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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 | CantIntroduce Term
89 | NoSuchVariable Name
90 | NoTypeDecl Name
91 | NotInjective Term Term Term
92 | CantResolve Term
93 | CantResolveAlts [String]
94 | IncompleteTerm Term
95 | UniverseError
96 | ProgramLineComment
97 | Inaccessible Name
98 | NonCollapsiblePostulate Name
99 | AlreadyDefined Name
100 | ProofSearchFail Err
101 | NoRewriting Term
102 | At FC Err
103 | Elaborating String Name Err
104 | ProviderError String
105 | LoadingFailed String Err
106 deriving Eq
107{-!
108deriving instance NFData Err
109!-}
111instance Sized Err where
112 size (Msg msg) = length msg
113 size (InternalMsg msg) = length msg
114 size (CantUnify _ left right err _ score) = size left + size right + size err
115 size (InfiniteUnify _ right _) = size right
116 size (CantConvert left right _) = size left + size right
117 size (UnifyScope _ _ right _) = size right
118 size (NoSuchVariable name) = size name
119 size (NoTypeDecl name) = size name
120 size (NotInjective l c r) = size l + size c + size r
121 size (CantResolve trm) = size trm
122 size (NoRewriting trm) = size trm
123 size (CantResolveAlts _) = 1
124 size (IncompleteTerm trm) = size trm
125 size UniverseError = 1
126 size ProgramLineComment = 1
127 size (At fc err) = size fc + size err
128 size (Elaborating _ n err) = size err
129 size (ProviderError msg) = length msg
130 size (LoadingFailed fn e) = 1 + length fn + size e
131 size _ = 1
133score :: Err -> Int
134score (CantUnify _ _ _ m _ s) = s + score m
135score (CantResolve _) = 20
136score (NoSuchVariable _) = 1000
137score (ProofSearchFail _) = 10000
138score (InternalMsg _) = -1
139score _ = 0
141instance Show Err where
142 show (Msg s) = s
143 show (InternalMsg s) = "Internal error: " ++ show s
144 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
145 ++ show e ++ " in " ++ show sc ++ " " ++ show i
146 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
147 show (ProviderError msg) = "Type provider error: " ++ msg
148 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: " ++ show e
149 show _ = "Error"
151instance Pretty Err where
152 pretty (Msg m) = text m
153 pretty (CantUnify _ l r e _ i) =
154 if size l + size r > breakingSize then
155 text "Cannot unify" <+> colon $$
156 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
157 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
158 else
159 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
160 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
161 pretty (ProviderError msg) = text msg
162 pretty err@(LoadingFailed _ _) = text (show err)
163 pretty _ = text "Error"
165instance Error Err where
166 strMsg = Msg
168data TC a = OK a
169 | Error Err
170 deriving (Eq, Functor)
172instance Pretty a => Pretty (TC a) where
173 pretty (OK ok) = pretty ok
174 pretty (Error err) =
175 if size err > breakingSize then
176 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
177 else
178 text "Error" <+> colon <+> pretty err
180instance Show a => Show (TC a) where
181 show (OK x) = show x
182 show (Error str) = "Error: " ++ show str
184-- at some point, this instance should also carry type checking options
185-- (e.g. Type:Type)
187instance Monad TC where
188 return = OK
189 x >>= k = case x of
190 OK v -> k v
191 Error e -> Error e
192 fail e = Error (InternalMsg e)
194tfail :: Err -> TC a
195tfail e = Error e
197trun :: FC -> TC a -> TC a
198trun fc (OK a) = OK a
199trun fc (Error e) = Error (At fc e)
201instance MonadPlus TC where
202 mzero = fail "Unknown error"
203 (OK x) `mplus` _ = OK x
204 _ `mplus` (OK y) = OK y
205 err `mplus` _ = err
207discard :: Monad m => m a -> m ()
208discard f = f >> return ()
210showSep :: String -> [String] -> String
211showSep sep [] = ""
212showSep sep [x] = x
213showSep sep (x:xs) = x ++ sep ++ showSep sep xs
215pmap f (x, y) = (f x, f y)
217traceWhen True msg a = trace msg a
218traceWhen False _ a = a
220-- RAW TERMS ----------------------------------------------------------------
222-- | Names are hierarchies of strings, describing scope (so no danger of
223-- duplicate names, but need to be careful on lookup).
