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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 | NoSuchVariable Name
52 | NoTypeDecl Name
53 | NotInjective Term Term Term
54 | CantResolve Term
55 | CantResolveAlts [String]
56 | IncompleteTerm Term
57 | UniverseError
58 | ProgramLineComment
59 | Inaccessible Name
60 | At FC Err
61 deriving Eq
63instance Sized Err where
64 size (Msg msg) = length msg
65 size (InternalMsg msg) = length msg
66 size (CantUnify _ left right err _ score) = size left + size right + size err
67 size (NoSuchVariable name) = size name
68 size (NoTypeDecl name) = size name
69 size (NotInjective l c r) = size l + size c + size r
70 size (CantResolve trm) = size trm
71 size (CantResolveAlts _) = 1
72 size (IncompleteTerm trm) = size trm
73 size UniverseError = 1
74 size ProgramLineComment = 1
75 size (At fc err) = size fc + size err
76 size (Inaccessible _) = 1
78score :: Err -> Int
79score (CantUnify _ _ _ m _ s) = s + score m
80score (CantResolve _) = 20
81score (NoSuchVariable _) = 1000
82score _ = 0
84instance Show Err where
85 show (Msg s) = s
86 show (InternalMsg s) = "Internal error: " ++ show s
87 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
88 ++ show e ++ " in " ++ show sc ++ " " ++ show i
89 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
90 show _ = "Error"
92instance Pretty Err where
93 pretty (Msg m) = text m
94 pretty (CantUnify _ l r e _ i) =
95 if size l + size r > breakingSize then
96 text "Cannot unify" <+> colon $$
97 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
98 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
99 else
100 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
101 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
102 pretty _ = text "Error"
104data TC a = OK a
105 | Error Err
106 deriving (Eq, Functor)
108instance Pretty a => Pretty (TC a) where
109 pretty (OK ok) = pretty ok
110 pretty (Error err) =
111 if size err > breakingSize then
112 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
113 else
114 text "Error" <+> colon <+> pretty err
116instance Show a => Show (TC a) where
117 show (OK x) = show x
118 show (Error str) = "Error: " ++ show str
120-- at some point, this instance should also carry type checking options
121-- (e.g. Set:Set)
123instance Monad TC where
124 return = OK
125 x >>= k = case x of
126 OK v -> k v
127 Error e -> Error e
128 fail e = Error (InternalMsg e)
130tfail :: Err -> TC a
131tfail e = Error e
133trun :: FC -> TC a -> TC a
134trun fc (OK a) = OK a
135trun fc (Error e) = Error (At fc e)
137instance MonadPlus TC where
138 mzero = fail "Unknown error"
139 (OK x) `mplus` _ = OK x
140 _ `mplus` (OK y) = OK y
141 err `mplus` _ = err
143discard :: Monad m => m a -> m ()
144discard f = f >> return ()
146showSep :: String -> [String] -> String
147showSep sep [] = ""
148showSep sep [x] = x
149showSep sep (x:xs) = x ++ sep ++ showSep sep xs
151pmap f (x, y) = (f x, f y)
153traceWhen True msg a = trace msg a
154traceWhen False _ a = a
156-- RAW TERMS ----------------------------------------------------------------
158-- Names are hierarchies of strings, describing scope (so no danger of
159-- duplicate names, but need to be careful on lookup).
160-- Also MN for machine chosen names
162data Name = UN String
163 | NS Name [String] -- root, namespaces
164 | MN Int String
165 | NErased -- name of somethng which is never used in scope
166 deriving (Eq, Ord)
167{-!
168deriving instance Binary Name
169!-}
171instance Sized Name where
172 size (UN n) = 1
173 size (NS n els) = 1 + length els
174 size (MN i n) = 1
175 size NErased = 1
177instance Pretty Name where
178 pretty (UN n) = text n
179 pretty (NS n s) = pretty n
180 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
182instance Show Name where
183 show (UN n) = n
184 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
185 show (MN i s) = "{" ++ s ++ show i ++ "}"
186 show NErased = "_"
188-- Contexts allow us to map names to things. A root name maps to a collection
189-- of things in different namespaces with that name.
