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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 Control.Monad.Trans.Error (Error(..))
25import Debug.Trace
26import qualified Data.Map as Map
27import Data.Char
28import Data.List
29import Data.Vector.Unboxed (Vector)
30import qualified Data.Vector.Unboxed as V
31import qualified Data.Binary as B
32import Data.Binary hiding (get, put)
33import Foreign.Storable (sizeOf)
35import Util.Pretty hiding (Str)
37data Option = TTypeInTType
38 | CheckConv
39 deriving Eq
41-- | Source location. These are typically produced by the parser 'Idris.Parser.getFC'
42data FC = FC { fc_fname :: String, -- ^ Filename
43 fc_line :: Int, -- ^ Line number
44 fc_column :: Int -- ^ Column number
45 }
47-- | Ignore source location equality (so deriving classes do not compare FCs)
48instance Eq FC where
49 _ == _ = True
51-- | FC with equality
52newtype FC' = FC' { unwrapFC :: FC }
54instance Eq FC' where
55 FC' fc == FC' fc' = fcEq fc fc'
56 where fcEq (FC n l c) (FC n' l' c') = n == n' && l == l' && c == c'
58-- | Empty source location
59emptyFC :: FC
60emptyFC = fileFC ""
62-- | Source location with file only
63fileFC :: String -> FC
64fileFC s = FC s 0 0
66{-!
67deriving instance Binary FC
68deriving instance NFData FC
69!-}
71instance Sized FC where
72 size (FC f l c) = 1 + length f
74instance Show FC where
75 show (FC f l c) = f ++ ":" ++ show l ++ ":" ++ show c
77data Err = Msg String
78 | InternalMsg String
79 | CantUnify Bool Term Term Err [(Name, Type)] Int
80 -- Int is 'score' - how much we did unify
81 -- Bool indicates recoverability, True indicates more info may make
82 -- unification succeed
83 | InfiniteUnify Name Term [(Name, Type)]
84 | CantConvert Term Term [(Name, Type)]
85 | UnifyScope Name Name Term [(Name, Type)]
86 | CantInferType String
87 | NonFunctionType Term Term
88 | TooManyArguments Name
89 | CantIntroduce Term
90 | NoSuchVariable Name
91 | NoTypeDecl Name
92 | NotInjective Term Term Term
93 | CantResolve Term
94 | CantResolveAlts [String]
95 | IncompleteTerm Term
96 | UniverseError
97 | ProgramLineComment
98 | Inaccessible Name
99 | NonCollapsiblePostulate Name
100 | AlreadyDefined Name
101 | ProofSearchFail Err
102 | NoRewriting Term
103 | At FC Err
104 | Elaborating String Name Err
105 | ProviderError String
106 | LoadingFailed String Err
107 deriving Eq
108{-!
109deriving instance NFData Err
110!-}
112instance Sized Err where
113 size (Msg msg) = length msg
114 size (InternalMsg msg) = length msg
115 size (CantUnify _ left right err _ score) = size left + size right + size err
116 size (InfiniteUnify _ right _) = size right
117 size (CantConvert left right _) = size left + size right
118 size (UnifyScope _ _ right _) = size right
119 size (NoSuchVariable name) = size name
120 size (NoTypeDecl name) = size name
121 size (NotInjective l c r) = size l + size c + size r
122 size (CantResolve trm) = size trm
123 size (NoRewriting trm) = size trm
124 size (CantResolveAlts _) = 1
125 size (IncompleteTerm trm) = size trm
126 size UniverseError = 1
127 size ProgramLineComment = 1
128 size (At fc err) = size fc + size err
129 size (Elaborating _ n err) = size err
130 size (ProviderError msg) = length msg
131 size (LoadingFailed fn e) = 1 + length fn + size e
132 size _ = 1
134score :: Err -> Int
135score (CantUnify _ _ _ m _ s) = s + score m
136score (CantResolve _) = 20
137score (NoSuchVariable _) = 1000
138score (ProofSearchFail _) = 10000
139score (InternalMsg _) = -1
140score _ = 0
142instance Show Err where
143 show (Msg s) = s
144 show (InternalMsg s) = "Internal error: " ++ show s
145 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
146 ++ show e ++ " in " ++ show sc ++ " " ++ show i
147 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
148 show (ProviderError msg) = "Type provider error: " ++ msg
149 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: " ++ show e
150 show _ = "Error"
152instance Pretty Err where
153 pretty (Msg m) = text m
154 pretty (CantUnify _ l r e _ i) =
155 if size l + size r > breakingSize then
156 text "Cannot unify" <+> colon $$
157 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
