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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
9import Data.List
10import qualified Data.Binary as B
11import Data.Binary hiding (get, put)
13import Util.Pretty hiding (Str)
15{- The language has:
16 * Full dependent types
17 * A hierarchy of universes, with cumulativity: Set : Set1, Set1 : Set2, ...
18 * Pattern matching letrec binding
19 * (primitive types defined externally)
21 Some technical stuff:
22 * Typechecker is kept as simple as possible
23 - no unification, just a checker for incomplete terms.
24 * We have a simple collection of tactics which we use to elaborate source
25 programs with implicit syntax into fully explicit terms.
26-}
28data Option = SetInSet
29 | CheckConv
30 deriving Eq
32data FC = FC { fc_fname :: String,
33 fc_line :: Int }
34 deriving Eq
35{-!
36deriving instance Binary FC
37!-}
39instance Sized FC where
40 size (FC f l) = 1 + length f
42instance Show FC where
43 show (FC f l) = f ++ ":" ++ show l
45data Err = Msg String
46 | CantUnify Term Term Err Int -- Int is 'score' - how much we did unify
47 | NoSuchVariable Name
48 | NotInjective Term Term Term
49 | CantResolve Term
50 | IncompleteTerm Term
51 | UniverseError
52 | ProgramLineComment
53 | Inaccessible Name
54 | At FC Err
55 deriving Eq
57instance Sized Err where
58 size (Msg msg) = length msg
59 size (CantUnify left right err score) = size left + size right + size err
60 size (NoSuchVariable name) = size name
61 size (NotInjective l c r) = size l + size c + size r
62 size (CantResolve trm) = size trm
63 size (IncompleteTerm trm) = size trm
64 size UniverseError = 1
65 size ProgramLineComment = 1
66 size (At fc err) = size fc + size err
67 size (Inaccessible _) = 1
69score :: Err -> Int
70score (CantUnify _ _ m s) = s + score m
71score (CantResolve _) = 20
72score (NoSuchVariable _) = 1000
73score _ = 0
75instance Show Err where
76 show (Msg s) = s
77 show (CantUnify l r e i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
78 ++ show e ++ " " ++ show i
79 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
80 show _ = "Error"
82instance Pretty Err where
83 pretty (Msg m) = text m
84 pretty (CantUnify l r e i) =
85 if size l + size r > breakingSize then
86 text "Cannot unify" <+> colon $$
87 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
88 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
89 else
90 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
91 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
92 pretty _ = text "Error"
94data TC a = OK a
95 | Error Err
96 deriving (Eq, Functor)
98instance Pretty a => Pretty (TC a) where
99 pretty (OK ok) = pretty ok
100 pretty (Error err) =
101 if size err > breakingSize then
102 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
103 else
104 text "Error" <+> colon <+> pretty err
106instance Show a => Show (TC a) where
107 show (OK x) = show x
108 show (Error str) = "Error: " ++ show str
110-- at some point, this instance should also carry type checking options
111-- (e.g. Set:Set)
113instance Monad TC where
114 return = OK
115 x >>= k = case x of
116 OK v -> k v
117 Error e -> Error e
118 fail e = Error (Msg e)
120tfail :: Err -> TC a
121tfail e = Error e
123trun :: FC -> TC a -> TC a
124trun fc (OK a) = OK a
125trun fc (Error e) = Error (At fc e)
127instance MonadPlus TC where
128 mzero = fail "Unknown error"
129 (OK x) `mplus` _ = OK x
130 _ `mplus` (OK y) = OK y
131 err `mplus` _ = err
133discard :: Monad m => m a -> m ()
134discard f = f >> return ()
136showSep :: String -> [String] -> String
137showSep sep [] = ""
138showSep sep [x] = x
139showSep sep (x:xs) = x ++ sep ++ showSep sep xs
141pmap f (x, y) = (f x, f y)
143traceWhen True msg a = trace msg a
144traceWhen False _ a = a
146-- RAW TERMS ----------------------------------------------------------------
148-- Names are hierarchies of strings, describing scope (so no danger of
149-- duplicate names, but need to be careful on lookup).
150-- Also MN for machine chosen names
152data Name = UN String
153 | NS Name [String] -- root, namespaces
154 | MN Int String
155 deriving (Eq, Ord)
156{-!
157deriving instance Binary Name
158!-}
160instance Sized Name where
161 size (UN n) = 1
162 size (NS n els) = 1 + length els
163 size (MN i n) = 1
165instance Pretty Name where
166 pretty (UN n) = text n
167 pretty (NS n s) = pretty n
168 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
170instance Show Name where
171 show (UN n) = n
172 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
173 show (MN i s) = "{" ++ s ++ show i ++ "}"
176-- Contexts allow us to map names to things. A root name maps to a collection
177-- of things in different namespaces with that name.