191type Ctxt a = Map.Map Name (Map.Map Name a)
192emptyContext = Map.empty
194nsroot (NS n _) = n
195nsroot n = n
197addDef :: Name -> a -> Ctxt a -> Ctxt a
198addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
199 Nothing -> Map.insert (nsroot n)
200 (Map.insert n v Map.empty) ctxt
201 Just xs -> Map.insert (nsroot n)
202 (Map.insert n v xs) ctxt
204{- lookup a name in the context, given an optional namespace.
205 The name (n) may itself have a (partial) namespace given.
207 Rules for resolution:
208 - if an explicit namespace is given, return the names which match it. If none
209 match, return all names.
210 - if the name has has explicit namespace given, return the names which match it
211 and ignore the given namespace.
212 - otherwise, return all names.
214-}
216lookupCtxtName :: Maybe [String] -> Name -> Ctxt a -> [(Name, a)]
217lookupCtxtName nspace n ctxt = case Map.lookup (nsroot n) ctxt of
218 Just xs -> filterNS (Map.toList xs)
219 Nothing -> []
220 where
221 filterNS [] = []
222 filterNS ((found, v) : xs)
223 | nsmatch n found = (found, v) : filterNS xs
224 | otherwise = filterNS xs
226 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
227 nsmatch (NS _ _) _ = False
228 nsmatch looking found = True
230lookupCtxt :: Maybe [String] -> Name -> Ctxt a -> [a]
231lookupCtxt ns n ctxt = map snd (lookupCtxtName ns n ctxt)
233updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
234updateDef n f ctxt
235 = let ds = lookupCtxtName Nothing n ctxt in
236 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
238toAlist :: Ctxt a -> [(Name, a)]
239toAlist ctxt = let allns = map snd (Map.toList ctxt) in
240 concat (map (Map.toList) allns)
242addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
243addAlist [] ctxt = ctxt
244addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
246data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
247 | IType | BIType | FlType | ChType | StrType
248 | PtrType | VoidType | Forgot
249 deriving (Eq, Ord)
250{-!
251deriving instance Binary Const
252!-}
254instance Sized Const where
255 size _ = 1
257instance Pretty Const where
258 pretty (I i) = text . show $ i
259 pretty (BI i) = text . show $ i
260 pretty (Fl f) = text . show $ f
261 pretty (Ch c) = text . show $ c
262 pretty (Str s) = text s
263 pretty IType = text "Int"
264 pretty BIType = text "BigInt"
265 pretty FlType = text "Float"
266 pretty ChType = text "Char"
267 pretty StrType = text "String"
268 pretty PtrType = text "Ptr"
269 pretty VoidType = text "Void"
270 pretty Forgot = text "Forgot"
272data Raw = Var Name
273 | RBind Name (Binder Raw) Raw
274 | RApp Raw Raw
275 | RSet
276 | RForce Raw
277 | RConstant Const
278 deriving (Show, Eq)
280instance Sized Raw where
281 size (Var name) = 1
282 size (RBind name bind right) = 1 + size bind + size right
283 size (RApp left right) = 1 + size left + size right
284 size RSet = 1
285 size (RForce raw) = 1 + size raw
286 size (RConstant const) = size const
288instance Pretty Raw where
289 pretty = text . show
291{-!
292deriving instance Binary Raw
293!-}
295data Binder b = Lam { binderTy :: b }
296 | Pi { binderTy :: b }
297 | Let { binderTy :: b,
298 binderVal :: b }
299 | NLet { binderTy :: b,
300 binderVal :: b }
301 | Hole { binderTy :: b}
302 | GHole { binderTy :: b}
303 | Guess { binderTy :: b,
304 binderVal :: b }
305 | PVar { binderTy :: b }
306 | PVTy { binderTy :: b }
307 deriving (Show, Eq, Ord, Functor)
308{-!
