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Idris-dev/src/Core/TT.hs
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1{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, DeriveFunctor #-}
3{-| TT is the core language of Idris. The language has:
5 * Full dependent types
7 * A hierarchy of universes, with cumulativity: Type : Type1, Type1 : Type2, ...
9 * Pattern matching letrec binding
11 * (primitive types defined externally)
13 Some technical stuff:
15 * Typechecker is kept as simple as possible - 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-}
21module Core.TT where
23import Control.Monad.State
24import Debug.Trace
25import qualified Data.Map as Map
26import Data.Char
27import Data.List
28import Data.Vector.Unboxed (Vector)
29import qualified Data.Vector.Unboxed as V
30import qualified Data.Binary as B
31import Data.Binary hiding (get, put)
32import Foreign.Storable (sizeOf)
34import Util.Pretty hiding (Str)
36data Option = TTypeInTType
37 | CheckConv
38 deriving Eq
40-- | Source location. These are typically produced by the parser 'Idris.Parser.pfc'
41data FC = FC { fc_fname :: String, -- ^ Filename
42 fc_line :: Int -- ^ Line number
43 }
44 deriving Eq
45{-!
46deriving instance Binary FC
47!-}
49instance Sized FC where
50 size (FC f l) = 1 + length f
52instance Show FC where
53 show (FC f l) = f ++ ":" ++ show l
55data Err = Msg String
56 | InternalMsg String
57 | CantUnify Bool Term Term Err [(Name, Type)] Int
58 -- Int is 'score' - how much we did unify
59 -- Bool indicates recoverability, True indicates more info may make
60 -- unification succeed
61 | InfiniteUnify Name Term [(Name, Type)]
62 | CantConvert Term Term [(Name, Type)]
63 | CantInferType String
64 | NonFunctionType Term Term
65 | CantIntroduce Term
66 | NoSuchVariable Name
67 | NoTypeDecl Name
68 | NotInjective Term Term Term
69 | CantResolve Term
70 | CantResolveAlts [String]
71 | IncompleteTerm Term
72 | UniverseError
73 | ProgramLineComment
74 | Inaccessible Name
75 | NonCollapsiblePostulate Name
76 | AlreadyDefined Name
77 | ProofSearchFail Err
78 | NoRewriting Term
79 | At FC Err
80 | ProviderError String
81 deriving Eq
83instance Sized Err where
84 size (Msg msg) = length msg
85 size (InternalMsg msg) = length msg
86 size (CantUnify _ left right err _ score) = size left + size right + size err
87 size (InfiniteUnify _ right _) = size right
88 size (CantConvert left right _) = size left + size right
89 size (NoSuchVariable name) = size name
90 size (NoTypeDecl name) = size name
91 size (NotInjective l c r) = size l + size c + size r
92 size (CantResolve trm) = size trm
93 size (NoRewriting trm) = size trm
94 size (CantResolveAlts _) = 1
95 size (IncompleteTerm trm) = size trm
96 size UniverseError = 1
97 size ProgramLineComment = 1
98 size (At fc err) = size fc + size err
99 size (ProviderError msg) = length msg
100 size _ = 1
102score :: Err -> Int
103score (CantUnify _ _ _ m _ s) = s + score m
104score (CantResolve _) = 20
105score (NoSuchVariable _) = 1000
106score (ProofSearchFail _) = 10000
107score (InternalMsg _) = -1
108score _ = 0
110instance Show Err where
111 show (Msg s) = s
112 show (InternalMsg s) = "Internal error: " ++ show s
113 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
114 ++ show e ++ " in " ++ show sc ++ " " ++ show i
115 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
116 show (ProviderError msg) = "Type provider error: " ++ msg
117 show _ = "Error"
119instance Pretty Err where
120 pretty (Msg m) = text m
121 pretty (CantUnify _ l r e _ i) =
122 if size l + size r > breakingSize then
123 text "Cannot unify" <+> colon $$