158 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
159 else
160 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
161 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
162 pretty (ProviderError msg) = text msg
163 pretty err@(LoadingFailed _ _) = text (show err)
164 pretty _ = text "Error"
166instance Error Err where
167 strMsg = Msg
169data TC a = OK a
170 | Error Err
171 deriving (Eq, Functor)
173instance Pretty a => Pretty (TC a) where
174 pretty (OK ok) = pretty ok
175 pretty (Error err) =
176 if size err > breakingSize then
177 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
178 else
179 text "Error" <+> colon <+> pretty err
181instance Show a => Show (TC a) where
182 show (OK x) = show x
183 show (Error str) = "Error: " ++ show str
185-- at some point, this instance should also carry type checking options
186-- (e.g. Type:Type)
188instance Monad TC where
189 return = OK
190 x >>= k = case x of
191 OK v -> k v
192 Error e -> Error e
193 fail e = Error (InternalMsg e)
195tfail :: Err -> TC a
196tfail e = Error e
198trun :: FC -> TC a -> TC a
199trun fc (OK a) = OK a
200trun fc (Error e) = Error (At fc e)
202instance MonadPlus TC where
203 mzero = fail "Unknown error"
204 (OK x) `mplus` _ = OK x
205 _ `mplus` (OK y) = OK y
206 err `mplus` _ = err
208discard :: Monad m => m a -> m ()
209discard f = f >> return ()
211showSep :: String -> [String] -> String
212showSep sep [] = ""
213showSep sep [x] = x
214showSep sep (x:xs) = x ++ sep ++ showSep sep xs
216pmap f (x, y) = (f x, f y)
218traceWhen True msg a = trace msg a
219traceWhen False _ a = a
221-- RAW TERMS ----------------------------------------------------------------
223-- | Names are hierarchies of strings, describing scope (so no danger of
224-- duplicate names, but need to be careful on lookup).
225data Name = UN String -- ^ User-provided name
226 | NS Name [String] -- ^ Root, namespaces
227 | MN Int String -- ^ Machine chosen names
228 | NErased -- ^ Name of somethng which is never used in scope
229 | SN SpecialName -- ^ Decorated function names
230 deriving (Eq, Ord)
231{-!
232deriving instance Binary Name
233deriving instance NFData Name
234!-}
236data SpecialName = WhereN Int Name Name
237 | InstanceN Name [String]
238 | ParentN Name String
239 | MethodN Name
240 | CaseN Name
241 | ElimN Name
242 deriving (Eq, Ord)
243{-!
244deriving instance Binary SpecialName
245deriving instance NFData SpecialName
246!-}
248instance Sized Name where
249 size (UN n) = 1
250 size (NS n els) = 1 + length els
251 size (MN i n) = 1
252 size _ = 1
254instance Pretty Name where
255 pretty (UN n) = text n
256 pretty (NS n s) = pretty n
257 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
258 pretty (SN s) = text (show s)
260instance Show Name where
261 show (UN n) = n
262 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
263 show (MN _ "underscore") = "_"
264 show (MN i s) = "{" ++ s ++ show i ++ "}"
265 show (SN s) = show s
266 show NErased = "_"
268instance Show SpecialName where
269 show (WhereN i p c) = show p ++ ", " ++ show c
270 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
271 show (MethodN m) = "method " ++ show m
272 show (ParentN p c) = show p ++ "#" ++ c
273 show (CaseN n) = "case block in " ++ show n
274 show (ElimN n) = "<<" ++ show n ++ " eliminator>>"
276-- Show a name in a way decorated for code generation, not human reading
277showCG :: Name -> String
278showCG (UN n) = n
279showCG (NS n s) = showSep "." (reverse s) ++ "." ++ showCG n
280showCG (MN _ "underscore") = "_"
281showCG (MN i s) = "{" ++ s ++ show i ++ "}"
282showCG (SN s) = showCG' s
283 where showCG' (WhereN i p c) = showCG p ++ ":" ++ showCG c ++ ":" ++ show i
284 showCG' (InstanceN cl inst) = '@':showCG cl ++ '$':showSep ":" inst
285 showCG' (MethodN m) = '!':showCG m
286 showCG' (ParentN p c) = showCG p ++ "#" ++ show c
287 showCG' (CaseN c) = showCG c ++ "_case"
288 showCG' (ElimN sn) = showCG sn ++ "_elim"
289showCG NErased = "_"
292-- |Contexts allow us to map names to things. A root name maps to a collection
293-- of things in different namespaces with that name.