224data Name = UN String -- ^ User-provided name
225 | NS Name [String] -- ^ Root, namespaces
226 | MN Int String -- ^ Machine chosen names
227 | NErased -- ^ Name of somethng which is never used in scope
228 | SN SpecialName -- ^ Decorated function names
229 deriving (Eq, Ord)
230{-!
231deriving instance Binary Name
232deriving instance NFData Name
233!-}
235data SpecialName = WhereN Int Name Name
236 | InstanceN Name [String]
237 | ParentN Name String
238 | MethodN Name
239 | CaseN Name
240 | ElimN Name
241 deriving (Eq, Ord)
242{-!
243deriving instance Binary SpecialName
244deriving instance NFData SpecialName
245!-}
247instance Sized Name where
248 size (UN n) = 1
249 size (NS n els) = 1 + length els
250 size (MN i n) = 1
251 size _ = 1
253instance Pretty Name where
254 pretty (UN n) = text n
255 pretty (NS n s) = pretty n
256 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
257 pretty (SN s) = text (show s)
259instance Show Name where
260 show (UN n) = n
261 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
262 show (MN _ "underscore") = "_"
263 show (MN i s) = "{" ++ s ++ show i ++ "}"
264 show (SN s) = show s
265 show NErased = "_"
267instance Show SpecialName where
268 show (WhereN i p c) = show p ++ ", " ++ show c
269 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
270 show (MethodN m) = "method " ++ show m
271 show (ParentN p c) = show p ++ "#" ++ c
272 show (CaseN n) = "case block in " ++ show n
273 show (ElimN n) = "<<" ++ show n ++ " eliminator>>"
275-- Show a name in a way decorated for code generation, not human reading
276showCG :: Name -> String
277showCG (UN n) = n
278showCG (NS n s) = showSep "." (reverse s) ++ "." ++ showCG n
279showCG (MN _ "underscore") = "_"
280showCG (MN i s) = "{" ++ s ++ show i ++ "}"
281showCG (SN s) = showCG' s
282 where showCG' (WhereN i p c) = showCG p ++ ":" ++ showCG c ++ ":" ++ show i
283 showCG' (InstanceN cl inst) = '@':showCG cl ++ '$':showSep ":" inst
284 showCG' (MethodN m) = '!':showCG m
285 showCG' (ParentN p c) = showCG p ++ "#" ++ show c
286 showCG' (CaseN c) = showCG c ++ "_case"
287showCG NErased = "_"
290-- |Contexts allow us to map names to things. A root name maps to a collection
291-- of things in different namespaces with that name.
292type Ctxt a = Map.Map Name (Map.Map Name a)
293emptyContext = Map.empty
295tcname (UN ('@':_)) = True
296tcname (NS n _) = tcname n
297tcname (SN (InstanceN _ _)) = True
298tcname (SN (MethodN _)) = True
299tcname (SN (ParentN _ _)) = True
300tcname _ = False
302implicitable (NS n _) = implicitable n
303implicitable (UN (x:xs)) = isLower x
304implicitable (MN _ _) = True
305implicitable _ = False
307nsroot (NS n _) = n
308nsroot n = n
310addDef :: Name -> a -> Ctxt a -> Ctxt a
311addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
312 Nothing -> Map.insert (nsroot n)
313 (Map.insert n v Map.empty) ctxt
314 Just xs -> Map.insert (nsroot n)
315 (Map.insert n v xs) ctxt
317{-| Look up a name in the context, given an optional namespace.
318 The name (n) may itself have a (partial) namespace given.
320 Rules for resolution:
322 - if an explicit namespace is given, return the names which match it. If none
323 match, return all names.