124 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
125 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
126 else
127 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
128 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
129 pretty (ProviderError msg) = text msg
130 pretty _ = text "Error"
132data TC a = OK a
133 | Error Err
134 deriving (Eq, Functor)
136instance Pretty a => Pretty (TC a) where
137 pretty (OK ok) = pretty ok
138 pretty (Error err) =
139 if size err > breakingSize then
140 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
141 else
142 text "Error" <+> colon <+> pretty err
144instance Show a => Show (TC a) where
145 show (OK x) = show x
146 show (Error str) = "Error: " ++ show str
148-- at some point, this instance should also carry type checking options
149-- (e.g. Type:Type)
151instance Monad TC where
152 return = OK
153 x >>= k = case x of
154 OK v -> k v
155 Error e -> Error e
156 fail e = Error (InternalMsg e)
158tfail :: Err -> TC a
159tfail e = Error e
161trun :: FC -> TC a -> TC a
162trun fc (OK a) = OK a
163trun fc (Error e) = Error (At fc e)
165instance MonadPlus TC where
166 mzero = fail "Unknown error"
167 (OK x) `mplus` _ = OK x
168 _ `mplus` (OK y) = OK y
169 err `mplus` _ = err
171discard :: Monad m => m a -> m ()
172discard f = f >> return ()
174showSep :: String -> [String] -> String
175showSep sep [] = ""
176showSep sep [x] = x
177showSep sep (x:xs) = x ++ sep ++ showSep sep xs
179pmap f (x, y) = (f x, f y)
181traceWhen True msg a = trace msg a
182traceWhen False _ a = a
184-- RAW TERMS ----------------------------------------------------------------
186-- | Names are hierarchies of strings, describing scope (so no danger of
187-- duplicate names, but need to be careful on lookup).
188data Name = UN String -- ^ User-provided name
189 | NS Name [String] -- ^ Root, namespaces
190 | MN Int String -- ^ Machine chosen names
191 | NErased -- ^ Name of somethng which is never used in scope
192 deriving (Eq, Ord)
193{-!
194deriving instance Binary Name
195!-}
197instance Sized Name where
198 size (UN n) = 1
199 size (NS n els) = 1 + length els
200 size (MN i n) = 1
201 size NErased = 1
203instance Pretty Name where
204 pretty (UN n) = text n
205 pretty (NS n s) = pretty n
206 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
208instance Show Name where
209 show (UN n) = n
210 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
211 show (MN i s) = "{" ++ s ++ show i ++ "}"
212 show NErased = "_"
214-- |Contexts allow us to map names to things. A root name maps to a collection
215-- of things in different namespaces with that name.
216type Ctxt a = Map.Map Name (Map.Map Name a)
217emptyContext = Map.empty
219tcname (UN ('@':_)) = True
220tcname (NS n _) = tcname n
221tcname _ = False
223implicitable (NS n _) = implicitable n
224implicitable (UN (x:xs)) = isLower x
225implicitable _ = False
227nsroot (NS n _) = n
228nsroot n = n
230addDef :: Name -> a -> Ctxt a -> Ctxt a
231addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
232 Nothing -> Map.insert (nsroot n)
233 (Map.insert n v Map.empty) ctxt
234 Just xs -> Map.insert (nsroot n)
235 (Map.insert n v xs) ctxt
237{-| Look up a name in the context, given an optional namespace.
238 The name (n) may itself have a (partial) namespace given.
240 Rules for resolution:
242 - if an explicit namespace is given, return the names which match it. If none
243 match, return all names.
245 - if the name has has explicit namespace given, return the names which match it
246 and ignore the given namespace.
248 - otherwise, return all names.
