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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 | InternalMsg String
47 | CantUnify Bool Term Term Err [(Name, Type)] Int
48 -- Int is 'score' - how much we did unify
49 -- Bool indicates recoverability, True indicates more info may make
50 -- unification succeed
51 | InfiniteUnify Name Term [(Name, Type)]
52 | CantConvert Term Term [(Name, Type)]
53 | NoSuchVariable Name
54 | NoTypeDecl Name
55 | NotInjective Term Term Term
56 | CantResolve Term
57 | CantResolveAlts [String]
58 | IncompleteTerm Term
59 | UniverseError
60 | ProgramLineComment
61 | Inaccessible Name
62 | At FC Err
63 deriving Eq
65instance Sized Err where
66 size (Msg msg) = length msg
67 size (InternalMsg msg) = length msg
68 size (CantUnify _ left right err _ score) = size left + size right + size err
69 size (InfiniteUnify _ right _) = size right
70 size (CantConvert left right _) = size left + size right
71 size (NoSuchVariable name) = size name
72 size (NoTypeDecl name) = size name
73 size (NotInjective l c r) = size l + size c + size r
74 size (CantResolve trm) = size trm
75 size (CantResolveAlts _) = 1
76 size (IncompleteTerm trm) = size trm
77 size UniverseError = 1
78 size ProgramLineComment = 1
79 size (At fc err) = size fc + size err
80 size (Inaccessible _) = 1
82score :: Err -> Int
83score (CantUnify _ _ _ m _ s) = s + score m
84score (CantResolve _) = 20
85score (NoSuchVariable _) = 1000
86score _ = 0
88instance Show Err where
89 show (Msg s) = s
90 show (InternalMsg s) = "Internal error: " ++ show s
91 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
92 ++ show e ++ " in " ++ show sc ++ " " ++ show i
93 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
94 show _ = "Error"
96instance Pretty Err where
97 pretty (Msg m) = text m
98 pretty (CantUnify _ l r e _ i) =
99 if size l + size r > breakingSize then
100 text "Cannot unify" <+> colon $$
101 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
102 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
103 else
104 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
105 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
106 pretty _ = text "Error"
108data TC a = OK a
109 | Error Err
110 deriving (Eq, Functor)
112instance Pretty a => Pretty (TC a) where
113 pretty (OK ok) = pretty ok
114 pretty (Error err) =
115 if size err > breakingSize then
116 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
117 else
118 text "Error" <+> colon <+> pretty err
120instance Show a => Show (TC a) where
121 show (OK x) = show x
122 show (Error str) = "Error: " ++ show str
124-- at some point, this instance should also carry type checking options
125-- (e.g. Set:Set)
127instance Monad TC where
128 return = OK
129 x >>= k = case x of
130 OK v -> k v
131 Error e -> Error e
132 fail e = Error (InternalMsg e)
134tfail :: Err -> TC a
135tfail e = Error e
137trun :: FC -> TC a -> TC a
138trun fc (OK a) = OK a
139trun fc (Error e) = Error (At fc e)
141instance MonadPlus TC where
142 mzero = fail "Unknown error"
143 (OK x) `mplus` _ = OK x
144 _ `mplus` (OK y) = OK y
145 err `mplus` _ = err
147discard :: Monad m => m a -> m ()
148discard f = f >> return ()
150showSep :: String -> [String] -> String
151showSep sep [] = ""
152showSep sep [x] = x
153showSep sep (x:xs) = x ++ sep ++ showSep sep xs
155pmap f (x, y) = (f x, f y)
157traceWhen True msg a = trace msg a
158traceWhen False _ a = a
160-- RAW TERMS ----------------------------------------------------------------
162-- Names are hierarchies of strings, describing scope (so no danger of
163-- duplicate names, but need to be careful on lookup).
164-- Also MN for machine chosen names
166data Name = UN String
167 | NS Name [String] -- root, namespaces
168 | MN Int String
169 | NErased -- name of somethng which is never used in scope
170 deriving (Eq, Ord)
171{-!