325 - if the name has has explicit namespace given, return the names which match it
326 and ignore the given namespace.
328 - otherwise, return all names.
330-}
332lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
333lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
334 Just xs -> filterNS (Map.toList xs)
335 Nothing -> []
336 where
337 filterNS [] = []
338 filterNS ((found, v) : xs)
339 | nsmatch n found = (found, v) : filterNS xs
340 | otherwise = filterNS xs
342 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
343 nsmatch (NS _ _) _ = False
344 nsmatch looking found = True
346lookupCtxt :: Name -> Ctxt a -> [a]
347lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
349lookupCtxtExact :: Name -> Ctxt a -> [a]
350lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
352updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
353updateDef n f ctxt
354 = let ds = lookupCtxtName n ctxt in
355 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
357toAlist :: Ctxt a -> [(Name, a)]
358toAlist ctxt = let allns = map snd (Map.toList ctxt) in
359 concat (map (Map.toList) allns)
361addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
362addAlist [] ctxt = ctxt
363addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
365data NativeTy = IT8 | IT16 | IT32 | IT64
366 deriving (Show, Eq, Ord, Enum)
368instance Pretty NativeTy where
369 pretty IT8 = text "Bits8"
370 pretty IT16 = text "Bits16"
371 pretty IT32 = text "Bits32"
372 pretty IT64 = text "Bits64"
374data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
375 | ITVec NativeTy Int
376 deriving (Show, Eq, Ord)
378data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
379 deriving (Show, Eq, Ord)
380{-!
381deriving instance NFData IntTy
382deriving instance NFData NativeTy
383deriving instance NFData ArithTy
384!-}
386instance Pretty ArithTy where
387 pretty (ATInt ITNative) = text "Int"
388 pretty (ATInt ITBig) = text "BigInt"
389 pretty (ATInt ITChar) = text "Char"
390 pretty (ATInt (ITFixed n)) = pretty n
391 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
392 pretty ATFloat = text "Float"
394nativeTyWidth :: NativeTy -> Int
395nativeTyWidth IT8 = 8
396nativeTyWidth IT16 = 16
397nativeTyWidth IT32 = 32
398nativeTyWidth IT64 = 64
400{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
401intTyWidth :: IntTy -> Int
402intTyWidth (ITFixed n) = nativeTyWidth n
403intTyWidth ITNative = 8 * sizeOf (0 :: Int)
404intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
405intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
407data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
408 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
409 | B8V (Vector Word8) | B16V (Vector Word16)
410 | B32V (Vector Word32) | B64V (Vector Word64)
411 | AType ArithTy | StrType
412 | PtrType | VoidType | Forgot
413 deriving (Eq, Ord)
414{-!
415deriving instance Binary Const
416deriving instance NFData Const
417!-}
419instance Sized Const where
420 size _ = 1
422instance Pretty Const where
423 pretty (I i) = text . show $ i
424 pretty (BI i) = text . show $ i
425 pretty (Fl f) = text . show $ f
426 pretty (Ch c) = text . show $ c
427 pretty (Str s) = text s
428 pretty (AType a) = pretty a
429 pretty StrType = text "String"
430 pretty PtrType = text "Ptr"
431 pretty VoidType = text "Void"
432 pretty Forgot = text "Forgot"
433 pretty (B8 w) = text . show $ w
434 pretty (B16 w) = text . show $ w
435 pretty (B32 w) = text . show $ w
436 pretty (B64 w) = text . show $ w
438data Raw = Var Name
439 | RBind Name (Binder Raw) Raw
440 | RApp Raw Raw
441 | RType
442 | RForce Raw
443 | RConstant Const
444 deriving (Show, Eq)
446instance Sized Raw where
447 size (Var name) = 1
448 size (RBind name bind right) = 1 + size bind + size right
449 size (RApp left right) = 1 + size left + size right
450 size RType = 1
451 size (RForce raw) = 1 + size raw
452 size (RConstant const) = size const
454instance Pretty Raw where
455 pretty = text . show
457{-!