250-}
252lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
253lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
254 Just xs -> filterNS (Map.toList xs)
255 Nothing -> []
256 where
257 filterNS [] = []
258 filterNS ((found, v) : xs)
259 | nsmatch n found = (found, v) : filterNS xs
260 | otherwise = filterNS xs
262 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
263 nsmatch (NS _ _) _ = False
264 nsmatch looking found = True
266lookupCtxt :: Name -> Ctxt a -> [a]
267lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
269updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
270updateDef n f ctxt
271 = let ds = lookupCtxtName n ctxt in
272 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
274toAlist :: Ctxt a -> [(Name, a)]
275toAlist ctxt = let allns = map snd (Map.toList ctxt) in
276 concat (map (Map.toList) allns)
278addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
279addAlist [] ctxt = ctxt
280addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
282data NativeTy = IT8 | IT16 | IT32 | IT64
283 deriving (Show, Eq, Ord, Enum)
285instance Pretty NativeTy where
286 pretty IT8 = text "Bits8"
287 pretty IT16 = text "Bits16"
288 pretty IT32 = text "Bits32"
289 pretty IT64 = text "Bits64"
291data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
292 | ITVec NativeTy Int
293 deriving (Show, Eq, Ord)
295data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
296 deriving (Show, Eq, Ord)
298instance Pretty ArithTy where
299 pretty (ATInt ITNative) = text "Int"
300 pretty (ATInt ITBig) = text "BigInt"
301 pretty (ATInt ITChar) = text "Char"
302 pretty (ATInt (ITFixed n)) = pretty n
303 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
304 pretty ATFloat = text "Float"
306nativeTyWidth :: NativeTy -> Int
307nativeTyWidth IT8 = 8
308nativeTyWidth IT16 = 16
309nativeTyWidth IT32 = 32
310nativeTyWidth IT64 = 64
312{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
313intTyWidth :: IntTy -> Int
314intTyWidth (ITFixed n) = nativeTyWidth n
315intTyWidth ITNative = 8 * sizeOf (0 :: Int)
316intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
317intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
319data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
320 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
321 | B8V (Vector Word8) | B16V (Vector Word16)
322 | B32V (Vector Word32) | B64V (Vector Word64)
323 | AType ArithTy | StrType
324 | PtrType | VoidType | Forgot
325 deriving (Eq, Ord)
326{-!
327deriving instance Binary Const
328!-}
330instance Sized Const where
331 size _ = 1
333instance Pretty Const where
334 pretty (I i) = text . show $ i
335 pretty (BI i) = text . show $ i
336 pretty (Fl f) = text . show $ f
337 pretty (Ch c) = text . show $ c
338 pretty (Str s) = text s
339 pretty (AType a) = pretty a
340 pretty StrType = text "String"
341 pretty PtrType = text "Ptr"
342 pretty VoidType = text "Void"
343 pretty Forgot = text "Forgot"
344 pretty (B8 w) = text . show $ w
345 pretty (B16 w) = text . show $ w
346 pretty (B32 w) = text . show $ w
347 pretty (B64 w) = text . show $ w
349data Raw = Var Name
350 | RBind Name (Binder Raw) Raw
351 | RApp Raw Raw
352 | RType
353 | RForce Raw
354 | RConstant Const
355 deriving (Show, Eq)
357instance Sized Raw where
358 size (Var name) = 1
359 size (RBind name bind right) = 1 + size bind + size right
360 size (RApp left right) = 1 + size left + size right
361 size RType = 1
362 size (RForce raw) = 1 + size raw
363 size (RConstant const) = size const
365instance Pretty Raw where
366 pretty = text . show
368{-!
369deriving instance Binary Raw
370!-}
372-- | All binding forms are represented in a unform fashion.
373data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
374 | Pi { binderTy :: b }
375 | Let { binderTy :: b,
376 binderVal :: b {-^ value for bound variable-}}
377 | NLet { binderTy :: b,
378 binderVal :: b }
379 | Hole { binderTy :: b}
380 | GHole { binderTy :: b}
381 | Guess { binderTy :: b,
382 binderVal :: b }
383 | PVar { binderTy :: b }
384 | PVTy { binderTy :: b }
385 deriving (Show, Eq, Ord, Functor)
386{-!
387deriving instance Binary Binder
388!-}
390instance Sized a => Sized (Binder a) where
391 size (Lam ty) = 1 + size ty
392 size (Pi ty) = 1 + size ty
393 size (Let ty val) = 1 + size ty + size val
394 size (NLet ty val) = 1 + size ty + size val
395 size (Hole ty) = 1 + size ty
396 size (GHole ty) = 1 + size ty
397 size (Guess ty val) = 1 + size ty + size val
398 size (PVar ty) = 1 + size ty
399 size (PVTy ty) = 1 + size ty
401fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
402fmapMB f (Let t v) = liftM2 Let (f t) (f v)
403fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
404fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
405fmapMB f (Lam t) = liftM Lam (f t)
406fmapMB f (Pi t) = liftM Pi (f t)
407fmapMB f (Hole t) = liftM Hole (f t)
408fmapMB f (GHole t) = liftM GHole (f t)
409fmapMB f (PVar t) = liftM PVar (f t)
410fmapMB f (PVTy t) = liftM PVTy (f t)
412raw_apply :: Raw -> [Raw] -> Raw
413raw_apply f [] = f
414raw_apply f (a : as) = raw_apply (RApp f a) as
416raw_unapply :: Raw -> (Raw, [Raw])
417raw_unapply t = ua [] t where
418 ua args (RApp f a) = ua (a:args) f
419 ua args t = (t, args)
421data RawFun = RawFun { rtype :: Raw,
422 rval :: Raw
423 }
424 deriving Show
426data RawDatatype = RDatatype Name Raw [(Name, Raw)]
427 deriving Show
429data RDef = RFunction RawFun
430 | RConst Raw
431 | RData RawDatatype
432 deriving Show
434type RProgram = [(Name, RDef)]
436-- WELL TYPED TERMS ---------------------------------------------------------
438-- | Universe expressions for universe checking
439data UExp = UVar Int -- ^ universe variable
440 | UVal Int -- ^ explicit universe level
441 deriving (Eq, Ord)
443instance Sized UExp where
444 size _ = 1
446-- We assume that universe levels have been checked, so anything external
447-- can just have the same universe variable and we won't get any new
448-- cycles.