179type Ctxt a = Map.Map Name (Map.Map Name a)
180emptyContext = Map.empty
182nsroot (NS n _) = n
183nsroot n = n
185addDef :: Name -> a -> Ctxt a -> Ctxt a
186addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
187 Nothing -> Map.insert (nsroot n)
188 (Map.insert n v Map.empty) ctxt
189 Just xs -> Map.insert (nsroot n)
190 (Map.insert n v xs) ctxt
192{- lookup a name in the context, given an optional namespace.
193 The name (n) may itself have a (partial) namespace given.
195 Rules for resolution:
196 - if an explicit namespace is given, return the names which match it. If none
197 match, return all names.
198 - if the name has has explicit namespace given, return the names which match it
199 and ignore the given namespace.
200 - otherwise, return all names.
202-}
204lookupCtxtName :: Maybe [String] -> Name -> Ctxt a -> [(Name, a)]
205lookupCtxtName nspace n ctxt = case Map.lookup (nsroot n) ctxt of
206 Just xs -> filterNS (Map.toList xs)
207 Nothing -> []
208 where
209 filterNS [] = []
210 filterNS ((found, v) : xs)
211 | nsmatch n found = (found, v) : filterNS xs
212 | otherwise = filterNS xs
214 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
215 nsmatch (NS _ _) _ = False
216 nsmatch looking found = True
218lookupCtxt :: Maybe [String] -> Name -> Ctxt a -> [a]
219lookupCtxt ns n ctxt = map snd (lookupCtxtName ns n ctxt)
221updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
222updateDef n f ctxt
223 = let ds = lookupCtxtName Nothing n ctxt in
224 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
226toAlist :: Ctxt a -> [(Name, a)]
227toAlist ctxt = let allns = map snd (Map.toList ctxt) in
228 concat (map (Map.toList) allns)
230addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
231addAlist [] ctxt = ctxt
232addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
234data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
235 | IType | BIType | FlType | ChType | StrType
236 | PtrType | Forgot
237 deriving Eq
238{-!
239deriving instance Binary Const
240!-}
242instance Sized Const where
243 size _ = 1
245instance Pretty Const where
246 pretty (I i) = text . show $ i
247 pretty (BI i) = text . show $ i
248 pretty (Fl f) = text . show $ f
249 pretty (Ch c) = text . show $ c
250 pretty (Str s) = text s
251 pretty IType = text "Int"
252 pretty BIType = text "BigInt"
253 pretty FlType = text "Float"
254 pretty ChType = text "Char"
255 pretty StrType = text "String"
256 pretty PtrType = text "Ptr"
257 pretty Forgot = text "Forgot"
259data Raw = Var Name
260 | RBind Name (Binder Raw) Raw
261 | RApp Raw Raw
262 | RSet
263 | RForce Raw
264 | RConstant Const
265 deriving (Show, Eq)
267instance Sized Raw where
268 size (Var name) = 1
269 size (RBind name bind right) = 1 + size bind + size right
270 size (RApp left right) = 1 + size left + size right
271 size RSet = 1
272 size (RForce raw) = 1 + size raw
273 size (RConstant const) = size const
275instance Pretty Raw where
276 pretty = text . show
278{-!
279deriving instance Binary Raw
280!-}
282data Binder b = Lam { binderTy :: b }
283 | Pi { binderTy :: b }
284 | Let { binderTy :: b,
285 binderVal :: b }
286 | NLet { binderTy :: b,
287 binderVal :: b }
288 | Hole { binderTy :: b}
289 | GHole { binderTy :: b}
290 | Guess { binderTy :: b,
291 binderVal :: b }
292 | PVar { binderTy :: b }
293 | PVTy { binderTy :: b }
294 deriving (Show, Eq, Functor)
295{-!