294type Ctxt a = Map.Map Name (Map.Map Name a)
295emptyContext = Map.empty
297tcname (UN ('@':_)) = True
298tcname (NS n _) = tcname n
299tcname (SN (InstanceN _ _)) = True
300tcname (SN (MethodN _)) = True
301tcname (SN (ParentN _ _)) = True
302tcname _ = False
304implicitable (NS n _) = implicitable n
305implicitable (UN (x:xs)) = isLower x
306implicitable (MN _ _) = True
307implicitable _ = False
309nsroot (NS n _) = n
310nsroot n = n
312addDef :: Name -> a -> Ctxt a -> Ctxt a
313addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
314 Nothing -> Map.insert (nsroot n)
315 (Map.insert n v Map.empty) ctxt
316 Just xs -> Map.insert (nsroot n)
317 (Map.insert n v xs) ctxt
319{-| Look up a name in the context, given an optional namespace.
320 The name (n) may itself have a (partial) namespace given.
322 Rules for resolution:
324 - if an explicit namespace is given, return the names which match it. If none
325 match, return all names.
327 - if the name has has explicit namespace given, return the names which match it
328 and ignore the given namespace.
330 - otherwise, return all names.
332-}
334lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
335lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
336 Just xs -> filterNS (Map.toList xs)
337 Nothing -> []
338 where
339 filterNS [] = []
340 filterNS ((found, v) : xs)
341 | nsmatch n found = (found, v) : filterNS xs
342 | otherwise = filterNS xs
344 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
345 nsmatch (NS _ _) _ = False
346 nsmatch looking found = True
348lookupCtxt :: Name -> Ctxt a -> [a]
349lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
351lookupCtxtExact :: Name -> Ctxt a -> [a]
352lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
354updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
355updateDef n f ctxt
356 = let ds = lookupCtxtName n ctxt in
357 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
359toAlist :: Ctxt a -> [(Name, a)]
360toAlist ctxt = let allns = map snd (Map.toList ctxt) in
361 concat (map (Map.toList) allns)
363addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
364addAlist [] ctxt = ctxt
365addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
367data NativeTy = IT8 | IT16 | IT32 | IT64
368 deriving (Show, Eq, Ord, Enum)
370instance Pretty NativeTy where
371 pretty IT8 = text "Bits8"
372 pretty IT16 = text "Bits16"
373 pretty IT32 = text "Bits32"
374 pretty IT64 = text "Bits64"
376data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
377 | ITVec NativeTy Int
378 deriving (Show, Eq, Ord)
380data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
381 deriving (Show, Eq, Ord)
382{-!
383deriving instance NFData IntTy
384deriving instance NFData NativeTy
385deriving instance NFData ArithTy
386!-}
388instance Pretty ArithTy where
389 pretty (ATInt ITNative) = text "Int"
390 pretty (ATInt ITBig) = text "BigInt"
391 pretty (ATInt ITChar) = text "Char"
392 pretty (ATInt (ITFixed n)) = pretty n
393 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
394 pretty ATFloat = text "Float"
396nativeTyWidth :: NativeTy -> Int
397nativeTyWidth IT8 = 8
398nativeTyWidth IT16 = 16
399nativeTyWidth IT32 = 32
400nativeTyWidth IT64 = 64
402{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
403intTyWidth :: IntTy -> Int
404intTyWidth (ITFixed n) = nativeTyWidth n
405intTyWidth ITNative = 8 * sizeOf (0 :: Int)
406intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
407intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
409data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
410 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
411 | B8V (Vector Word8) | B16V (Vector Word16)
412 | B32V (Vector Word32) | B64V (Vector Word64)
413 | AType ArithTy | StrType
414 | PtrType | VoidType | Forgot
415 deriving (Eq, Ord)
416{-!
