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Idris-dev/src/Idris/Core/TT.hs
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1{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, DeriveFunctor, DeriveDataTypeable #-}
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 Idris.Core.TT where
23import Control.Applicative (Applicative (..), Alternative)
24import qualified Control.Applicative as A (Alternative (..))
25import Control.Monad.State.Strict
26import Control.Monad.Trans.Except (Except (..))
27import Debug.Trace
28import qualified Data.Map.Strict as Map
29import Data.Char
30import Data.Data (Data)
31import Numeric (showIntAtBase)
32import qualified Data.Text as T
33import Data.List hiding (group, insert)
34import Data.Set(Set, member, fromList, insert)
35import Data.Maybe (listToMaybe)
36import Data.Foldable (Foldable)
37import Data.Traversable (Traversable)
38import Data.Typeable (Typeable)
39import Data.Vector.Unboxed (Vector)
40import qualified Data.Vector.Unboxed as V
41import qualified Data.Binary as B
42import Data.Binary hiding (get, put)
43import Foreign.Storable (sizeOf)
45import Util.Pretty hiding (Str)
47data Option = TTypeInTType
48 | CheckConv
49 deriving Eq
51-- | Source location. These are typically produced by the parser 'Idris.Parser.getFC'
52data FC = FC { fc_fname :: String, -- ^ Filename
53 fc_start :: (Int, Int), -- ^ Line and column numbers for the start of the location span
54 fc_end :: (Int, Int) -- ^ Line and column numbers for the end of the location span
55 }
56 deriving (Data, Typeable, Ord)
58-- | Ignore source location equality (so deriving classes do not compare FCs)
59instance Eq FC where
60 _ == _ = True
62-- | FC with equality
63newtype FC' = FC' { unwrapFC :: FC }
65instance Eq FC' where
66 FC' fc == FC' fc' = fcEq fc fc'
67 where fcEq (FC n s e) (FC n' s' e') = n == n' && s == s' && e == e'
69-- | Empty source location
70emptyFC :: FC
71emptyFC = fileFC ""
73-- | Source location with file only
74fileFC :: String -> FC
75fileFC s = FC s (0, 0) (0, 0)
77{-!
78deriving instance Binary FC
79deriving instance NFData FC
80!-}
82instance Sized FC where
83 size (FC f s e) = 4 + length f
85instance Show FC where
86 show (FC f s e) = f ++ ":" ++ showLC s e
87 where showLC (sl, sc) (el, ec) | sl == el && sc == ec = show sl ++ ":" ++ show sc
88 | sl == el = show sl ++ ":" ++ show sc ++ "-" ++ show ec
89 | otherwise = show sl ++ ":" ++ show sc ++ "-" ++ show el ++ ":" ++ show ec
91-- | Output annotation for pretty-printed name - decides colour
92data NameOutput = TypeOutput | FunOutput | DataOutput | MetavarOutput | PostulateOutput
94-- | Text formatting output
95data TextFormatting = BoldText | ItalicText | UnderlineText
97-- | Output annotations for pretty-printing
98data OutputAnnotation = AnnName Name (Maybe NameOutput) (Maybe String) (Maybe String)
99 -- ^^ The name, classification, docs overview, and pretty-printed type
100 | AnnBoundName Name Bool
101 -- ^^ The name and whether it is implicit
102 | AnnConst Const
103 | AnnData String String -- ^ type, doc overview
104 | AnnType String String -- ^ name, doc overview
105 | AnnKeyword
106 | AnnFC FC
107 | AnnTextFmt TextFormatting
108 | AnnTerm [(Name, Bool)] (TT Name) -- ^ pprint bound vars, original term
109 | AnnSearchResult Ordering -- ^ more general, isomorphic, or more specific
110 | AnnErr Err
112-- | Used for error reflection
113data ErrorReportPart = TextPart String
114 | NamePart Name
115 | TermPart Term
116 | SubReport [ErrorReportPart]
117 deriving (Show, Eq, Data, Typeable)
120-- Please remember to keep Err synchronised with
121-- Language.Reflection.Errors.Err in the stdlib!
123data Provenance = ExpectedType
124 | TooManyArgs Term
125 | InferredVal
126 | GivenVal
127 | SourceTerm Term
128 deriving (Show, Eq, Data, Typeable)
129{-!