296deriving instance Binary Binder
297!-}
299instance Sized a => Sized (Binder a) where
300 size (Lam ty) = 1 + size ty
301 size (Pi ty) = 1 + size ty
302 size (Let ty val) = 1 + size ty + size val
303 size (NLet ty val) = 1 + size ty + size val
304 size (Hole ty) = 1 + size ty
305 size (GHole ty) = 1 + size ty
306 size (Guess ty val) = 1 + size ty + size val
307 size (PVar ty) = 1 + size ty
308 size (PVTy ty) = 1 + size ty
310fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
311fmapMB f (Let t v) = liftM2 Let (f t) (f v)
312fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
313fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
314fmapMB f (Lam t) = liftM Lam (f t)
315fmapMB f (Pi t) = liftM Pi (f t)
316fmapMB f (Hole t) = liftM Hole (f t)
317fmapMB f (GHole t) = liftM GHole (f t)
318fmapMB f (PVar t) = liftM PVar (f t)
319fmapMB f (PVTy t) = liftM PVTy (f t)
321raw_apply :: Raw -> [Raw] -> Raw
322raw_apply f [] = f
323raw_apply f (a : as) = raw_apply (RApp f a) as
325raw_unapply :: Raw -> (Raw, [Raw])
326raw_unapply t = ua [] t where
327 ua args (RApp f a) = ua (a:args) f
328 ua args t = (t, args)
330data RawFun = RawFun { rtype :: Raw,
331 rval :: Raw
332 }
333 deriving Show
335data RawDatatype = RDatatype Name Raw [(Name, Raw)]
336 deriving Show
338data RDef = RFunction RawFun
339 | RConst Raw
340 | RData RawDatatype
341 deriving Show
343type RProgram = [(Name, RDef)]
345-- WELL TYPED TERMS ---------------------------------------------------------
347data UExp = UVar Int -- universe variable
348 | UVal Int -- explicit universe level
349 deriving (Eq, Ord)
351instance Sized UExp where
352 size _ = 1
354-- We assume that universe levels have been checked, so anything external
355-- can just have the same universe variable and we won't get any new
356-- cycles.
358instance Binary UExp where
359 put x = return ()
360 get = return (UVar (-1))
362instance Show UExp where
363 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
364 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
365 show (UVal x) = show x
366-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
368data UConstraint = ULT UExp UExp
369 | ULE UExp UExp
370 deriving Eq
372instance Show UConstraint where
373 show (ULT x y) = show x ++ " < " ++ show y
374 show (ULE x y) = show x ++ " <= " ++ show y
376type UCs = (Int, [UConstraint])
378data NameType = Bound | Ref | DCon Int Int | TCon Int Int
379 deriving (Show)
380{-!
381deriving instance Binary NameType
382!-}
384instance Sized NameType where
385 size _ = 1
387instance Pretty NameType where
388 pretty = text . show
390instance Eq NameType where
391 Bound == Bound = True
392 Ref == Ref = True
393 DCon _ a == DCon _ b = (a == b) -- ignore tag
394 TCon _ a == TCon _ b = (a == b) -- ignore tag
395 _ == _ = False
397data TT n = P NameType n (TT n) -- embed type
398 | V Int
399 | Bind n (Binder (TT n)) (TT n)
400 | App (TT n) (TT n) -- function, function type, arg
401 | Constant Const
402 | Erased
403 | Set UExp
404 deriving Functor
405{-!
406deriving instance Binary TT
407!-}
409instance Sized a => Sized (TT a) where
410 size (P name n trm) = 1 + size name + size n + size trm
411 size (V v) = 1
412 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
413 size (App l r) = 1 + size l + size r
414 size (Constant c) = size c
415 size Erased = 1
416 size (Set u) = 1 + size u
418instance Pretty a => Pretty (TT a) where
419 pretty _ = text "test"
421type EnvTT n = [(n, Binder (TT n))]
423data Datatype n = Data { d_typename :: n,
424 d_typetag :: Int,
425 d_type :: (TT n),
426 d_cons :: [(n, TT n)] }
427 deriving (Show, Functor, Eq)
429instance Eq n => Eq (TT n) where
430 (==) (P xt x _) (P yt y _) = xt == yt && x == y
431 (==) (V x) (V y) = x == y
432 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
433 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
434 (==) (Set _) (Set _) = True -- deal with constraints later
435 (==) (Constant x) (Constant y) = x == y
436 (==) Erased _ = True
437 (==) _ Erased = True
438 (==) _ _ = False
440-- A few handy operations on well typed terms:
442isInjective :: TT n -> Bool
443isInjective (P (DCon _ _) _ _) = True
444isInjective (P (TCon _ _) _ _) = True
445isInjective (Constant _) = True
446isInjective (Set x) = True
447isInjective (Bind _ (Pi _) sc) = True
448isInjective (App f a) = isInjective f
449isInjective _ = False
451instantiate :: TT n -> TT n -> TT n
452instantiate e = subst 0 where
453 subst i (V x) | i == x = e
454 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
455 subst i (App f a) = App (subst i f) (subst i a)
456 subst i t = t
458pToV :: Eq n => n -> TT n -> TT n
459pToV n = pToV' n 0
460pToV' n i (P _ x _) | n == x = V i
461pToV' n i (Bind x b sc)
462 | n == x = Bind x (fmap (pToV' n i) b) sc
463 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
464pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
465pToV' n i t = t
467-- Convert several names. First in the list comes out as V 0
468pToVs :: Eq n => [n] -> TT n -> TT n
469pToVs ns tm = pToVs' ns tm 0 where
470 pToVs' [] tm i = tm
471 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
473vToP :: TT n -> TT n
474vToP = vToP' [] where
475 vToP' env (V i) = let (n, b) = (env !! i) in
476 P Bound n (binderTy b)
477 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
478 Bind n b' (vToP' ((n, b'):env) sc)
479 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
480 vToP' env t = t
482finalise :: Eq n => TT n -> TT n
483finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
484finalise (App f a) = App (finalise f) (finalise a)
485finalise t = t
487subst :: Eq n => n -> TT n -> TT n -> TT n
488subst n v tm = instantiate v (pToV n tm)
490substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
491substNames [] t = t
492substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
494-- Returns true if V 0 and bound name n do not occur in the term
496noOccurrence :: Eq n => n -> TT n -> Bool
497noOccurrence n t = no' 0 t
498 where
499 no' i (V x) = not (i == x)
500 no' i (P Bound x _) = not (n == x)
501 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
502 where noB' i (Let t v) = no' i t && no' i v
503 noB' i (Guess t v) = no' i t && no' i v
504 noB' i b = no' i (binderTy b)
505 no' i (App f a) = no' i f && no' i a
506 no' i _ = True
508-- Returns all names used free in the term
510freeNames :: Eq n => TT n -> [n]
511freeNames (P _ n _) = [n]
512freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
513 ++ freeNames t
514freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
515freeNames (App f a) = nub $ freeNames f ++ freeNames a
516freeNames _ = []
518-- Return the arity of a (normalised) type
520arity :: TT n -> Int
521arity (Bind n (Pi t) sc) = 1 + arity sc
522arity _ = 0
524-- deconstruct an application; returns the function and a list of arguments
526unApply :: TT n -> (TT n, [TT n])
527unApply t = ua [] t where
528 ua args (App f a) = ua (a:args) f
529 ua args t = (t, args)
531mkApp :: TT n -> [TT n] -> TT n
532mkApp f [] = f
533mkApp f (a:as) = mkApp (App f a) as
535forget :: TT Name -> Raw
536forget tm = fe [] tm
537 where
538 fe env (P _ n _) = Var n
539 fe env (V i) = Var (env !! i)
540 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
541 (fe (n:env) sc)
542 fe env (App f a) = RApp (fe env f) (fe env a)
543 fe env (Constant c)
544 = RConstant c
545 fe env (Set i) = RSet
546 fe env Erased = RConstant Forgot
548bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
549bindAll [] t =t
550bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
552bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
553bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
555getArgTys :: TT n -> [(n, TT n)]
556getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
557getArgTys _ = []
559getRetTy :: TT n -> TT n
560getRetTy (Bind n (PVar _) sc) = getRetTy sc
561getRetTy (Bind n (PVTy _) sc) = getRetTy sc
562getRetTy (Bind n (Pi _) sc) = getRetTy sc
563getRetTy sc = sc
565uniqueName :: Name -> [Name] -> Name
566uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
567 | otherwise = n
569nextName (NS x s) = NS (nextName x) s
570nextName (MN i n) = MN (i+1) n
571nextName (UN x) = let (num', nm') = span isDigit (reverse x)
572 nm = reverse nm'
573 num = readN (reverse num') in
574 UN (nm ++ show (num+1))
575 where
576 readN "" = 0
577 readN x = read x
579type Term = TT Name
580type Type = Term
582type Env = EnvTT Name
584-- an environment with de Bruijn indices 'normalised' so that they all refer to
585-- this environment
587newtype WkEnvTT n = Wk (EnvTT n)
588type WkEnv = WkEnvTT Name
590instance (Eq n, Show n) => Show (TT n) where
591 show t = showEnv [] t
593instance Show Const where
594 show (I i) = show i
595 show (BI i) = show i ++ "L"
596 show (Fl f) = show f
597 show (Ch c) = show c
598 show (Str s) = show s
599 show IType = "Int"
600 show BIType = "Integer"
601 show FlType = "Float"
602 show ChType = "Char"
603 show StrType = "String"
604 show PtrType = "Ptr"
606showEnv env t = showEnv' env t False
607showEnvDbg env t = showEnv' env t True
609prettyEnv env t = prettyEnv' env t False
610 where
611 prettyEnv' env t dbg = prettySe 10 env t dbg
613 bracket outer inner p
614 | inner > outer = lparen <> p <> rparen
615 | otherwise = p
617 prettySe p env (P nt n t) debug =
618 pretty n <+>
619 if debug then
620 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
621 else
622 empty
623 prettySe p env (V i) debug
624 | i < length env =
625 if debug then
626 text . show . fst $ env!!i
627 else
628 lbrack <+> text (show i) <+> rbrack
629 | otherwise = text "unbound" <+> text (show i) <+> text "!"