309deriving instance Binary Binder
310!-}
312instance Sized a => Sized (Binder a) where
313 size (Lam ty) = 1 + size ty
314 size (Pi ty) = 1 + size ty
315 size (Let ty val) = 1 + size ty + size val
316 size (NLet ty val) = 1 + size ty + size val
317 size (Hole ty) = 1 + size ty
318 size (GHole ty) = 1 + size ty
319 size (Guess ty val) = 1 + size ty + size val
320 size (PVar ty) = 1 + size ty
321 size (PVTy ty) = 1 + size ty
323fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
324fmapMB f (Let t v) = liftM2 Let (f t) (f v)
325fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
326fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
327fmapMB f (Lam t) = liftM Lam (f t)
328fmapMB f (Pi t) = liftM Pi (f t)
329fmapMB f (Hole t) = liftM Hole (f t)
330fmapMB f (GHole t) = liftM GHole (f t)
331fmapMB f (PVar t) = liftM PVar (f t)
332fmapMB f (PVTy t) = liftM PVTy (f t)
334raw_apply :: Raw -> [Raw] -> Raw
335raw_apply f [] = f
336raw_apply f (a : as) = raw_apply (RApp f a) as
338raw_unapply :: Raw -> (Raw, [Raw])
339raw_unapply t = ua [] t where
340 ua args (RApp f a) = ua (a:args) f
341 ua args t = (t, args)
343data RawFun = RawFun { rtype :: Raw,
344 rval :: Raw
345 }
346 deriving Show
348data RawDatatype = RDatatype Name Raw [(Name, Raw)]
349 deriving Show
351data RDef = RFunction RawFun
352 | RConst Raw
353 | RData RawDatatype
354 deriving Show
356type RProgram = [(Name, RDef)]
358-- WELL TYPED TERMS ---------------------------------------------------------
360data UExp = UVar Int -- universe variable
361 | UVal Int -- explicit universe level
362 deriving (Eq, Ord)
364instance Sized UExp where
365 size _ = 1
367-- We assume that universe levels have been checked, so anything external
368-- can just have the same universe variable and we won't get any new
369-- cycles.
371instance Binary UExp where
372 put x = return ()
373 get = return (UVar (-1))
375instance Show UExp where
376 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
377 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
378 show (UVal x) = show x
379-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
381data UConstraint = ULT UExp UExp
382 | ULE UExp UExp
383 deriving Eq
385instance Show UConstraint where
386 show (ULT x y) = show x ++ " < " ++ show y
387 show (ULE x y) = show x ++ " <= " ++ show y
389type UCs = (Int, [UConstraint])
391data NameType = Bound | Ref | DCon Int Int | TCon Int Int
392 deriving (Show, Ord)
393{-!
394deriving instance Binary NameType
395!-}
397instance Sized NameType where
398 size _ = 1
400instance Pretty NameType where
401 pretty = text . show
403instance Eq NameType where
404 Bound == Bound = True
405 Ref == Ref = True
406 DCon _ a == DCon _ b = (a == b) -- ignore tag
407 TCon _ a == TCon _ b = (a == b) -- ignore tag
408 _ == _ = False
410data TT n = P NameType n (TT n) -- embed type
411 | V Int
412 | Bind n (Binder (TT n)) (TT n)
413 | App (TT n) (TT n) -- function, function type, arg
414 | Constant Const
415 | Proj (TT n) Int -- argument projection; runtime only
416 | Erased
417 | Set UExp
418 deriving (Ord, Functor)
419{-!