172deriving instance Binary Name
173!-}
175instance Sized Name where
176 size (UN n) = 1
177 size (NS n els) = 1 + length els
178 size (MN i n) = 1
179 size NErased = 1
181instance Pretty Name where
182 pretty (UN n) = text n
183 pretty (NS n s) = pretty n
184 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
186instance Show Name where
187 show (UN n) = n
188 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
189 show (MN i s) = "{" ++ s ++ show i ++ "}"
190 show NErased = "_"
192-- Contexts allow us to map names to things. A root name maps to a collection
193-- of things in different namespaces with that name.
195type Ctxt a = Map.Map Name (Map.Map Name a)
196emptyContext = Map.empty
198tcname (UN ('@':_)) = True
199tcname (NS n _) = tcname n
200tcname _ = False
202implicitable (NS n _) = implicitable n
203implicitable (UN (x:xs)) = isLower x
204implicitable _ = False
206nsroot (NS n _) = n
207nsroot n = n
209addDef :: Name -> a -> Ctxt a -> Ctxt a
210addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
211 Nothing -> Map.insert (nsroot n)
212 (Map.insert n v Map.empty) ctxt
213 Just xs -> Map.insert (nsroot n)
214 (Map.insert n v xs) ctxt
216{- lookup a name in the context, given an optional namespace.
217 The name (n) may itself have a (partial) namespace given.
219 Rules for resolution:
220 - if an explicit namespace is given, return the names which match it. If none
221 match, return all names.
222 - if the name has has explicit namespace given, return the names which match it
223 and ignore the given namespace.
224 - otherwise, return all names.
226-}
228lookupCtxtName :: Maybe [String] -> Name -> Ctxt a -> [(Name, a)]
229lookupCtxtName nspace n ctxt = case Map.lookup (nsroot n) ctxt of
230 Just xs -> filterNS (Map.toList xs)
231 Nothing -> []
232 where
233 filterNS [] = []
234 filterNS ((found, v) : xs)
235 | nsmatch n found = (found, v) : filterNS xs
236 | otherwise = filterNS xs
238 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
239 nsmatch (NS _ _) _ = False
240 nsmatch looking found = True
242lookupCtxt :: Maybe [String] -> Name -> Ctxt a -> [a]
243lookupCtxt ns n ctxt = map snd (lookupCtxtName ns n ctxt)
245updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
246updateDef n f ctxt
247 = let ds = lookupCtxtName Nothing n ctxt in
248 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
250toAlist :: Ctxt a -> [(Name, a)]
251toAlist ctxt = let allns = map snd (Map.toList ctxt) in
252 concat (map (Map.toList) allns)
254addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
255addAlist [] ctxt = ctxt
256addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
258data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
259 | IType | BIType | FlType | ChType | StrType
260 | PtrType | VoidType | Forgot
261 deriving (Eq, Ord)
262{-!
263deriving instance Binary Const
264!-}
266instance Sized Const where
267 size _ = 1
269instance Pretty Const where
270 pretty (I i) = text . show $ i
271 pretty (BI i) = text . show $ i
272 pretty (Fl f) = text . show $ f
273 pretty (Ch c) = text . show $ c
274 pretty (Str s) = text s
275 pretty IType = text "Int"
276 pretty BIType = text "BigInt"
277 pretty FlType = text "Float"
278 pretty ChType = text "Char"
279 pretty StrType = text "String"
280 pretty PtrType = text "Ptr"
281 pretty VoidType = text "Void"
282 pretty Forgot = text "Forgot"
284data Raw = Var Name
285 | RBind Name (Binder Raw) Raw
286 | RApp Raw Raw
287 | RSet
288 | RForce Raw
289 | RConstant Const
290 deriving (Show, Eq)
292instance Sized Raw where
293 size (Var name) = 1
294 size (RBind name bind right) = 1 + size bind + size right
295 size (RApp left right) = 1 + size left + size right
296 size RSet = 1
297 size (RForce raw) = 1 + size raw
298 size (RConstant const) = size const
300instance Pretty Raw where
301 pretty = text . show
303{-!