417deriving instance Binary Const
418deriving instance NFData Const
419!-}
421instance Sized Const where
422 size _ = 1
424instance Pretty Const where
425 pretty (I i) = text . show $ i
426 pretty (BI i) = text . show $ i
427 pretty (Fl f) = text . show $ f
428 pretty (Ch c) = text . show $ c
429 pretty (Str s) = text s
430 pretty (AType a) = pretty a
431 pretty StrType = text "String"
432 pretty PtrType = text "Ptr"
433 pretty VoidType = text "Void"
434 pretty Forgot = text "Forgot"
435 pretty (B8 w) = text . show $ w
436 pretty (B16 w) = text . show $ w
437 pretty (B32 w) = text . show $ w
438 pretty (B64 w) = text . show $ w
440data Raw = Var Name
441 | RBind Name (Binder Raw) Raw
442 | RApp Raw Raw
443 | RType
444 | RForce Raw
445 | RConstant Const
446 deriving (Show, Eq)
448instance Sized Raw where
449 size (Var name) = 1
450 size (RBind name bind right) = 1 + size bind + size right
451 size (RApp left right) = 1 + size left + size right
452 size RType = 1
453 size (RForce raw) = 1 + size raw
454 size (RConstant const) = size const
456instance Pretty Raw where
457 pretty = text . show
459{-!
460deriving instance Binary Raw
461deriving instance NFData Raw
462!-}
464-- | All binding forms are represented in a unform fashion.
465data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
466 | Pi { binderTy :: b }
467 | Let { binderTy :: b,
468 binderVal :: b {-^ value for bound variable-}}
469 | NLet { binderTy :: b,
470 binderVal :: b }
471 | Hole { binderTy :: b}
472 | GHole { envlen :: Int,
473 binderTy :: b}
474 | Guess { binderTy :: b,
475 binderVal :: b }
476 | PVar { binderTy :: b }
477 | PVTy { binderTy :: b }
478 deriving (Show, Eq, Ord, Functor)
479{-!
480deriving instance Binary Binder
481deriving instance NFData Binder
482!-}
484instance Sized a => Sized (Binder a) where
485 size (Lam ty) = 1 + size ty
486 size (Pi ty) = 1 + size ty
487 size (Let ty val) = 1 + size ty + size val
488 size (NLet ty val) = 1 + size ty + size val
489 size (Hole ty) = 1 + size ty
490 size (GHole _ ty) = 1 + size ty
491 size (Guess ty val) = 1 + size ty + size val
492 size (PVar ty) = 1 + size ty
493 size (PVTy ty) = 1 + size ty
495fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
496fmapMB f (Let t v) = liftM2 Let (f t) (f v)
497fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
498fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
499fmapMB f (Lam t) = liftM Lam (f t)
500fmapMB f (Pi t) = liftM Pi (f t)
501fmapMB f (Hole t) = liftM Hole (f t)
502fmapMB f (GHole i t) = liftM (GHole i) (f t)
503fmapMB f (PVar t) = liftM PVar (f t)
504fmapMB f (PVTy t) = liftM PVTy (f t)
506raw_apply :: Raw -> [Raw] -> Raw
507raw_apply f [] = f
508raw_apply f (a : as) = raw_apply (RApp f a) as
510raw_unapply :: Raw -> (Raw, [Raw])
511raw_unapply t = ua [] t where
512 ua args (RApp f a) = ua (a:args) f
513 ua args t = (t, args)
515data RawFun = RawFun { rtype :: Raw,
516 rval :: Raw
517 }
518 deriving Show
520data RawDatatype = RDatatype Name Raw [(Name, Raw)]
521 deriving Show
523data RDef = RFunction RawFun
524 | RConst Raw
525 | RData RawDatatype
526 deriving Show
528type RProgram = [(Name, RDef)]
530-- WELL TYPED TERMS ---------------------------------------------------------
532-- | Universe expressions for universe checking
533data UExp = UVar Int -- ^ universe variable
534 | UVal Int -- ^ explicit universe level
535 deriving (Eq, Ord)
536{-!
537deriving instance NFData UExp
538!-}
540instance Sized UExp where
541 size _ = 1
543-- We assume that universe levels have been checked, so anything external
544-- can just have the same universe variable and we won't get any new
545-- cycles.