420deriving instance Binary TT
421!-}
423class TermSize a where
424 termsize :: a -> Int
426instance TermSize a => TermSize [a] where
427 termsize [] = 0
428 termsize (x : xs) = termsize x + termsize xs
430instance TermSize (TT a) where
431 termsize (P _ _ _) = 1
432 termsize (V _) = 1
433 termsize (Bind n (Let t v) sc) = termsize v + termsize sc
434 termsize (App f a) = termsize f + termsize a
435 termsize _ = 1
437instance Sized a => Sized (TT a) where
438 size (P name n trm) = 1 + size name + size n + size trm
439 size (V v) = 1
440 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
441 size (App l r) = 1 + size l + size r
442 size (Constant c) = size c
443 size Erased = 1
444 size (Set u) = 1 + size u
446instance Pretty a => Pretty (TT a) where
447 pretty _ = text "test"
449type EnvTT n = [(n, Binder (TT n))]
451data Datatype n = Data { d_typename :: n,
452 d_typetag :: Int,
453 d_type :: (TT n),
454 d_cons :: [(n, TT n)] }
455 deriving (Show, Functor, Eq)
457instance Eq n => Eq (TT n) where
458 (==) (P xt x _) (P yt y _) = xt == yt && x == y
459 (==) (V x) (V y) = x == y
460 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
461 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
462 (==) (Set _) (Set _) = True -- deal with constraints later
463 (==) (Constant x) (Constant y) = x == y
464 (==) (Proj x i) (Proj y j) = x == y && i == j
465 (==) Erased _ = True
466 (==) _ Erased = True
467 (==) _ _ = False
469-- A few handy operations on well typed terms:
471isInjective :: TT n -> Bool
472isInjective (P (DCon _ _) _ _) = True
473isInjective (P (TCon _ _) _ _) = True
474isInjective (Constant _) = True
475isInjective (Set x) = True
476isInjective (Bind _ (Pi _) sc) = True
477isInjective (App f a) = isInjective f
478isInjective _ = False
480-- Count the number of instances of a de Bruijn index in a term
481vinstances :: Int -> TT n -> Int
482vinstances i (V x) | i == x = 1
483vinstances i (App f a) = vinstances i f + vinstances i a
484vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
485 where instancesB (Let t v) = vinstances i v
486 instancesB _ = 0
487vinstances i t = 0
489instantiate :: TT n -> TT n -> TT n
490instantiate e = subst 0 where
491 subst i (V x) | i == x = e
492 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
493 subst i (App f a) = App (subst i f) (subst i a)
494 subst i (Proj x idx) = Proj (subst i x) idx
495 subst i t = t
497pToV :: Eq n => n -> TT n -> TT n
498pToV n = pToV' n 0
499pToV' n i (P _ x _) | n == x = V i
500pToV' n i (Bind x b sc)
501 | n == x = Bind x (fmap (pToV' n i) b) sc
502 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
503pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
504pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
505pToV' n i t = t
507-- Convert several names. First in the list comes out as V 0
508pToVs :: Eq n => [n] -> TT n -> TT n
509pToVs ns tm = pToVs' ns tm 0 where
510 pToVs' [] tm i = tm
511 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
513vToP :: TT n -> TT n
514vToP = vToP' [] where
515 vToP' env (V i) = let (n, b) = (env !! i) in
516 P Bound n (binderTy b)
517 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
518 Bind n b' (vToP' ((n, b'):env) sc)
519 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
520 vToP' env t = t
522finalise :: Eq n => TT n -> TT n
523finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
524finalise (App f a) = App (finalise f) (finalise a)
525finalise t = t
527subst :: Eq n => n -> TT n -> TT n -> TT n
528subst n v tm = instantiate v (pToV n tm)
530substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
531substNames [] t = t
532substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
534-- Returns true if V 0 and bound name n do not occur in the term
536noOccurrence :: Eq n => n -> TT n -> Bool