630 prettySe p env (Bind n b@(Pi t) sc) debug
631 | noOccurrence n sc && not debug =
632 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
633 prettySe p env (Bind n b sc) debug =
634 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
635 prettySe p env (App f a) debug =
636 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
637 prettySe p env (Constant c) debug = pretty c
638 prettySe p env Erased debug = text "[_]"
639 prettySe p env (Set i) debug = text "Set" <+> (text . show $ i)
641 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
642 prettySb env n (Hole t) = prettyB env "?defer" "." n t
643 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
644 prettySb env n (PVar t) = prettyB env "pat" "." n t
645 prettySb env n (PVTy t) = prettyB env "pty" "." n t
646 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
647 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
649 prettyB env op sc n t debug =
650 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
652 prettyBv env op sc n t v debug =
653 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
654 prettySe 10 env v debug <> text sc
657showEnv' env t dbg = se 10 env t where
658 se p env (P nt n t) = show n
659 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
660 se p env (V i) | i < length env = (show $ fst $ env!!i) ++
661 if dbg then "{" ++ show i ++ "}" else ""
662 | otherwise = "!!V " ++ show i ++ "!!"
663 se p env (Bind n b@(Pi t) sc)
664 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
665 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
666 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
667 se p env (Constant c) = show c
668 se p env Erased = "[__]"
669 se p env (Set i) = "Set " ++ show i
671 sb env n (Lam t) = showb env "\\ " " => " n t
672 sb env n (Hole t) = showb env "? " ". " n t
673 sb env n (GHole t) = showb env "?defer " ". " n t
674 sb env n (Pi t) = showb env "(" ") -> " n t
675 sb env n (PVar t) = showb env "pat " ". " n t
676 sb env n (PVTy t) = showb env "pty " ". " n t
677 sb env n (Let t v) = showbv env "let " " in " n t v
678 sb env n (Guess t v) = showbv env "?? " " in " n t v
680 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
681 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
682 se 10 env v ++ sc
684 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
685 | otherwise = str
687-- Check whether a term has any holes in it - impure if so
689pureTerm :: TT n -> Bool
690pureTerm (App f a) = pureTerm f && pureTerm a
691pureTerm (Bind n b sc) = pureBinder b && pureTerm sc where
692 pureBinder (Hole _) = False
693 pureBinder (Guess _ _) = False
694 pureBinder (Let t v) = pureTerm t && pureTerm v
695 pureBinder t = pureTerm (binderTy t)
696pureTerm _ = True
698-- weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
700weakenTm :: Int -> TT n -> TT n
701weakenTm i t = wk i 0 t
702 where wk i min (V x) | x >= min = V (i + x)
703 wk i m (App f a) = App (wk i m f) (wk i m a)
704 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
705 wk i m t = t
706 wkb i m t = fmap (wk i m) t
708-- weaken an environment so that all the de Bruijn indices are correct according
709-- to the latest bound variable
711weakenEnv :: EnvTT n -> EnvTT n
712weakenEnv env = wk (length env - 1) env
713 where wk i [] = []
714 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
715 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
716 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
717 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
719weakenTmEnv :: Int -> EnvTT n -> EnvTT n
720weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
722orderPats :: Term -> Term
723orderPats tm = op [] tm
724 where
725 op ps (Bind n (PVar t) sc) = op ((n, t) : ps) sc
726 op ps sc = bindAll (map (\ (n, t) -> (n, PVar t)) (sortP ps)) sc
728 sortP ps = pick [] (reverse ps)
730 namesIn (P _ n _) = [n]
731 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
732 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
733 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
734 nb t = namesIn (binderTy t)
735 namesIn (App f a) = nub (namesIn f ++ namesIn a)
736 namesIn _ = []
738 pick acc [] = reverse acc
739 pick acc ((n, t) : ps) = pick (insert n t acc) ps
741 insert n t [] = [(n, t)]
742 insert n t ((n',t') : ps)
743 | n `elem` (namesIn t' ++ concatMap namesIn (map snd ps))
744 = (n', t') : insert n t ps
745 | otherwise = (n,t):(n',t'):ps