n -> TT n
243subst n v tm = instantiate v (pToV n tm)
245substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
246substNames [] t = t
247substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
249-- Returns true if V 0 and bound name n do not occur in the term
251noOccurrence :: Eq n => n -> TT n -> Bool
252noOccurrence n t = no' 0 t
253 where
254 no' i (V x) = not (i == x)
255 no' i (P Bound x _) = not (n == x)
256 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
257 where noB' i (Let t v) = no' i t && no' i v
258 noB' i (Guess t v) = no' i t && no' i v
259 noB' i b = no' i (binderTy b)
260 no' i (App f a) = no' i f && no' i a
261 no' i _ = True
263-- Return the arity of a (normalised) type
265arity :: TT n -> Int
266arity (Bind n (Pi t) sc) = 1 + arity sc
267arity _ = 0
269-- deconstruct an application; returns the function and a list of arguments
271unApply :: TT n -> (TT n, [TT n])
272unApply t = ua [] t where
273 ua args (App f a) = ua (a:args) f
274 ua args t = (t, args)
276mkApp :: TT n -> [TT n] -> TT n
277mkApp f [] = f
278mkApp f (a:as) = mkApp (App f a) as
280forget :: TT Name -> Raw
281forget tm = fe [] tm
282 where
283 fe env (P _ n _) = Var n
284 fe env (V i) = Var (env !! i)
285 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
286 (fe (n:env) sc)
287 fe env (App f a) = RApp (fe env f) (fe env a)
288 fe env (Constant c)
289 = RConstant c
290 fe env (Set i) = RSet i
292bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
293bindAll [] t =t
294bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
296bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
297bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
299getArgTys :: TT n -> [(n, TT n)]
300getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
301getArgTys _ = []
303uniqueName :: Name -> [Name] -> Name
304uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
305 | otherwise = n
307nextName (MN i n) = MN (i+1) n
308nextName (UN (x:xs)) = let (num', nm') = span isDigit (reverse x)
309 nm = reverse nm'
310 num = readN (reverse num') in
311 UN ((nm ++ show (num+1)) : xs)
312 where
313 readN "" = 0
314 readN x = read x
316type Term = TT Name
317type Type = Term
319type Env = EnvTT Name
321-- an environment with de Bruijn indices 'normalised' so that they all refer to
322-- this environment
324newtype WkEnvTT n = Wk (EnvTT n)
325type WkEnv = WkEnvTT Name
327instance (Eq n, Show n) => Show (TT n) where
328 show t = showEnv [] t
330instance Show Const where
331 show (I i) = show i
332 show (Fl f) = show f
333 show (Ch c) = show c
334 show (Str s) = show s
335 show IType = "Int"
336 show FlType = "Float"
337 show ChType = "Char"
338 show StrType = "String"
339 show PtrType = "Ptr"
341showEnv env t = showEnv' env t False
342showEnvDbg env t = showEnv' env t True
344showEnv' env t dbg = se 10 env t where
345 se p env (P nt n t) = show n
346 -- ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
347 se p env (V i) | i < length env = (show $ fst $ env!!i) ++
348 if dbg then "{" ++ show i ++ "}" else ""
349 | otherwise = "!!V " ++ show i ++ "!!"
350 se p env (Bind n b@(Pi t) sc)
351 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
352 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
353 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
354 se p env (Constant c) = show c
355 se p env (Set i) = "Set" ++ show i
357 sb env n (Lam t) = showb env "\\ " " => " n t
358 sb env n (Hole t) = showb env "? " ". " n t
359 sb env n (GHole t) = showb env "?defer " ". " n t
360 sb env n (Pi t) = showb env "(" ") -> " n t
361 sb env n (PVar t) = showb env "pat " ". " n t
362 sb env n (PVTy t) = showb env "pty " ". " n t
363 sb env n (Let t v) = showbv env "let " " in " n t v
364 sb env n (Guess t v) = showbv env "?? " " in " n t v
366 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
367 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
368 se 10 env v ++ sc
370 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
371 | otherwise = str
373-- Check whether a term has any holes in it - impure if so
375pureTerm :: TT n -> Bool
376pureTerm (App f a) = pureTerm f && pureTerm a
377pureTerm (Bind n b sc) = pureBinder b && pureTerm sc where
378 pureBinder (Hole _) = False
379 pureBinder (Guess _ _) = False
380 pureBinder (Let t v) = pureTerm t && pureTerm v
381 pureBinder t = pureTerm (binderTy t)
382pureTerm _ = True
384-- weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
386weakenTm :: Int -> TT n -> TT n
387weakenTm i t = wk i 0 t
388 where wk i min (V x) | x >= min = V (i + x)
389 wk i m (App f a) = App (wk i m f) (wk i m a)
390 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
391 wk i m t = t
392 wkb i m t = fmap (wk i m) t
394-- weaken an environment so that all the de Bruijn indices are correct according
395-- to the latest bound variable
397weakenEnv :: EnvTT n -> EnvTT n
398weakenEnv env = wk (length env - 1) env
399 where wk i [] = []
400 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
401 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
402 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
403 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
405weakenTmEnv :: Int -> EnvTT n -> EnvTT n
406weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))