304deriving instance Binary Raw
305!-}
307data Binder b = Lam { binderTy :: b }
308 | Pi { binderTy :: b }
309 | Let { binderTy :: b,
310 binderVal :: b }
311 | NLet { binderTy :: b,
312 binderVal :: b }
313 | Hole { binderTy :: b}
314 | GHole { binderTy :: b}
315 | Guess { binderTy :: b,
316 binderVal :: b }
317 | PVar { binderTy :: b }
318 | PVTy { binderTy :: b }
319 deriving (Show, Eq, Ord, Functor)
320{-!
321deriving instance Binary Binder
322!-}
324instance Sized a => Sized (Binder a) where
325 size (Lam ty) = 1 + size ty
326 size (Pi ty) = 1 + size ty
327 size (Let ty val) = 1 + size ty + size val
328 size (NLet ty val) = 1 + size ty + size val
329 size (Hole ty) = 1 + size ty
330 size (GHole ty) = 1 + size ty
331 size (Guess ty val) = 1 + size ty + size val
332 size (PVar ty) = 1 + size ty
333 size (PVTy ty) = 1 + size ty
335fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
336fmapMB f (Let t v) = liftM2 Let (f t) (f v)
337fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
338fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
339fmapMB f (Lam t) = liftM Lam (f t)
340fmapMB f (Pi t) = liftM Pi (f t)
341fmapMB f (Hole t) = liftM Hole (f t)
342fmapMB f (GHole t) = liftM GHole (f t)
343fmapMB f (PVar t) = liftM PVar (f t)
344fmapMB f (PVTy t) = liftM PVTy (f t)
346raw_apply :: Raw -> [Raw] -> Raw
347raw_apply f [] = f
348raw_apply f (a : as) = raw_apply (RApp f a) as
350raw_unapply :: Raw -> (Raw, [Raw])
351raw_unapply t = ua [] t where
352 ua args (RApp f a) = ua (a:args) f
353 ua args t = (t, args)
355data RawFun = RawFun { rtype :: Raw,
356 rval :: Raw
357 }
358 deriving Show
360data RawDatatype = RDatatype Name Raw [(Name, Raw)]
361 deriving Show
363data RDef = RFunction RawFun
364 | RConst Raw
365 | RData RawDatatype
366 deriving Show
368type RProgram = [(Name, RDef)]
370-- WELL TYPED TERMS ---------------------------------------------------------
372data UExp = UVar Int -- universe variable
373 | UVal Int -- explicit universe level
374 deriving (Eq, Ord)
376instance Sized UExp where
377 size _ = 1
379-- We assume that universe levels have been checked, so anything external
380-- can just have the same universe variable and we won't get any new
381-- cycles.
383instance Binary UExp where
384 put x = return ()
385 get = return (UVar (-1))
387instance Show UExp where
388 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
389 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
390 show (UVal x) = show x
391-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
393data UConstraint = ULT UExp UExp
394 | ULE UExp UExp
395 deriving Eq
397instance Show UConstraint where
398 show (ULT x y) = show x ++ " < " ++ show y
399 show (ULE x y) = show x ++ " <= " ++ show y
401type UCs = (Int, [UConstraint])
403data NameType = Bound | Ref | DCon Int Int | TCon Int Int
404 deriving (Show, Ord)
405{-!
406deriving instance Binary NameType
407!-}
409instance Sized NameType where
410 size _ = 1
412instance Pretty NameType where
413 pretty = text . show
415instance Eq NameType where
416 Bound == Bound = True
417 Ref == Ref = True
418 DCon _ a == DCon _ b = (a == b) -- ignore tag
419 TCon _ a == TCon _ b = (a == b) -- ignore tag
420 _ == _ = False
422data TT n = P NameType n (TT n) -- embed type
423 | V Int
424 | Bind n (Binder (TT n)) (TT n)
425 | App (TT n) (TT n) -- function, function type, arg
426 | Constant Const
427 | Proj (TT n) Int -- argument projection; runtime only
428 | Erased
429 | Impossible -- special case for totality checking
430 | Set UExp
431 deriving (Ord, Functor)
432{-!