458deriving instance Binary Raw
459deriving instance NFData Raw
460!-}
462-- | All binding forms are represented in a unform fashion.
463data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
464 | Pi { binderTy :: b }
465 | Let { binderTy :: b,
466 binderVal :: b {-^ value for bound variable-}}
467 | NLet { binderTy :: b,
468 binderVal :: b }
469 | Hole { binderTy :: b}
470 | GHole { envlen :: Int,
471 binderTy :: b}
472 | Guess { binderTy :: b,
473 binderVal :: b }
474 | PVar { binderTy :: b }
475 | PVTy { binderTy :: b }
476 deriving (Show, Eq, Ord, Functor)
477{-!
478deriving instance Binary Binder
479deriving instance NFData Binder
480!-}
482instance Sized a => Sized (Binder a) where
483 size (Lam ty) = 1 + size ty
484 size (Pi ty) = 1 + size ty
485 size (Let ty val) = 1 + size ty + size val
486 size (NLet ty val) = 1 + size ty + size val
487 size (Hole ty) = 1 + size ty
488 size (GHole _ ty) = 1 + size ty
489 size (Guess ty val) = 1 + size ty + size val
490 size (PVar ty) = 1 + size ty
491 size (PVTy ty) = 1 + size ty
493fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
494fmapMB f (Let t v) = liftM2 Let (f t) (f v)
495fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
496fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
497fmapMB f (Lam t) = liftM Lam (f t)
498fmapMB f (Pi t) = liftM Pi (f t)
499fmapMB f (Hole t) = liftM Hole (f t)
500fmapMB f (GHole i t) = liftM (GHole i) (f t)
501fmapMB f (PVar t) = liftM PVar (f t)
502fmapMB f (PVTy t) = liftM PVTy (f t)
504raw_apply :: Raw -> [Raw] -> Raw
505raw_apply f [] = f
506raw_apply f (a : as) = raw_apply (RApp f a) as
508raw_unapply :: Raw -> (Raw, [Raw])
509raw_unapply t = ua [] t where
510 ua args (RApp f a) = ua (a:args) f
511 ua args t = (t, args)
513data RawFun = RawFun { rtype :: Raw,
514 rval :: Raw
515 }
516 deriving Show
518data RawDatatype = RDatatype Name Raw [(Name, Raw)]
519 deriving Show
521data RDef = RFunction RawFun
522 | RConst Raw
523 | RData RawDatatype
524 deriving Show
526type RProgram = [(Name, RDef)]
528-- WELL TYPED TERMS ---------------------------------------------------------
530-- | Universe expressions for universe checking
531data UExp = UVar Int -- ^ universe variable
532 | UVal Int -- ^ explicit universe level
533 deriving (Eq, Ord)
534{-!
535deriving instance NFData UExp
536!-}
538instance Sized UExp where
539 size _ = 1
541-- We assume that universe levels have been checked, so anything external
542-- can just have the same universe variable and we won't get any new
543-- cycles.
545instance Binary UExp where
546 put x = return ()
547 get = return (UVar (-1))
549instance Show UExp where
550 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
551 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
552 show (UVal x) = show x
553-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
555-- | Universe constraints
556data UConstraint = ULT UExp UExp -- ^ Strictly less than
557 | ULE UExp UExp -- ^ Less than or equal to
558 deriving Eq
560instance Show UConstraint where
561 show (ULT x y) = show x ++ " < " ++ show y
562 show (ULE x y) = show x ++ " <= " ++ show y
564type UCs = (Int, [UConstraint])
566data NameType = Bound
567 | Ref
568 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
569 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
570 deriving (Show, Ord)
571{-!