450instance Binary UExp where
451 put x = return ()
452 get = return (UVar (-1))
454instance Show UExp where
455 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
456 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
457 show (UVal x) = show x
458-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
460-- | Universe constraints
461data UConstraint = ULT UExp UExp -- ^ Strictly less than
462 | ULE UExp UExp -- ^ Less than or equal to
463 deriving Eq
465instance Show UConstraint where
466 show (ULT x y) = show x ++ " < " ++ show y
467 show (ULE x y) = show x ++ " <= " ++ show y
469type UCs = (Int, [UConstraint])
471data NameType = Bound
472 | Ref
473 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
474 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
475 deriving (Show, Ord)
476{-!
477deriving instance Binary NameType
478!-}
480instance Sized NameType where
481 size _ = 1
483instance Pretty NameType where
484 pretty = text . show
486instance Eq NameType where
487 Bound == Bound = True
488 Ref == Ref = True
489 DCon _ a == DCon _ b = (a == b) -- ignore tag
490 TCon _ a == TCon _ b = (a == b) -- ignore tag
491 _ == _ = False
493-- | Terms in the core language
494data TT n = P NameType n (TT n) -- ^ named references
495 | V Int -- ^ a resolved de Bruijn-indexed variable
496 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
497 | App (TT n) (TT n) -- ^ function, function type, arg
498 | Constant Const -- ^ constant
499 | Proj (TT n) Int -- ^ argument projection; runtime only
500 | Erased -- ^ an erased term
501 | Impossible -- ^ special case for totality checking
502 | TType UExp -- ^ the type of types at some level
503 deriving (Ord, Functor)
504{-!
505deriving instance Binary TT
506!-}
508class TermSize a where
509 termsize :: Name -> a -> Int
511instance TermSize a => TermSize [a] where
512 termsize n [] = 0
513 termsize n (x : xs) = termsize n x + termsize n xs
515instance TermSize (TT Name) where
516 termsize n (P _ x _)
517 | x == n = 1000000 -- recursive => really big
518 | otherwise = 1
519 termsize n (V _) = 1
520 termsize n (Bind n' (Let t v) sc)
521 = let rn = if n == n' then MN 0 "noname" else n in
522 termsize rn v + termsize rn sc
523 termsize n (Bind n' b sc)
524 = let rn = if n == n' then MN 0 "noname" else n in
525 termsize rn sc
526 termsize n (App f a) = termsize n f + termsize n a
527 termsize n (Proj t i) = termsize n t
528 termsize n _ = 1
530instance Sized a => Sized (TT a) where
531 size (P name n trm) = 1 + size name + size n + size trm
532 size (V v) = 1
533 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
534 size (App l r) = 1 + size l + size r
535 size (Constant c) = size c
536 size Erased = 1
537 size (TType u) = 1 + size u
539instance Pretty a => Pretty (TT a) where
540 pretty _ = text "test"
542type EnvTT n = [(n, Binder (TT n))]
544data Datatype n = Data { d_typename :: n,
545 d_typetag :: Int,
546 d_type :: (TT n),
547 d_cons :: [(n, TT n)] }
548 deriving (Show, Functor, Eq)
550instance Eq n => Eq (TT n) where
551 (==) (P xt x _) (P yt y _) = x == y
552 (==) (V x) (V y) = x == y
553 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
554 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
555 (==) (TType _) (TType _) = True -- deal with constraints later
556 (==) (Constant x) (Constant y) = x == y
557 (==) (Proj x i) (Proj y j) = x == y && i == j
558 (==) Erased _ = True
559 (==) _ Erased = True
560 (==) _ _ = False
562-- * A few handy operations on well typed terms:
564-- | A term is injective iff it is a data constructor, type constructor,
565-- constant, the type Type, pi-binding, or an application of an injective
566-- term.