547instance Binary UExp where
548 put x = return ()
549 get = return (UVar (-1))
551instance Show UExp where
552 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
553 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
554 show (UVal x) = show x
555-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
557-- | Universe constraints
558data UConstraint = ULT UExp UExp -- ^ Strictly less than
559 | ULE UExp UExp -- ^ Less than or equal to
560 deriving Eq
562instance Show UConstraint where
563 show (ULT x y) = show x ++ " < " ++ show y
564 show (ULE x y) = show x ++ " <= " ++ show y
566type UCs = (Int, [UConstraint])
568data NameType = Bound
569 | Ref
570 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
571 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
572 deriving (Show, Ord)
573{-!
574deriving instance Binary NameType
575deriving instance NFData NameType
576!-}
578instance Sized NameType where
579 size _ = 1
581instance Pretty NameType where
582 pretty = text . show
584instance Eq NameType where
585 Bound == Bound = True
586 Ref == Ref = True
587 DCon _ a == DCon _ b = (a == b) -- ignore tag
588 TCon _ a == TCon _ b = (a == b) -- ignore tag
589 _ == _ = False
591-- | Terms in the core language
592data TT n = P NameType n (TT n) -- ^ named references
593 | V Int -- ^ a resolved de Bruijn-indexed variable
594 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
595 | App (TT n) (TT n) -- ^ function, function type, arg
596 | Constant Const -- ^ constant
597 | Proj (TT n) Int -- ^ argument projection; runtime only
598 -- (-1) is a special case for 'subtract one from BI'
599 | Erased -- ^ an erased term
600 | Impossible -- ^ special case for totality checking
601 | TType UExp -- ^ the type of types at some level
602 deriving (Ord, Functor)
603{-!
604deriving instance Binary TT
605deriving instance NFData TT
606!-}
608class TermSize a where
609 termsize :: Name -> a -> Int
611instance TermSize a => TermSize [a] where
612 termsize n [] = 0
613 termsize n (x : xs) = termsize n x + termsize n xs
615instance TermSize (TT Name) where
616 termsize n (P _ x _)
617 | x == n = 1000000 -- recursive => really big
618 | otherwise = 1
619 termsize n (V _) = 1
620 termsize n (Bind n' (Let t v) sc)
621 = let rn = if n == n' then MN 0 "noname" else n in
622 termsize rn v + termsize rn sc
623 termsize n (Bind n' b sc)
624 = let rn = if n == n' then MN 0 "noname" else n in
625 termsize rn sc
626 termsize n (App f a) = termsize n f + termsize n a
627 termsize n (Proj t i) = termsize n t
628 termsize n _ = 1
630instance Sized a => Sized (TT a) where
631 size (P name n trm) = 1 + size name + size n + size trm
632 size (V v) = 1
633 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
634 size (App l r) = 1 + size l + size r
635 size (Constant c) = size c
636 size Erased = 1
637 size (TType u) = 1 + size u
639instance Pretty a => Pretty (TT a) where
640 pretty _ = text "test"
642type EnvTT n = [(n, Binder (TT n))]
644data Datatype n = Data { d_typename :: n,
645 d_typetag :: Int,
646 d_type :: (TT n),
647 d_cons :: [(n, TT n)] }
648 deriving (Show, Functor, Eq)
650instance Eq n => Eq (TT n) where
651 (==) (P xt x _) (P yt y _) = x == y
652 (==) (V x) (V y) = x == y
653 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
654 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
655 (==) (TType _) (TType _) = True -- deal with constraints later
656 (==) (Constant x) (Constant y) = x == y
657 (==) (Proj x i) (Proj y j) = x == y && i == j
658 (==) Erased _ = True
659 (==) _ Erased = True
660 (==) _ _ = False
662-- * A few handy operations on well typed terms:
664-- | A term is injective iff it is a data constructor, type constructor,
665-- constant, the type Type, pi-binding, or an application of an injective
666-- term.