433deriving instance Binary TT
434!-}
436class TermSize a where
437 termsize :: Name -> a -> Int
439instance TermSize a => TermSize [a] where
440 termsize n [] = 0
441 termsize n (x : xs) = termsize n x + termsize n xs
443instance TermSize (TT Name) where
444 termsize n (P _ x _)
445 | x == n = 1000000 -- recursive => really big
446 | otherwise = 1
447 termsize n (V _) = 1
448 termsize n (Bind n' (Let t v) sc)
449 = let rn = if n == n' then MN 0 "noname" else n in
450 termsize rn v + termsize rn sc
451 termsize n (App f a) = termsize n f + termsize n a
452 termsize n _ = 1
454instance Sized a => Sized (TT a) where
455 size (P name n trm) = 1 + size name + size n + size trm
456 size (V v) = 1
457 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
458 size (App l r) = 1 + size l + size r
459 size (Constant c) = size c
460 size Erased = 1
461 size (Set u) = 1 + size u
463instance Pretty a => Pretty (TT a) where
464 pretty _ = text "test"
466type EnvTT n = [(n, Binder (TT n))]
468data Datatype n = Data { d_typename :: n,
469 d_typetag :: Int,
470 d_type :: (TT n),
471 d_cons :: [(n, TT n)] }
472 deriving (Show, Functor, Eq)
474instance Eq n => Eq (TT n) where
475 (==) (P xt x _) (P yt y _) = xt == yt && x == y
476 (==) (V x) (V y) = x == y
477 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
478 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
479 (==) (Set _) (Set _) = True -- deal with constraints later
480 (==) (Constant x) (Constant y) = x == y
481 (==) (Proj x i) (Proj y j) = x == y && i == j
482 (==) Erased _ = True
483 (==) _ Erased = True
484 (==) _ _ = False
486-- A few handy operations on well typed terms:
488isInjective :: TT n -> Bool
489isInjective (P (DCon _ _) _ _) = True
490isInjective (P (TCon _ _) _ _) = True
491isInjective (Constant _) = True
492isInjective (Set x) = True
493isInjective (Bind _ (Pi _) sc) = True
494isInjective (App f a) = isInjective f
495isInjective _ = False
497-- Count the number of instances of a de Bruijn index in a term
498vinstances :: Int -> TT n -> Int
499vinstances i (V x) | i == x = 1
500vinstances i (App f a) = vinstances i f + vinstances i a
501vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
502 where instancesB (Let t v) = vinstances i v
503 instancesB _ = 0
504vinstances i t = 0
506instantiate :: TT n -> TT n -> TT n
507instantiate e = subst 0 where
508 subst i (V x) | i == x = e
509 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
510 subst i (App f a) = App (subst i f) (subst i a)
511 subst i (Proj x idx) = Proj (subst i x) idx
512 subst i t = t
514pToV :: Eq n => n -> TT n -> TT n
515pToV n = pToV' n 0
516pToV' n i (P _ x _) | n == x = V i
517pToV' n i (Bind x b sc)
518-- We can assume the inner scope has been pToVed already, so continue to
519-- resolve names from the *outer* scope which may happen to have the same id.