572deriving instance Binary NameType
573deriving instance NFData NameType
574!-}
576instance Sized NameType where
577 size _ = 1
579instance Pretty NameType where
580 pretty = text . show
582instance Eq NameType where
583 Bound == Bound = True
584 Ref == Ref = True
585 DCon _ a == DCon _ b = (a == b) -- ignore tag
586 TCon _ a == TCon _ b = (a == b) -- ignore tag
587 _ == _ = False
589-- | Terms in the core language
590data TT n = P NameType n (TT n) -- ^ named references
591 | V Int -- ^ a resolved de Bruijn-indexed variable
592 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
593 | App (TT n) (TT n) -- ^ function, function type, arg
594 | Constant Const -- ^ constant
595 | Proj (TT n) Int -- ^ argument projection; runtime only
596 -- (-1) is a special case for 'subtract one from BI'
597 | Erased -- ^ an erased term
598 | Impossible -- ^ special case for totality checking
599 | TType UExp -- ^ the type of types at some level
600 deriving (Ord, Functor)
601{-!
602deriving instance Binary TT
603deriving instance NFData TT
604!-}
606class TermSize a where
607 termsize :: Name -> a -> Int
609instance TermSize a => TermSize [a] where
610 termsize n [] = 0
611 termsize n (x : xs) = termsize n x + termsize n xs
613instance TermSize (TT Name) where
614 termsize n (P _ x _)
615 | x == n = 1000000 -- recursive => really big
616 | otherwise = 1
617 termsize n (V _) = 1
618 termsize n (Bind n' (Let t v) sc)
619 = let rn = if n == n' then MN 0 "noname" else n in
620 termsize rn v + termsize rn sc
621 termsize n (Bind n' b sc)
622 = let rn = if n == n' then MN 0 "noname" else n in
623 termsize rn sc
624 termsize n (App f a) = termsize n f + termsize n a
625 termsize n (Proj t i) = termsize n t
626 termsize n _ = 1
628instance Sized a => Sized (TT a) where
629 size (P name n trm) = 1 + size name + size n + size trm
630 size (V v) = 1
631 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
632 size (App l r) = 1 + size l + size r
633 size (Constant c) = size c
634 size Erased = 1
635 size (TType u) = 1 + size u
637instance Pretty a => Pretty (TT a) where
638 pretty _ = text "test"
640type EnvTT n = [(n, Binder (TT n))]
642data Datatype n = Data { d_typename :: n,
643 d_typetag :: Int,
644 d_type :: (TT n),
645 d_cons :: [(n, TT n)] }
646 deriving (Show, Functor, Eq)
648instance Eq n => Eq (TT n) where
649 (==) (P xt x _) (P yt y _) = x == y
650 (==) (V x) (V y) = x == y
651 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
652 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
653 (==) (TType _) (TType _) = True -- deal with constraints later
654 (==) (Constant x) (Constant y) = x == y
655 (==) (Proj x i) (Proj y j) = x == y && i == j
656 (==) Erased _ = True
657 (==) _ Erased = True
658 (==) _ _ = False
660-- * A few handy operations on well typed terms:
662-- | A term is injective iff it is a data constructor, type constructor,
663-- constant, the type Type, pi-binding, or an application of an injective
664-- term.
665isInjective :: TT n -> Bool
666isInjective (P (DCon _ _) _ _) = True
667isInjective (P (TCon _ _) _ _) = True
668isInjective (Constant _) = True
669isInjective (TType x) = True
670isInjective (Bind _ (Pi _) sc) = True
671isInjective (App f a) = isInjective f
672isInjective _ = False
674-- | Count the number of instances of a de Bruijn index in a term
675vinstances :: Int -> TT n -> Int
676vinstances i (V x) | i == x = 1
677vinstances i (App f a) = vinstances i f + vinstances i a
678vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
679 where instancesB (Let t v) = vinstances i v
680 instancesB _ = 0
681vinstances i t = 0
683instantiate :: TT n -> TT n -> TT n
684instantiate e = subst 0 where
685 subst i (V x) | i == x = e
686 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
687 subst i (App f a) = App (subst i f) (subst i a)
688 subst i (Proj x idx) = Proj (subst i x) idx
689 subst i t = t
691substV :: TT n -> TT n -> TT n
692substV x tm = dropV 0 (instantiate x tm) where
693 dropV i (V x) | x > i = V (x - 1)
694 | otherwise = V x
695 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
696 dropV i (App f a) = App (dropV i f) (dropV i a)
697 dropV i (Proj x idx) = Proj (dropV i x) idx
698 dropV i t = t
700explicitNames :: TT n -> TT n
701explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
702 Bind x b'
703 (explicitNames (instantiate
704 (P Bound x (binderTy b')) sc))
705explicitNames (App f a) = App (explicitNames f) (explicitNames a)
706explicitNames (Proj x idx) = Proj (explicitNames x) idx
707explicitNames t = t
709pToV :: Eq n => n -> TT n -> TT n
710pToV n = pToV' n 0
711pToV' n i (P _ x _) | n == x = V i
712pToV' n i (Bind x b sc)
713-- We can assume the inner scope has been pToVed already, so continue to
714-- resolve names from the *outer* scope which may happen to have the same id.