667isInjective :: TT n -> Bool
668isInjective (P (DCon _ _) _ _) = True
669isInjective (P (TCon _ _) _ _) = True
670isInjective (Constant _) = True
671isInjective (TType x) = True
672isInjective (Bind _ (Pi _) sc) = True
673isInjective (App f a) = isInjective f
674isInjective _ = False
676-- | Count the number of instances of a de Bruijn index in a term
677vinstances :: Int -> TT n -> Int
678vinstances i (V x) | i == x = 1
679vinstances i (App f a) = vinstances i f + vinstances i a
680vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
681 where instancesB (Let t v) = vinstances i v
682 instancesB _ = 0
683vinstances i t = 0
685instantiate :: TT n -> TT n -> TT n
686instantiate e = subst 0 where
687 subst i (V x) | i == x = e
688 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
689 subst i (App f a) = App (subst i f) (subst i a)
690 subst i (Proj x idx) = Proj (subst i x) idx
691 subst i t = t
693substV :: TT n -> TT n -> TT n
694substV x tm = dropV 0 (instantiate x tm) where
695 dropV i (V x) | x > i = V (x - 1)
696 | otherwise = V x
697 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
698 dropV i (App f a) = App (dropV i f) (dropV i a)
699 dropV i (Proj x idx) = Proj (dropV i x) idx
700 dropV i t = t
702explicitNames :: TT n -> TT n
703explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
704 Bind x b'
705 (explicitNames (instantiate
706 (P Bound x (binderTy b')) sc))
707explicitNames (App f a) = App (explicitNames f) (explicitNames a)
708explicitNames (Proj x idx) = Proj (explicitNames x) idx
709explicitNames t = t
711pToV :: Eq n => n -> TT n -> TT n
712pToV n = pToV' n 0
713pToV' n i (P _ x _) | n == x = V i
714pToV' n i (Bind x b sc)
715-- We can assume the inner scope has been pToVed already, so continue to
716-- resolve names from the *outer* scope which may happen to have the same id.
717 | n == x = Bind x (fmap (pToV' n i) b) sc
718 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
719pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
720pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
721pToV' n i t = t
723-- increase de Bruijn indices, as if a binder has been added
724addBinder :: TT n -> TT n
725addBinder t = ab 0 t
726 where
727 ab top (V i) | i >= top = V (i + 1)
728 | otherwise = V i
729 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
730 ab top (App f a) = App (ab top f) (ab top a)
731 ab top (Proj t idx) = Proj (ab top t) idx
732 ab top t = t
734-- | Convert several names. First in the list comes out as V 0
735pToVs :: Eq n => [n] -> TT n -> TT n
736pToVs ns tm = pToVs' ns tm 0 where
737 pToVs' [] tm i = tm
738 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
740vToP :: TT n -> TT n
741vToP = vToP' [] where
742 vToP' env (V i) = let (n, b) = (env !! i) in
743 P Bound n (binderTy b)
744 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
745 Bind n b' (vToP' ((n, b'):env) sc)
746 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
747 vToP' env t = t
749finalise :: Eq n => TT n -> TT n
750finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
751finalise (App f a) = App (finalise f) (finalise a)
752finalise t = t
754subst :: Eq n => n -> TT n -> TT n -> TT n
755subst n v tm = instantiate v (pToV n tm)
757substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
758substNames [] t = t
759substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
761substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
762substTerm old new = st where
763 st t | t == old = new
764 st (App f a) = App (st f) (st a)
765 st (Bind x b sc) = Bind x (fmap st b) (st sc)
766 st t = t
768-- Returns true if V 0 and bound name n do not occur in the term
770noOccurrence :: Eq n => n -> TT n -> Bool
771noOccurrence n t = no' 0 t
772 where
773 no' i (V x) = not (i == x)
774 no' i (P Bound x _) = not (n == x)
775 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
776 where noB' i (Let t v) = no' i t && no' i v
777 noB' i (Guess t v) = no' i t && no' i v
778 noB' i b = no' i (binderTy b)
779 no' i (App f a) = no' i f && no' i a
780 no' i (Proj x _) = no' i x
781 no' i _ = True
783-- | Returns all names used free in the term
784freeNames :: Eq n => TT n -> [n]
785freeNames (P _ n _) = [n]
786freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
787 ++ freeNames t
788freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