537noOccurrence n t = no' 0 t
538 where
539 no' i (V x) = not (i == x)
540 no' i (P Bound x _) = not (n == x)
541 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
542 where noB' i (Let t v) = no' i t && no' i v
543 noB' i (Guess t v) = no' i t && no' i v
544 noB' i b = no' i (binderTy b)
545 no' i (App f a) = no' i f && no' i a
546 no' i (Proj x _) = no' i x
547 no' i _ = True
549-- Returns all names used free in the term
551freeNames :: Eq n => TT n -> [n]
552freeNames (P _ n _) = [n]
553freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
554 ++ freeNames t
555freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
556freeNames (App f a) = nub $ freeNames f ++ freeNames a
557freeNames (Proj x i) = nub $ freeNames x
558freeNames _ = []
560-- Return the arity of a (normalised) type
562arity :: TT n -> Int
563arity (Bind n (Pi t) sc) = 1 + arity sc
564arity _ = 0
566-- deconstruct an application; returns the function and a list of arguments
568unApply :: TT n -> (TT n, [TT n])
569unApply t = ua [] t where
570 ua args (App f a) = ua (a:args) f
571 ua args t = (t, args)
573mkApp :: TT n -> [TT n] -> TT n
574mkApp f [] = f
575mkApp f (a:as) = mkApp (App f a) as
577forget :: TT Name -> Raw
578forget tm = fe [] tm
579 where
580 fe env (P _ n _) = Var n
581 fe env (V i) = Var (env !! i)
582 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
583 (fe (n:env) sc)
584 fe env (App f a) = RApp (fe env f) (fe env a)
585 fe env (Constant c)
586 = RConstant c
587 fe env (Set i) = RSet
588 fe env Erased = RConstant Forgot
590bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
591bindAll [] t =t
592bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
594bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
595bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
597getArgTys :: TT n -> [(n, TT n)]
598getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
599getArgTys _ = []
601getRetTy :: TT n -> TT n
602getRetTy (Bind n (PVar _) sc) = getRetTy sc
603getRetTy (Bind n (PVTy _) sc) = getRetTy sc
604getRetTy (Bind n (Pi _) sc) = getRetTy sc
605getRetTy sc = sc
607uniqueName :: Name -> [Name] -> Name
608uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
609 | otherwise = n
611nextName (NS x s) = NS (nextName x) s
612nextName (MN i n) = MN (i+1) n
613nextName (UN x) = let (num', nm') = span isDigit (reverse x)
614 nm = reverse nm'
615 num = readN (reverse num') in
616 UN (nm ++ show (num+1))
617 where
618 readN "" = 0
619 readN x = read x
621type Term = TT Name
622type Type = Term
624type Env = EnvTT Name
626-- an environment with de Bruijn indices 'normalised' so that they all refer to
627-- this environment
629newtype WkEnvTT n = Wk (EnvTT n)
630type WkEnv = WkEnvTT Name
632instance (Eq n, Show n) => Show (TT n) where
633 show t = showEnv [] t
635instance Show Const where
636 show (I i) = show i
637 show (BI i) = show i ++ "L"
638 show (Fl f) = show f
639 show (Ch c) = show c
640 show (Str s) = show s
641 show IType = "Int"
642 show BIType = "Integer"
643 show FlType = "Float"
644 show ChType = "Char"
645 show StrType = "String"
646 show PtrType = "Ptr"
647 show VoidType = "Void"
649showEnv env t = showEnv' env t False
650showEnvDbg env t = showEnv' env t True
652prettyEnv env t = prettyEnv' env t False
653 where
654 prettyEnv' env t dbg = prettySe 10 env t dbg
656 bracket outer inner p
657 | inner > outer = lparen <> p <> rparen
658 | otherwise = p
660 prettySe p env (P nt n t) debug =
661 pretty n <+>
662 if debug then
663 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
664 else
665 empty
666 prettySe p env (V i) debug
667 | i < length env =
668 if debug then
669 text . show . fst $ env!!i
670 else
671 lbrack <+> text (show i) <+> rbrack
672 | otherwise = text "unbound" <+> text (show i) <+> text "!"