715 | n == x = Bind x (fmap (pToV' n i) b) sc
716 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
717pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
718pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
719pToV' n i t = t
721-- increase de Bruijn indices, as if a binder has been added
722addBinder :: TT n -> TT n
723addBinder t = ab 0 t
724 where
725 ab top (V i) | i >= top = V (i + 1)
726 | otherwise = V i
727 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
728 ab top (App f a) = App (ab top f) (ab top a)
729 ab top (Proj t idx) = Proj (ab top t) idx
730 ab top t = t
732-- | Convert several names. First in the list comes out as V 0
733pToVs :: Eq n => [n] -> TT n -> TT n
734pToVs ns tm = pToVs' ns tm 0 where
735 pToVs' [] tm i = tm
736 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
738vToP :: TT n -> TT n
739vToP = vToP' [] where
740 vToP' env (V i) = let (n, b) = (env !! i) in
741 P Bound n (binderTy b)
742 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
743 Bind n b' (vToP' ((n, b'):env) sc)
744 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
745 vToP' env t = t
747finalise :: Eq n => TT n -> TT n
748finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
749finalise (App f a) = App (finalise f) (finalise a)
750finalise t = t
752subst :: Eq n => n -> TT n -> TT n -> TT n
753subst n v tm = instantiate v (pToV n tm)
755substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
756substNames [] t = t
757substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
759substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
760substTerm old new = st where
761 st t | t == old = new
762 st (App f a) = App (st f) (st a)
763 st (Bind x b sc) = Bind x (fmap st b) (st sc)
764 st t = t
766-- Returns true if V 0 and bound name n do not occur in the term
768noOccurrence :: Eq n => n -> TT n -> Bool
769noOccurrence n t = no' 0 t
770 where
771 no' i (V x) = not (i == x)
772 no' i (P Bound x _) = not (n == x)
773 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
774 where noB' i (Let t v) = no' i t && no' i v
775 noB' i (Guess t v) = no' i t && no' i v
776 noB' i b = no' i (binderTy b)
777 no' i (App f a) = no' i f && no' i a
778 no' i (Proj x _) = no' i x
779 no' i _ = True
781-- | Returns all names used free in the term
782freeNames :: Eq n => TT n -> [n]
783freeNames (P _ n _) = [n]
784freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
785 ++ freeNames t
786freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
787freeNames (App f a) = nub $ freeNames f ++ freeNames a
788freeNames (Proj x i) = nub $ freeNames x
789freeNames _ = []
791-- | Return the arity of a (normalised) type
792arity :: TT n -> Int
793arity (Bind n (Pi t) sc) = 1 + arity sc
794arity _ = 0
796-- | Deconstruct an application; returns the function and a list of arguments
797unApply :: TT n -> (TT n, [TT n])
798unApply t = ua [] t where
799 ua args (App f a) = ua (a:args) f
800 ua args t = (t, args)
802mkApp :: TT n -> [TT n] -> TT n
803mkApp f [] = f
804mkApp f (a:as) = mkApp (App f a) as
806forget :: TT Name -> Raw
807forget tm = fe [] tm
808 where
809 fe env (P _ n _) = Var n
810 fe env (V i) = Var (env !! i)
811 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
812 (fe (n:env) sc)
813 fe env (App f a) = RApp (fe env f) (fe env a)
814 fe env (Constant c)
815 = RConstant c