567isInjective :: TT n -> Bool
568isInjective (P (DCon _ _) _ _) = True
569isInjective (P (TCon _ _) _ _) = True
570isInjective (Constant _) = True
571isInjective (TType x) = True
572isInjective (Bind _ (Pi _) sc) = True
573isInjective (App f a) = isInjective f
574isInjective _ = False
576-- | Count the number of instances of a de Bruijn index in a term
577vinstances :: Int -> TT n -> Int
578vinstances i (V x) | i == x = 1
579vinstances i (App f a) = vinstances i f + vinstances i a
580vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
581 where instancesB (Let t v) = vinstances i v
582 instancesB _ = 0
583vinstances i t = 0
585instantiate :: TT n -> TT n -> TT n
586instantiate e = subst 0 where
587 subst i (V x) | i == x = e
588 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
589 subst i (App f a) = App (subst i f) (subst i a)
590 subst i (Proj x idx) = Proj (subst i x) idx
591 subst i t = t
593explicitNames :: TT n -> TT n
594explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
595 Bind x b'
596 (explicitNames (instantiate
597 (P Bound x (binderTy b')) sc))
598explicitNames (App f a) = App (explicitNames f) (explicitNames a)
599explicitNames (Proj x idx) = Proj (explicitNames x) idx
600explicitNames t = t
602pToV :: Eq n => n -> TT n -> TT n
603pToV n = pToV' n 0
604pToV' n i (P _ x _) | n == x = V i
605pToV' n i (Bind x b sc)
606-- We can assume the inner scope has been pToVed already, so continue to
607-- resolve names from the *outer* scope which may happen to have the same id.
608-- | n == x = Bind x (fmap (pToV' n i) b) sc
609 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
610pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
611pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
612pToV' n i t = t
614-- increase de Bruijn indices, as if a binder has been added
615addBinder :: TT n -> TT n
616addBinder t = ab 0 t
617 where
618 ab top (V i) | i >= top = V (i + 1)
619 | otherwise = V i
620 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
621 ab top (App f a) = App (ab top f) (ab top a)
622 ab top (Proj t idx) = Proj (ab top t) idx
623 ab top t = t
625-- | Convert several names. First in the list comes out as V 0
626pToVs :: Eq n => [n] -> TT n -> TT n
627pToVs ns tm = pToVs' ns tm 0 where
628 pToVs' [] tm i = tm
629 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
631vToP :: TT n -> TT n
632vToP = vToP' [] where
633 vToP' env (V i) = let (n, b) = (env !! i) in
634 P Bound n (binderTy b)
635 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
636 Bind n b' (vToP' ((n, b'):env) sc)
637 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
638 vToP' env t = t
640finalise :: Eq n => TT n -> TT n
641finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
642finalise (App f a) = App (finalise f) (finalise a)
643finalise t = t
645subst :: Eq n => n -> TT n -> TT n -> TT n
646subst n v tm = instantiate v (pToV n tm)
648substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
649substNames [] t = t
650substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
652substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
653substTerm old new = st where
654 st t | t == old = new
655 st (App f a) = App (st f) (st a)
656 st (Bind x b sc) = Bind x (fmap st b) (st sc)
657 st t = t
659-- Returns true if V 0 and bound name n do not occur in the term
661noOccurrence :: Eq n => n -> TT n -> Bool
662noOccurrence n t = no' 0 t
663 where
664 no' i (V x) = not (i == x)
665 no' i (P Bound x _) = not (n == x)
666 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
667 where noB' i (Let t v) = no' i t && no' i v
668 noB' i (Guess t v) = no' i t && no' i v
669 noB' i b = no' i (binderTy b)
670 no' i (App f a) = no' i f && no' i a
671 no' i (Proj x _) = no' i x
672 no' i _ = True
674-- | Returns all names used free in the term
675freeNames :: Eq n => TT n -> [n]
676freeNames (P _ n _) = [n]
677freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
678 ++ freeNames t
679freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