520-- | n == x = Bind x (fmap (pToV' n i) b) sc
521 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
522pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
523pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
524pToV' n i t = t
526-- Convert several names. First in the list comes out as V 0
527pToVs :: Eq n => [n] -> TT n -> TT n
528pToVs ns tm = pToVs' ns tm 0 where
529 pToVs' [] tm i = tm
530 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
532vToP :: TT n -> TT n
533vToP = vToP' [] where
534 vToP' env (V i) = let (n, b) = (env !! i) in
535 P Bound n (binderTy b)
536 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
537 Bind n b' (vToP' ((n, b'):env) sc)
538 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
539 vToP' env t = t
541finalise :: Eq n => TT n -> TT n
542finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
543finalise (App f a) = App (finalise f) (finalise a)
544finalise t = t
546subst :: Eq n => n -> TT n -> TT n -> TT n
547subst n v tm = instantiate v (pToV n tm)
549substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
550substNames [] t = t
551substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
553-- Returns true if V 0 and bound name n do not occur in the term
555noOccurrence :: Eq n => n -> TT n -> Bool
556noOccurrence n t = no' 0 t
557 where
558 no' i (V x) = not (i == x)
559 no' i (P Bound x _) = not (n == x)
560 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
561 where noB' i (Let t v) = no' i t && no' i v
562 noB' i (Guess t v) = no' i t && no' i v
563 noB' i b = no' i (binderTy b)
564 no' i (App f a) = no' i f && no' i a
565 no' i (Proj x _) = no' i x
566 no' i _ = True
568-- Returns all names used free in the term
570freeNames :: Eq n => TT n -> [n]
571freeNames (P _ n _) = [n]
572freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
573 ++ freeNames t
574freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
575freeNames (App f a) = nub $ freeNames f ++ freeNames a
576freeNames (Proj x i) = nub $ freeNames x
577freeNames _ = []
579-- Return the arity of a (normalised) type
581arity :: TT n -> Int
582arity (Bind n (Pi t) sc) = 1 + arity sc
583arity _ = 0
585-- deconstruct an application; returns the function and a list of arguments
587unApply :: TT n -> (TT n, [TT n])
588unApply t = ua [] t where
589 ua args (App f a) = ua (a:args) f
590 ua args t = (t, args)
592mkApp :: TT n -> [TT n] -> TT n
593mkApp f [] = f
594mkApp f (a:as) = mkApp (App f a) as
596forget :: TT Name -> Raw
597forget tm = fe [] tm
598 where
599 fe env (P _ n _) = Var n
600 fe env (V i) = Var (env !! i)
601 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
602 (fe (n:env) sc)
603 fe env (App f a) = RApp (fe env f) (fe env a)
604 fe env (Constant c)
605 = RConstant c
606 fe env (Set i) = RSet
607 fe env Erased = RConstant Forgot
609bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
610bindAll [] t =t
611bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
613bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
614bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
616getArgTys :: TT n -> [(n, TT n)]
617getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
618getArgTys _ = []
620getRetTy :: TT n -> TT n
621getRetTy (Bind n (PVar _) sc) = getRetTy sc
622getRetTy (Bind n (PVTy _) sc) = getRetTy sc
623getRetTy (Bind n (Pi _) sc) = getRetTy sc
624getRetTy sc = sc
626uniqueName :: Name -> [Name] -> Name
627uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
628 | otherwise = n
630nextName (NS x s) = NS (nextName x) s
631nextName (MN i n) = MN (i+1) n
632nextName (UN x) = let (num', nm') = span isDigit (reverse x)
633 nm = reverse nm'
634 num = readN (reverse num') in
635 UN (nm ++ show (num+1))
636 where
637 readN "" = 0
638 readN x = read x
640type Term = TT Name
641type Type = Term
643type Env = EnvTT Name
645-- an environment with de Bruijn indices 'normalised' so that they all refer to
646-- this environment
648newtype WkEnvTT n = Wk (EnvTT n)
649type WkEnv = WkEnvTT Name
651instance (Eq n, Show n) => Show (TT n) where
652 show t = showEnv [] t
654instance Show Const where
655 show (I i) = show i
656 show (BI i) = show i ++ "L"
657 show (Fl f) = show f
658 show (Ch c) = show c
659 show (Str s) = show s
660 show IType = "Int"
661 show BIType = "Integer"
662 show FlType = "Float"
663 show ChType = "Char"
664 show StrType = "String"
665 show PtrType = "Ptr"
666 show VoidType = "Void"
668showEnv env t = showEnv' env t False
669showEnvDbg env t = showEnv' env t True
671prettyEnv env t = prettyEnv' env t False
672 where
673 prettyEnv' env t dbg = prettySe 10 env t dbg
675 bracket outer inner p
676 | inner > outer = lparen <> p <> rparen
677 | otherwise = p
679 prettySe p env (P nt n t) debug =
680 pretty n <+>
681 if debug then
682 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
683 else
684 empty
685 prettySe p env (V i) debug
686 | i < length env =
687 if debug then
688 text . show . fst $ env!!i
689 else
690 lbrack <+> text (show i) <+> rbrack
691 | otherwise = text "unbound" <+> text (show i) <+> text "!"