816 fe env (TType i) = RType
817 fe env Erased = RConstant Forgot
819bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
820bindAll [] t =t
821bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
823bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
824bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
826getArgTys :: TT n -> [(n, TT n)]
827getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
828getArgTys _ = []
830getRetTy :: TT n -> TT n
831getRetTy (Bind n (PVar _) sc) = getRetTy sc
832getRetTy (Bind n (PVTy _) sc) = getRetTy sc
833getRetTy (Bind n (Pi _) sc) = getRetTy sc
834getRetTy sc = sc
836uniqueName :: Name -> [Name] -> Name
837uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
838 | otherwise = n
840uniqueBinders :: [Name] -> TT Name -> TT Name
841uniqueBinders ns (Bind n b sc)
842 = let n' = uniqueName n ns in
843 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
844uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
845uniqueBinders ns t = t
848nextName (NS x s) = NS (nextName x) s
849nextName (MN i n) = MN (i+1) n
850nextName (UN x) = let (num', nm') = span isDigit (reverse x)
851 nm = reverse nm'
852 num = readN (reverse num') in
853 UN (nm ++ show (num+1))
854 where
855 readN "" = 0
856 readN x = read x
857nextName (SN x) = SN (nextName' x)
858 where
859 nextName' (WhereN i f x) = WhereN i f (nextName x)
860 nextName' (CaseN n) = CaseN (nextName n)
861 nextName' (MethodN n) = MethodN (nextName n)
863type Term = TT Name
864type Type = Term
866type Env = EnvTT Name
868-- an environment with de Bruijn indices 'normalised' so that they all refer to
869-- this environment
871newtype WkEnvTT n = Wk (EnvTT n)
872type WkEnv = WkEnvTT Name
874instance (Eq n, Show n) => Show (TT n) where
875 show t = showEnv [] t
877itBitsName IT8 = "Bits8"
878itBitsName IT16 = "Bits16"
879itBitsName IT32 = "Bits32"
880itBitsName IT64 = "Bits64"
882instance Show Const where
883 show (I i) = show i
884 show (BI i) = show i
885 show (Fl f) = show f
886 show (Ch c) = show c
887 show (Str s) = show s
888 show (B8 x) = show x
889 show (B16 x) = show x
890 show (B32 x) = show x
891 show (B64 x) = show x
892 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
893 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
894 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
895 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
896 show (AType ATFloat) = "Float"
897 show (AType (ATInt ITBig)) = "Integer"
898 show (AType (ATInt ITNative)) = "Int"
899 show (AType (ATInt ITChar)) = "Char"
900 show (AType (ATInt (ITFixed it))) = itBitsName it
901 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
902 show StrType = "String"
903 show PtrType = "Ptr"
904 show VoidType = "Void"
906showEnv env t = showEnv' env t False
907showEnvDbg env t = showEnv' env t True
909prettyEnv env t = prettyEnv' env t False
910 where
911 prettyEnv' env t dbg = prettySe 10 env t dbg
913 bracket outer inner p
914 | inner > outer = lparen <> p <> rparen
915 | otherwise = p
917 prettySe p env (P nt n t) debug =
918 pretty n <+>
919 if debug then
920 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
921 else
922 empty
923 prettySe p env (V i) debug
924 | i < length env =
925 if debug then
926 text . show . fst $ env!!i
927 else
928 lbrack <+> text (show i) <+> rbrack
929 | otherwise = text "unbound" <+> text (show i) <+> text "!"