789freeNames (App f a) = nub $ freeNames f ++ freeNames a
790freeNames (Proj x i) = nub $ freeNames x
791freeNames _ = []
793-- | Return the arity of a (normalised) type
794arity :: TT n -> Int
795arity (Bind n (Pi t) sc) = 1 + arity sc
796arity _ = 0
798-- | Deconstruct an application; returns the function and a list of arguments
799unApply :: TT n -> (TT n, [TT n])
800unApply t = ua [] t where
801 ua args (App f a) = ua (a:args) f
802 ua args t = (t, args)
804mkApp :: TT n -> [TT n] -> TT n
805mkApp f [] = f
806mkApp f (a:as) = mkApp (App f a) as
808forget :: TT Name -> Raw
809forget tm = fe [] tm
810 where
811 fe env (P _ n _) = Var n
812 fe env (V i) = Var (env !! i)
813 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
814 (fe (n:env) sc)
815 fe env (App f a) = RApp (fe env f) (fe env a)
816 fe env (Constant c)
817 = RConstant c
818 fe env (TType i) = RType
819 fe env Erased = RConstant Forgot
821bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
822bindAll [] t =t
823bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
825bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
826bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
828getArgTys :: TT n -> [(n, TT n)]
829getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
830getArgTys _ = []
832getRetTy :: TT n -> TT n
833getRetTy (Bind n (PVar _) sc) = getRetTy sc
834getRetTy (Bind n (PVTy _) sc) = getRetTy sc
835getRetTy (Bind n (Pi _) sc) = getRetTy sc
836getRetTy sc = sc
838uniqueNameFrom :: [Name] -> [Name] -> Name
839uniqueNameFrom (s : supply) hs
840 | s `elem` hs = uniqueNameFrom supply hs
841 | otherwise = s
843uniqueName :: Name -> [Name] -> Name
844uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
845 | otherwise = n
847uniqueBinders :: [Name] -> TT Name -> TT Name
848uniqueBinders ns (Bind n b sc)
849 = let n' = uniqueName n ns in
850 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
851uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
852uniqueBinders ns t = t
855nextName (NS x s) = NS (nextName x) s
856nextName (MN i n) = MN (i+1) n
857nextName (UN x) = let (num', nm') = span isDigit (reverse x)
858 nm = reverse nm'
859 num = readN (reverse num') in
860 UN (nm ++ show (num+1))
861 where
862 readN "" = 0
863 readN x = read x
864nextName (SN x) = SN (nextName' x)
865 where
866 nextName' (WhereN i f x) = WhereN i f (nextName x)
867 nextName' (CaseN n) = CaseN (nextName n)
868 nextName' (MethodN n) = MethodN (nextName n)
870type Term = TT Name
871type Type = Term
873type Env = EnvTT Name
875-- an environment with de Bruijn indices 'normalised' so that they all refer to
876-- this environment
878newtype WkEnvTT n = Wk (EnvTT n)
879type WkEnv = WkEnvTT Name
881instance (Eq n, Show n) => Show (TT n) where
882 show t = showEnv [] t
884itBitsName IT8 = "Bits8"
885itBitsName IT16 = "Bits16"
886itBitsName IT32 = "Bits32"
887itBitsName IT64 = "Bits64"
889instance Show Const where
890 show (I i) = show i
891 show (BI i) = show i
892 show (Fl f) = show f
893 show (Ch c) = show c
894 show (Str s) = show s
895 show (B8 x) = show x
896 show (B16 x) = show x
897 show (B32 x) = show x
898 show (B64 x) = show x
899 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
900 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
901 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
902 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
903 show (AType ATFloat) = "Float"
904 show (AType (ATInt ITBig)) = "Integer"
905 show (AType (ATInt ITNative)) = "Int"
906 show (AType (ATInt ITChar)) = "Char"
907 show (AType (ATInt (ITFixed it))) = itBitsName it
908 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
909 show StrType = "String"
910 show PtrType = "Ptr"
911 show VoidType = "Void"
913showEnv env t = showEnv' env t False
914showEnvDbg env t = showEnv' env t True
916prettyEnv env t = prettyEnv' env t False
917 where
918 prettyEnv' env t dbg = prettySe 10 env t dbg
920 bracket outer inner p
921 | inner > outer = lparen <> p <> rparen
922 | otherwise = p
924 prettySe p env (P nt n t) debug =
925 pretty n <+>
926 if debug then
927 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
928 else
929 empty
930 prettySe p env (V i) debug
931 | i < length env =
932 if debug then
933 text . show . fst $ env!!i
934 else
935 lbrack <+> text (show i) <+> rbrack
936 | otherwise = text "unbound" <+> text (show i) <+> text "!"