130deriving instance NFData Err
131deriving instance Binary Err
132!-}
134-- | Idris errors. Used as exceptions in the compiler, but reported to users
135-- if they reach the top level.
136data Err' t
137 = Msg String
138 | InternalMsg String
139 | CantUnify Bool (t, Maybe Provenance) -- Expected type, provenance
140 (t, Maybe Provenance) -- Actual type, provenance
141 (Err' t) [(Name, t)] Int
142 -- Int is 'score' - how much we did unify
143 -- Bool indicates recoverability, True indicates more info may make
144 -- unification succeed
145 | InfiniteUnify Name t [(Name, t)]
146 | CantConvert t t [(Name, t)]
147 | CantSolveGoal t [(Name, t)]
148 | UnifyScope Name Name t [(Name, t)]
149 | CantInferType String
150 | NonFunctionType t t
151 | NotEquality t t
152 | TooManyArguments Name
153 | CantIntroduce t
154 | NoSuchVariable Name
155 | WithFnType t
156 | NoTypeDecl Name
157 | NotInjective t t t
158 | CantResolve Bool -- True if postponed, False if fatal
159 t
160 | InvalidTCArg Name t
161 | CantResolveAlts [Name]
162 | IncompleteTerm t
163 | NoEliminator String t
164 | UniverseError
165 | UniqueError Universe Name
166 | UniqueKindError Universe Name
167 | ProgramLineComment
168 | Inaccessible Name
169 | CantMatch t
170 | NonCollapsiblePostulate Name
171 | AlreadyDefined Name
172 | ProofSearchFail (Err' t)
173 | NoRewriting t
174 | At FC (Err' t)
175 | Elaborating String Name (Err' t)
176 | ElaboratingArg Name Name [(Name, Name)] (Err' t)
177 | ProviderError String
178 | LoadingFailed String (Err' t)
179 | ReflectionError [[ErrorReportPart]] (Err' t)
180 | ReflectionFailed String (Err' t)
181 | ElabDebug (Maybe String) t [(Name, t, [(Name, Binder t)])]
182 -- ^ User-specified message, proof term, goals with context (first goal is focused)
183 deriving (Eq, Functor, Data, Typeable)
185type Err = Err' Term
187data TC a = OK !a
188 | Error Err
189 deriving (Eq, Functor)
191bindTC :: TC a -> (a -> TC b) -> TC b
192bindTC x k = case x of
193 OK v -> k v
194 Error e -> Error e
195{-# INLINE bindTC #-}
197instance Monad TC where
198 return x = OK x
199 x >>= k = bindTC x k
200 fail e = Error (InternalMsg 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
209instance Applicative TC where
210 pure = return
211 (<*>) = ap
213instance Alternative TC where
214 empty = mzero
215 (<|>) = mplus
217{-!
218deriving instance NFData Err
219!-}
221instance Sized ErrorReportPart where
222 size (TextPart msg) = 1 + length msg
223 size (TermPart t) = 1 + size t
224 size (NamePart n) = 1 + size n
225 size (SubReport rs) = 1 + size rs
227instance Sized Err where
228 size (Msg msg) = length msg
229 size (InternalMsg msg) = length msg
230 size (CantUnify _ left right err _ score) = size (fst left) + size (fst right) + size err
231 size (InfiniteUnify _ right _) = size right
232 size (CantConvert left right _) = size left + size right
233 size (UnifyScope _ _ right _) = size right
234 size (NoSuchVariable name) = size name
235 size (NoTypeDecl name) = size name
236 size (NotInjective l c r) = size l + size c + size r
237 size (CantResolve _ trm) = size trm
238 size (NoRewriting trm) = size trm
239 size (CantResolveAlts _) = 1
240 size (IncompleteTerm trm) = size trm
241 size UniverseError = 1
242 size ProgramLineComment = 1
243 size (At fc err) = size fc + size err
244 size (Elaborating _ n err) = size err
245 size (ElaboratingArg _ _ _ err) = size err
246 size (ProviderError msg) = length msg
247 size (LoadingFailed fn e) = 1 + length fn + size e
248 size _ = 1
250score :: Err -> Int
251score (CantUnify _ _ _ m _ s) = s + score m
252score (CantResolve _ _) = 20
253score (NoSuchVariable _) = 1000