930 prettySe p env (Bind n b@(Pi t) sc) debug
931 | noOccurrence n sc && not debug =
932 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
933 prettySe p env (Bind n b sc) debug =
934 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
935 prettySe p env (App f a) debug =
936 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
937 prettySe p env (Proj x i) debug =
938 prettySe 1 env x debug <+> text ("!" ++ show i)
939 prettySe p env (Constant c) debug = pretty c
940 prettySe p env Erased debug = text "[_]"
941 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
943 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
944 prettySb env n (Hole t) = prettyB env "?defer" "." n t
945 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
946 prettySb env n (PVar t) = prettyB env "pat" "." n t
947 prettySb env n (PVTy t) = prettyB env "pty" "." n t
948 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
949 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
951 prettyB env op sc n t debug =
952 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
954 prettyBv env op sc n t v debug =
955 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
956 prettySe 10 env v debug <> text sc
959showEnv' env t dbg = se 10 env t where
960 se p env (P nt n t) = show n
961 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
962 se p env (V i) | i < length env && i >= 0
963 = (show $ fst $ env!!i) ++
964 if dbg then "{" ++ show i ++ "}" else ""
965 | otherwise = "!!V " ++ show i ++ "!!"
966 se p env (Bind n b@(Pi t) sc)
967 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
968 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
969 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
970 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
971 se p env (Constant c) = show c
972 se p env Erased = "[__]"
973 se p env Impossible = "[impossible]"
974 se p env (TType i) = "Type " ++ show i
976 sb env n (Lam t) = showb env "\\ " " => " n t
977 sb env n (Hole t) = showb env "? " ". " n t
978 sb env n (GHole i t) = showb env "?defer " ". " n t
979 sb env n (Pi t) = showb env "(" ") -> " n t
980 sb env n (PVar t) = showb env "pat " ". " n t
981 sb env n (PVTy t) = showb env "pty " ". " n t
982 sb env n (Let t v) = showbv env "let " " in " n t v
983 sb env n (Guess t v) = showbv env "?? " " in " n t v
985 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
986 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
987 se 10 env v ++ sc
989 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
990 | otherwise = str
992-- | Check whether a term has any holes in it - impure if so
993pureTerm :: TT Name -> Bool
994pureTerm (App f a) = pureTerm f && pureTerm a
995pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
996 pureBinder (Hole _) = False
997 pureBinder (Guess _ _) = False
998 pureBinder (Let t v) = pureTerm t && pureTerm v
999 pureBinder t = pureTerm (binderTy t)
1001 notClassName (MN _ "class") = False
1002 notClassName _ = True
1004pureTerm _ = True
1006-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1007weakenTm :: Int -> TT n -> TT n
1008weakenTm i t = wk i 0 t
1009 where wk i min (V x) | x >= min = V (i + x)
1010 wk i m (App f a) = App (wk i m f) (wk i m a)
1011 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1012 wk i m t = t
1013 wkb i m t = fmap (wk i m) t
1015-- | Weaken an environment so that all the de Bruijn indices are correct according
1016-- to the latest bound variable
1018weakenEnv :: EnvTT n -> EnvTT n
1019weakenEnv env = wk (length env - 1) env
1020 where wk i [] = []
1021 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1022 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1023 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1024 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1026weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1027weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1029orderPats :: Term -> Term
1030orderPats tm = op [] tm
1031 where
1032 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1033 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1034 op ps sc = bindAll (sortP ps) sc
1036 sortP ps = pick [] (reverse ps)
1038 namesIn (P _ n _) = [n]
1039 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
1040 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
1041 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
1042 nb t = namesIn (binderTy t)
1043 namesIn (App f a) = nub (namesIn f ++ namesIn a)
1044 namesIn _ = []
1046 pick acc [] = reverse acc
1047 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1049 insert n t [] = [(n, t)]
1050 insert n t ((n',t') : ps)
1051 | n `elem` (namesIn (binderTy t') ++
1052 concatMap namesIn (map (binderTy . snd) ps))
1053 = (n', t') : insert n t ps
1054 | otherwise = (n,t):(n',t'):ps