680freeNames (App f a) = nub $ freeNames f ++ freeNames a
681freeNames (Proj x i) = nub $ freeNames x
682freeNames _ = []
684-- | Return the arity of a (normalised) type
685arity :: TT n -> Int
686arity (Bind n (Pi t) sc) = 1 + arity sc
687arity _ = 0
689-- | Deconstruct an application; returns the function and a list of arguments
690unApply :: TT n -> (TT n, [TT n])
691unApply t = ua [] t where
692 ua args (App f a) = ua (a:args) f
693 ua args t = (t, args)
695mkApp :: TT n -> [TT n] -> TT n
696mkApp f [] = f
697mkApp f (a:as) = mkApp (App f a) as
699forget :: TT Name -> Raw
700forget tm = fe [] tm
701 where
702 fe env (P _ n _) = Var n
703 fe env (V i) = Var (env !! i)
704 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
705 (fe (n:env) sc)
706 fe env (App f a) = RApp (fe env f) (fe env a)
707 fe env (Constant c)
708 = RConstant c
709 fe env (TType i) = RType
710 fe env Erased = RConstant Forgot
712bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
713bindAll [] t =t
714bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
716bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
717bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
719getArgTys :: TT n -> [(n, TT n)]
720getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
721getArgTys _ = []
723getRetTy :: TT n -> TT n
724getRetTy (Bind n (PVar _) sc) = getRetTy sc
725getRetTy (Bind n (PVTy _) sc) = getRetTy sc
726getRetTy (Bind n (Pi _) sc) = getRetTy sc
727getRetTy sc = sc
729uniqueName :: Name -> [Name] -> Name
730uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
731 | otherwise = n
733uniqueBinders :: [Name] -> TT Name -> TT Name
734uniqueBinders ns (Bind n b sc)
735 = let n' = uniqueName n ns in
736 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
737uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
738uniqueBinders ns t = t
741nextName (NS x s) = NS (nextName x) s
742nextName (MN i n) = MN (i+1) n
743nextName (UN x) = let (num', nm') = span isDigit (reverse x)
744 nm = reverse nm'
745 num = readN (reverse num') in
746 UN (nm ++ show (num+1))
747 where
748 readN "" = 0
749 readN x = read x
751type Term = TT Name
752type Type = Term
754type Env = EnvTT Name
756-- an environment with de Bruijn indices 'normalised' so that they all refer to
757-- this environment
759newtype WkEnvTT n = Wk (EnvTT n)
760type WkEnv = WkEnvTT Name
762instance (Eq n, Show n) => Show (TT n) where
763 show t = showEnv [] t
765itBitsName IT8 = "Bits8"
766itBitsName IT16 = "Bits16"
767itBitsName IT32 = "Bits32"
768itBitsName IT64 = "Bits64"
770instance Show Const where
771 show (I i) = show i
772 show (BI i) = show i ++ "L"
773 show (Fl f) = show f
774 show (Ch c) = show c
775 show (Str s) = show s
776 show (B8 x) = show x
777 show (B16 x) = show x
778 show (B32 x) = show x
779 show (B64 x) = show x
780 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
781 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
782 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
783 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
784 show (AType ATFloat) = "Float"
785 show (AType (ATInt ITBig)) = "Integer"
786 show (AType (ATInt ITNative)) = "Int"
787 show (AType (ATInt ITChar)) = "Char"
788 show (AType (ATInt (ITFixed it))) = itBitsName it
789 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
790 show StrType = "String"
791 show PtrType = "Ptr"
792 show VoidType = "Void"
794showEnv env t = showEnv' env t False
795showEnvDbg env t = showEnv' env t True
797prettyEnv env t = prettyEnv' env t False
798 where
799 prettyEnv' env t dbg = prettySe 10 env t dbg
801 bracket outer inner p
802 | inner > outer = lparen <> p <> rparen
803 | otherwise = p
805 prettySe p env (P nt n t) debug =
806 pretty n <+>
807 if debug then
808 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
809 else
810 empty
811 prettySe p env (V i) debug
812 | i < length env =
813 if debug then
814 text . show . fst $ env!!i
815 else
816 lbrack <+> text (show i) <+> rbrack
817 | otherwise = text "unbound" <+> text (show i) <+> text "!"