254score (ProofSearchFail e) = score e
255score (CantSolveGoal _ _) = 100000
256score (InternalMsg _) = -1
257score (At _ e) = score e
258score (ElaboratingArg _ _ _ e) = score e
259score (Elaborating _ _ e) = score e
260score _ = 0
262instance Show Err where
263 show (Msg s) = s
264 show (InternalMsg s) = "Internal error: " ++ show s
265 show (CantUnify rcv l r e sc i) = "CantUnify " ++ show rcv ++ " " ++
266 show l ++ " " ++ show r ++ " " ++
267 show e ++ " in " ++ show sc ++ " " ++ show i
268 show (CantSolveGoal g _) = "CantSolve " ++ show g
269 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
270 show (ProviderError msg) = "Type provider error: " ++ msg
271 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: (TT) " ++ show e
272 show ProgramLineComment = "Program line next to comment"
273 show (At f e) = show f ++ ":" ++ show e
274 show (ElaboratingArg f x prev e) = "Elaborating " ++ show f ++ " arg " ++
275 show x ++ ": " ++ show e
276 show (Elaborating what n e) = "Elaborating " ++ what ++ show n ++ ":" ++ show e
277 show (ProofSearchFail e) = "Proof search fail: " ++ show e
278 show _ = "Error"
280instance Pretty Err OutputAnnotation where
281 pretty (Msg m) = text m
282 pretty (CantUnify _ (l, _) (r, _) e _ i) =
283 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r <+>
284 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
285 pretty (ProviderError msg) = text msg
286 pretty err@(LoadingFailed _ _) = text (show err)
287 pretty _ = text "Error"
289instance (Pretty a OutputAnnotation) => Pretty (TC a) OutputAnnotation where
290 pretty (OK ok) = pretty ok
291 pretty (Error err) =
292 text "Error" <+> colon <+> pretty err
294instance Show a => Show (TC a) where
295 show (OK x) = show x
296 show (Error str) = "Error: " ++ show str
298tfail :: Err -> TC a
299tfail e = Error e
301failMsg :: String -> TC a
302failMsg str = Error (Msg str)
304trun :: FC -> TC a -> TC a
305trun fc (OK a) = OK a
306trun fc (Error e) = Error (At fc e)
308discard :: Monad m => m a -> m ()
309discard f = f >> return ()
311showSep :: String -> [String] -> String
312showSep sep [] = ""
313showSep sep [x] = x
314showSep sep (x:xs) = x ++ sep ++ showSep sep xs
316pmap f (x, y) = (f x, f y)
318traceWhen True msg a = trace msg a
319traceWhen False _ a = a
321-- RAW TERMS ----------------------------------------------------------------
323-- | Names are hierarchies of strings, describing scope (so no danger of
324-- duplicate names, but need to be careful on lookup).
325data Name = UN T.Text -- ^ User-provided name
326 | NS Name [T.Text] -- ^ Root, namespaces
327 | MN Int T.Text -- ^ Machine chosen names
328 | NErased -- ^ Name of something which is never used in scope
329 | SN SpecialName -- ^ Decorated function names
330 | SymRef Int -- ^ Reference to IBC file symbol table (used during serialisation)
331 deriving (Eq, Ord, Data, Typeable)
333txt :: String -> T.Text
334txt = T.pack
336str :: T.Text -> String
337str = T.unpack
339tnull :: T.Text -> Bool
340tnull = T.null
342thead :: T.Text -> Char
343thead = T.head
345-- Smart constructors for names, using old String style
346sUN :: String -> Name
347sUN s = UN (txt s)
349sNS :: Name -> [String] -> Name
350sNS n ss = NS n (map txt ss)
352sMN :: Int -> String -> Name
353sMN i s = MN i (txt s)
355{-!
356deriving instance Binary Name
357deriving instance NFData Name
358!-}
360data SpecialName = WhereN Int Name Name
361 | WithN Int Name
362 | InstanceN Name [T.Text]
363 | ParentN Name T.Text
364 | MethodN Name
365 | CaseN Name
366 | ElimN Name
367 | InstanceCtorN Name
368 deriving (Eq, Ord, Data, Typeable)
369{-!