692 prettySe p env (Bind n b@(Pi t) sc) debug
693 | noOccurrence n sc && not debug =
694 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
695 prettySe p env (Bind n b sc) debug =
696 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
697 prettySe p env (App f a) debug =
698 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
699 prettySe p env (Proj x i) debug =
700 prettySe 1 env x debug <+> text ("!" ++ show i)
701 prettySe p env (Constant c) debug = pretty c
702 prettySe p env Erased debug = text "[_]"
703 prettySe p env (Set i) debug = text "Set" <+> (text . show $ i)
705 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
706 prettySb env n (Hole t) = prettyB env "?defer" "." n t
707 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
708 prettySb env n (PVar t) = prettyB env "pat" "." n t
709 prettySb env n (PVTy t) = prettyB env "pty" "." n t
710 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
711 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
713 prettyB env op sc n t debug =
714 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
716 prettyBv env op sc n t v debug =
717 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
718 prettySe 10 env v debug <> text sc
721showEnv' env t dbg = se 10 env t where
722 se p env (P nt n t) = show n
723 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
724 se p env (V i) | i < length env = (show $ fst $ env!!i) ++
725 if dbg then "{" ++ show i ++ "}" else ""
726 | otherwise = "!!V " ++ show i ++ "!!"
727 se p env (Bind n b@(Pi t) sc)
728 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
729 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
730 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
731 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
732 se p env (Constant c) = show c
733 se p env Erased = "[__]"
734 se p env Impossible = "[impossible]"
735 se p env (Set i) = "Set " ++ show i
737 sb env n (Lam t) = showb env "\\ " " => " n t
738 sb env n (Hole t) = showb env "? " ". " n t
739 sb env n (GHole t) = showb env "?defer " ". " n t
740 sb env n (Pi t) = showb env "(" ") -> " n t
741 sb env n (PVar t) = showb env "pat " ". " n t
742 sb env n (PVTy t) = showb env "pty " ". " n t
743 sb env n (Let t v) = showbv env "let " " in " n t v
744 sb env n (Guess t v) = showbv env "?? " " in " n t v
746 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
747 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
748 se 10 env v ++ sc
750 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
751 | otherwise = str
753-- Check whether a term has any holes in it - impure if so
755pureTerm :: TT n -> Bool
756pureTerm (App f a) = pureTerm f && pureTerm a
757pureTerm (Bind n b sc) = pureBinder b && pureTerm sc where
758 pureBinder (Hole _) = False
759 pureBinder (Guess _ _) = False
760 pureBinder (Let t v) = pureTerm t && pureTerm v
761 pureBinder t = pureTerm (binderTy t)
762pureTerm _ = True
764-- weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
766weakenTm :: Int -> TT n -> TT n
767weakenTm i t = wk i 0 t
768 where wk i min (V x) | x >= min = V (i + x)
769 wk i m (App f a) = App (wk i m f) (wk i m a)
770 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
771 wk i m t = t
772 wkb i m t = fmap (wk i m) t
774-- weaken an environment so that all the de Bruijn indices are correct according
775-- to the latest bound variable
777weakenEnv :: EnvTT n -> EnvTT n
778weakenEnv env = wk (length env - 1) env
779 where wk i [] = []
780 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
781 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
782 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
783 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
785weakenTmEnv :: Int -> EnvTT n -> EnvTT n
786weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
788orderPats :: Term -> Term
789orderPats tm = op [] tm
790 where
791 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
792 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
793 op ps sc = bindAll (map (\ (n, t) -> (n, t)) (sortP ps)) sc
795 sortP ps = pick [] (reverse ps)
797 namesIn (P _ n _) = [n]
798 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
799 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
800 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
801 nb t = namesIn (binderTy t)
802 namesIn (App f a) = nub (namesIn f ++ namesIn a)
803 namesIn _ = []
805 pick acc [] = reverse acc
806 pick acc ((n, t) : ps) = pick (insert n t acc) ps
808 insert n t [] = [(n, t)]
809 insert n t ((n',t') : ps)
810 | n `elem` (namesIn (binderTy t') ++
811 concatMap namesIn (map (binderTy . snd) ps))
812 = (n', t') : insert n t ps
813 | otherwise = (n,t):(n',t'):ps