818 prettySe p env (Bind n b@(Pi t) sc) debug
819 | noOccurrence n sc && not debug =
820 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
821 prettySe p env (Bind n b sc) debug =
822 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
823 prettySe p env (App f a) debug =
824 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
825 prettySe p env (Proj x i) debug =
826 prettySe 1 env x debug <+> text ("!" ++ show i)
827 prettySe p env (Constant c) debug = pretty c
828 prettySe p env Erased debug = text "[_]"
829 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
831 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
832 prettySb env n (Hole t) = prettyB env "?defer" "." n t
833 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
834 prettySb env n (PVar t) = prettyB env "pat" "." n t
835 prettySb env n (PVTy t) = prettyB env "pty" "." n t
836 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
837 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
839 prettyB env op sc n t debug =
840 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
842 prettyBv env op sc n t v debug =
843 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
844 prettySe 10 env v debug <> text sc
847showEnv' env t dbg = se 10 env t where
848 se p env (P nt n t) = show n
849 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
850 se p env (V i) | i < length env && i >= 0
851 = (show $ fst $ env!!i) ++
852 if dbg then "{" ++ show i ++ "}" else ""
853 | otherwise = "!!V " ++ show i ++ "!!"
854 se p env (Bind n b@(Pi t) sc)
855 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
856 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
857 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
858 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
859 se p env (Constant c) = show c
860 se p env Erased = "[__]"
861 se p env Impossible = "[impossible]"
862 se p env (TType i) = "Type " ++ show i
864 sb env n (Lam t) = showb env "\\ " " => " n t
865 sb env n (Hole t) = showb env "? " ". " n t
866 sb env n (GHole t) = showb env "?defer " ". " n t
867 sb env n (Pi t) = showb env "(" ") -> " n t
868 sb env n (PVar t) = showb env "pat " ". " n t
869 sb env n (PVTy t) = showb env "pty " ". " n t
870 sb env n (Let t v) = showbv env "let " " in " n t v
871 sb env n (Guess t v) = showbv env "?? " " in " n t v
873 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
874 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
875 se 10 env v ++ sc
877 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
878 | otherwise = str
880-- | Check whether a term has any holes in it - impure if so
881pureTerm :: TT Name -> Bool
882pureTerm (App f a) = pureTerm f && pureTerm a
883pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
884 pureBinder (Hole _) = False
885 pureBinder (Guess _ _) = False
886 pureBinder (Let t v) = pureTerm t && pureTerm v
887 pureBinder t = pureTerm (binderTy t)
889 notClassName (MN _ "class") = False
890 notClassName _ = True
892pureTerm _ = True
894-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
895weakenTm :: Int -> TT n -> TT n
896weakenTm i t = wk i 0 t
897 where wk i min (V x) | x >= min = V (i + x)
898 wk i m (App f a) = App (wk i m f) (wk i m a)
899 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
900 wk i m t = t
901 wkb i m t = fmap (wk i m) t
903-- | Weaken an environment so that all the de Bruijn indices are correct according
904-- to the latest bound variable
906weakenEnv :: EnvTT n -> EnvTT n
907weakenEnv env = wk (length env - 1) env
908 where wk i [] = []
909 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
910 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
911 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
912 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
914weakenTmEnv :: Int -> EnvTT n -> EnvTT n
915weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
917orderPats :: Term -> Term
918orderPats tm = op [] tm
919 where
920 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
921 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
922 op ps sc = bindAll (map (\ (n, t) -> (n, t)) (sortP ps)) sc
924 sortP ps = pick [] (reverse ps)
926 namesIn (P _ n _) = [n]
927 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
928 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
929 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
930 nb t = namesIn (binderTy t)
931 namesIn (App f a) = nub (namesIn f ++ namesIn a)
932 namesIn _ = []
934 pick acc [] = reverse acc
935 pick acc ((n, t) : ps) = pick (insert n t acc) ps
937 insert n t [] = [(n, t)]
938 insert n t ((n',t') : ps)
939 | n `elem` (namesIn (binderTy t') ++
940 concatMap namesIn (map (binderTy . snd) ps))
941 = (n', t') : insert n t ps
942 | otherwise = (n,t):(n',t'):ps