370deriving instance Binary SpecialName
371deriving instance NFData SpecialName
372!-}
374sInstanceN :: Name -> [String] -> SpecialName
375sInstanceN n ss = InstanceN n (map T.pack ss)
377sParentN :: Name -> String -> SpecialName
378sParentN n s = ParentN n (T.pack s)
380instance Sized Name where
381 size (UN n) = 1
382 size (NS n els) = 1 + length els
383 size (MN i n) = 1
384 size _ = 1
386instance Pretty Name OutputAnnotation where
387 pretty n@(UN n') = annotate (AnnName n Nothing Nothing Nothing) $ text (T.unpack n')
388 pretty n@(NS un s) = annotate (AnnName n Nothing Nothing Nothing) . noAnnotate $ pretty un
389 pretty n@(MN i s) = annotate (AnnName n Nothing Nothing Nothing) $
390 lbrace <+> text (T.unpack s) <+> (text . show $ i) <+> rbrace
391 pretty n@(SN s) = annotate (AnnName n Nothing Nothing Nothing) $ text (show s)
393instance Pretty [Name] OutputAnnotation where
394 pretty = encloseSep empty empty comma . map pretty
396instance Show Name where
397 show (UN n) = str n
398 show (NS n s) = showSep "." (map T.unpack (reverse s)) ++ "." ++ show n
399 show (MN _ u) | u == txt "underscore" = "_"
400 show (MN i s) = "{" ++ str s ++ show i ++ "}"
401 show (SN s) = show s
402 show NErased = "_"
404instance Show SpecialName where
405 show (WhereN i p c) = show p ++ ", " ++ show c
406 show (WithN i n) = "with block in " ++ show n
407 show (InstanceN cl inst) = showSep ", " (map T.unpack inst) ++ " instance of " ++ show cl
408 show (MethodN m) = "method " ++ show m
409 show (ParentN p c) = show p ++ "#" ++ T.unpack c
410 show (CaseN n) = "case block in " ++ show n
411 show (ElimN n) = "<<" ++ show n ++ " eliminator>>"
412 show (InstanceCtorN n) = "constructor of " ++ show n
414-- Show a name in a way decorated for code generation, not human reading
415showCG :: Name -> String
416showCG (UN n) = T.unpack n
417showCG (NS n s) = showSep "." (map T.unpack (reverse s)) ++ "." ++ showCG n
418showCG (MN _ u) | u == txt "underscore" = "_"
419showCG (MN i s) = "{" ++ T.unpack s ++ show i ++ "}"
420showCG (SN s) = showCG' s
421 where showCG' (WhereN i p c) = showCG p ++ ":" ++ showCG c ++ ":" ++ show i
422 showCG' (WithN i n) = "_" ++ showCG n ++ "_with_" ++ show i
423 showCG' (InstanceN cl inst) = '@':showCG cl ++ '$':showSep ":" (map T.unpack inst)
424 showCG' (MethodN m) = '!':showCG m
425 showCG' (ParentN p c) = showCG p ++ "#" ++ show c
426 showCG' (CaseN c) = showCG c ++ "_case"
427 showCG' (ElimN sn) = showCG sn ++ "_elim"
428showCG NErased = "_"
431-- |Contexts allow us to map names to things. A root name maps to a collection
432-- of things in different namespaces with that name.
433type Ctxt a = Map.Map Name (Map.Map Name a)
434emptyContext = Map.empty
436mapCtxt :: (a -> b) -> Ctxt a -> Ctxt b
437mapCtxt = fmap . fmap
439-- |Return True if the argument 'Name' should be interpreted as the name of a
440-- typeclass.
441tcname (UN xs) | T.null xs = False
442 | otherwise = T.head xs == '@'
443tcname (NS n _) = tcname n
444tcname (SN (InstanceN _ _)) = True
445tcname (SN (MethodN _)) = True
446tcname (SN (ParentN _ _)) = True
447tcname _ = False
449implicitable (NS n _) = implicitable n
450implicitable (UN xs) | T.null xs = False
451 | otherwise = isLower (T.head xs) || T.head xs == '_'
452implicitable (MN _ x) = not (tnull x) && thead x /= '_'
453implicitable _ = False
455nsroot (NS n _) = n
456nsroot n = n
458-- this will overwrite already existing definitions
459addDef :: Name -> a -> Ctxt a -> Ctxt a
460addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
461 Nothing -> Map.insert (nsroot n)
462 (Map.insert n v Map.empty) ctxt
463 Just xs -> Map.insert (nsroot n)
464 (Map.insert n v xs) ctxt
466{-| Look up a name in the context, given an optional namespace.