673 prettySe p env (Bind n b@(Pi t) sc) debug
674 | noOccurrence n sc && not debug =
675 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
676 prettySe p env (Bind n b sc) debug =
677 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
678 prettySe p env (App f a) debug =
679 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
680 prettySe p env (Proj x i) debug =
681 prettySe 1 env x debug <+> text ("!" ++ show i)
682 prettySe p env (Constant c) debug = pretty c
683 prettySe p env Erased debug = text "[_]"
684 prettySe p env (Set i) debug = text "Set" <+> (text . show $ i)
686 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
687 prettySb env n (Hole t) = prettyB env "?defer" "." n t
688 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
689 prettySb env n (PVar t) = prettyB env "pat" "." n t
690 prettySb env n (PVTy t) = prettyB env "pty" "." n t
691 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
692 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
694 prettyB env op sc n t debug =
695 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
697 prettyBv env op sc n t v debug =
698 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
699 prettySe 10 env v debug <> text sc
702showEnv' env t dbg = se 10 env t where
703 se p env (P nt n t) = show n
704 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
705 se p env (V i) | i < length env = (show $ fst $ env!!i) ++
706 if dbg then "{" ++ show i ++ "}" else ""
707 | otherwise = "!!V " ++ show i ++ "!!"
708 se p env (Bind n b@(Pi t) sc)
709 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
710 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
711 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
712 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
713 se p env (Constant c) = show c
714 se p env Erased = "[__]"
715 se p env (Set i) = "Set " ++ show i
717 sb env n (Lam t) = showb env "\\ " " => " n t
718 sb env n (Hole t) = showb env "? " ". " n t
719 sb env n (GHole t) = showb env "?defer " ". " n t
720 sb env n (Pi t) = showb env "(" ") -> " n t
721 sb env n (PVar t) = showb env "pat " ". " n t
722 sb env n (PVTy t) = showb env "pty " ". " n t
723 sb env n (Let t v) = showbv env "let " " in " n t v
724 sb env n (Guess t v) = showbv env "?? " " in " n t v
726 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
727 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
728 se 10 env v ++ sc
730 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
731 | otherwise = str
733-- Check whether a term has any holes in it - impure if so
735pureTerm :: TT n -> Bool
736pureTerm (App f a) = pureTerm f && pureTerm a
737pureTerm (Bind n b sc) = pureBinder b && pureTerm sc where
738 pureBinder (Hole _) = False
739 pureBinder (Guess _ _) = False
740 pureBinder (Let t v) = pureTerm t && pureTerm v
741 pureBinder t = pureTerm (binderTy t)
742pureTerm _ = True
744-- weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
746weakenTm :: Int -> TT n -> TT n
747weakenTm i t = wk i 0 t
748 where wk i min (V x) | x >= min = V (i + x)
749 wk i m (App f a) = App (wk i m f) (wk i m a)
750 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
751 wk i m t = t
752 wkb i m t = fmap (wk i m) t
754-- weaken an environment so that all the de Bruijn indices are correct according
755-- to the latest bound variable
757weakenEnv :: EnvTT n -> EnvTT n
758weakenEnv env = wk (length env - 1) env
759 where wk i [] = []
760 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
761 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
762 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
763 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
765weakenTmEnv :: Int -> EnvTT n -> EnvTT n
766weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
768orderPats :: Term -> Term
769orderPats tm = op [] tm
770 where
771 op ps (Bind n (PVar t) sc) = op ((n, t) : ps) sc
772 op ps sc = bindAll (map (\ (n, t) -> (n, PVar t)) (sortP ps)) sc
774 sortP ps = pick [] (reverse ps)
776 namesIn (P _ n _) = [n]
777 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
778 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
779 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
780 nb t = namesIn (binderTy t)
781 namesIn (App f a) = nub (namesIn f ++ namesIn a)
782 namesIn _ = []
784 pick acc [] = reverse acc
785 pick acc ((n, t) : ps) = pick (insert n t acc) ps
787 insert n t [] = [(n, t)]
788 insert n t ((n',t') : ps)
789 | n `elem` (namesIn t' ++ concatMap namesIn (map snd ps))
790 = (n', t') : insert n t ps
791 | otherwise = (n,t):(n',t'):ps