937 prettySe p env (Bind n b@(Pi t) sc) debug
938 | noOccurrence n sc && not debug =
939 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
940 prettySe p env (Bind n b sc) debug =
941 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
942 prettySe p env (App f a) debug =
943 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
944 prettySe p env (Proj x i) debug =
945 prettySe 1 env x debug <+> text ("!" ++ show i)
946 prettySe p env (Constant c) debug = pretty c
947 prettySe p env Erased debug = text "[_]"
948 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
950 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
951 prettySb env n (Hole t) = prettyB env "?defer" "." n t
952 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
953 prettySb env n (PVar t) = prettyB env "pat" "." n t
954 prettySb env n (PVTy t) = prettyB env "pty" "." n t
955 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
956 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
958 prettyB env op sc n t debug =
959 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
961 prettyBv env op sc n t v debug =
962 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
963 prettySe 10 env v debug <> text sc
966showEnv' env t dbg = se 10 env t where
967 se p env (P nt n t) = show n
968 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
969 se p env (V i) | i < length env && i >= 0
970 = (show $ fst $ env!!i) ++
971 if dbg then "{" ++ show i ++ "}" else ""
972 | otherwise = "!!V " ++ show i ++ "!!"
973 se p env (Bind n b@(Pi t) sc)
974 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
975 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
976 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
977 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
978 se p env (Constant c) = show c
979 se p env Erased = "[__]"
980 se p env Impossible = "[impossible]"
981 se p env (TType i) = "Type " ++ show i
983 sb env n (Lam t) = showb env "\\ " " => " n t
984 sb env n (Hole t) = showb env "? " ". " n t
985 sb env n (GHole i t) = showb env "?defer " ". " n t
986 sb env n (Pi t) = showb env "(" ") -> " n t
987 sb env n (PVar t) = showb env "pat " ". " n t
988 sb env n (PVTy t) = showb env "pty " ". " n t
989 sb env n (Let t v) = showbv env "let " " in " n t v
990 sb env n (Guess t v) = showbv env "?? " " in " n t v
992 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
993 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
994 se 10 env v ++ sc
996 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
997 | otherwise = str
999-- | Check whether a term has any holes in it - impure if so
1000pureTerm :: TT Name -> Bool
1001pureTerm (App f a) = pureTerm f && pureTerm a
1002pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
1003 pureBinder (Hole _) = False
1004 pureBinder (Guess _ _) = False
1005 pureBinder (Let t v) = pureTerm t && pureTerm v
1006 pureBinder t = pureTerm (binderTy t)
1008 notClassName (MN _ "class") = False
1009 notClassName _ = True
1011pureTerm _ = True
1013-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1014weakenTm :: Int -> TT n -> TT n
1015weakenTm i t = wk i 0 t
1016 where wk i min (V x) | x >= min = V (i + x)
1017 wk i m (App f a) = App (wk i m f) (wk i m a)
1018 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1019 wk i m t = t
1020 wkb i m t = fmap (wk i m) t
1022-- | Weaken an environment so that all the de Bruijn indices are correct according
1023-- to the latest bound variable
1025weakenEnv :: EnvTT n -> EnvTT n
1026weakenEnv env = wk (length env - 1) env
1027 where wk i [] = []
1028 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1029 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1030 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1031 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1033weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1034weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1036orderPats :: Term -> Term
1037orderPats tm = op [] tm
1038 where
1039 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1040 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1041 op ps sc = bindAll (sortP ps) sc
1043 sortP ps = pick [] (reverse ps)
1045 namesIn (P _ n _) = [n]
1046 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
1047 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
1048 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
1049 nb t = namesIn (binderTy t)
1050 namesIn (App f a) = nub (namesIn f ++ namesIn a)
1051 namesIn _ = []
1053 pick acc [] = reverse acc
1054 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1056 insert n t [] = [(n, t)]
1057 insert n t ((n',t') : ps)
1058 | n `elem` (namesIn (binderTy t') ++
1059 concatMap namesIn (map (binderTy . snd) ps))
1060 = (n', t') : insert n t ps
1061 | otherwise = (n,t):(n',t'):ps