467 The name (n) may itself have a (partial) namespace given.
469 Rules for resolution:
471 - if an explicit namespace is given, return the names which match it. If none
472 match, return all names.
474 - if the name has has explicit namespace given, return the names which match it
475 and ignore the given namespace.
477 - otherwise, return all names.
479-}
481lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
482lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
483 Just xs -> filterNS (Map.toList xs)
484 Nothing -> []
485 where
486 filterNS [] = []
487 filterNS ((found, v) : xs)
488 | nsmatch n found = (found, v) : filterNS xs
489 | otherwise = filterNS xs
491 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
492 nsmatch (NS _ _) _ = False
493 nsmatch looking found = True
495lookupCtxt :: Name -> Ctxt a -> [a]
496lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
498lookupCtxtExact :: Name -> Ctxt a -> Maybe a
499lookupCtxtExact n ctxt = listToMaybe [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
501deleteDefExact :: Name -> Ctxt a -> Ctxt a
502deleteDefExact n = Map.adjust (Map.delete n) (nsroot n)
504updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
505updateDef n f ctxt
506 = let ds = lookupCtxtName n ctxt in
507 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
509toAlist :: Ctxt a -> [(Name, a)]
510toAlist ctxt = let allns = map snd (Map.toList ctxt) in
511 concatMap (Map.toList) allns
513addAlist :: [(Name, a)] -> Ctxt a -> Ctxt a
514addAlist [] ctxt = ctxt
515addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
517data NativeTy = IT8 | IT16 | IT32 | IT64
518 deriving (Show, Eq, Ord, Enum, Data, Typeable)
520instance Pretty NativeTy OutputAnnotation where
521 pretty IT8 = text "Bits8"
522 pretty IT16 = text "Bits16"
523 pretty IT32 = text "Bits32"
524 pretty IT64 = text "Bits64"
526data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
527 | ITVec NativeTy Int
528 deriving (Show, Eq, Ord, Data, Typeable)
530intTyName :: IntTy -> String
531intTyName ITNative = "Int"
532intTyName ITBig = "BigInt"
533intTyName (ITFixed sized) = "B" ++ show (nativeTyWidth sized)
534intTyName (ITChar) = "Char"
535intTyName (ITVec ity count) = "B" ++ show (nativeTyWidth ity) ++ "x" ++ show count
537data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors https://github.com/idris-lang/Idris-dev/issues/1723
538 deriving (Show, Eq, Ord, Data, Typeable)
539{-!
540deriving instance NFData IntTy
541deriving instance NFData NativeTy
542deriving instance NFData ArithTy
543!-}
545instance Pretty ArithTy OutputAnnotation where
546 pretty (ATInt ITNative) = text "Int"
547 pretty (ATInt ITBig) = text "BigInt"
548 pretty (ATInt ITChar) = text "Char"
549 pretty (ATInt (ITFixed n)) = pretty n
550 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
551 pretty ATFloat = text "Float"
553nativeTyWidth :: NativeTy -> Int
554nativeTyWidth IT8 = 8
555nativeTyWidth IT16 = 16
556nativeTyWidth IT32 = 32
557nativeTyWidth IT64 = 64
559{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
560intTyWidth :: IntTy -> Int
561intTyWidth (ITFixed n) = nativeTyWidth n
562intTyWidth ITNative = 8 * sizeOf (0 :: Int)
563intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
564intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
566data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
567 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
568 | B8V (Vector Word8) | B16V (Vector Word16)
569 | B32V (Vector Word32) | B64V (Vector Word64)
570 | AType ArithTy | StrType
571 | WorldType | TheWorld
572 | PtrType | ManagedPtrType | BufferType | VoidType | Forgot
573 deriving (Eq, Ord, Data, Typeable)
574{-!
575deriving instance Binary Const
576deriving instance NFData Const
577!-}
579isTypeConst :: Const -> Bool
580isTypeConst (AType _) = True
581isTypeConst StrType = True
582isTypeConst ManagedPtrType = True
583isTypeConst BufferType = True
584isTypeConst WorldType = True
585isTypeConst PtrType = True
586isTypeConst VoidType = True
587isTypeConst _ = False
589instance Sized Const where
590 size _ = 1
592instance Pretty Const OutputAnnotation where
593 pretty (I i) = text . show $ i
594 pretty (BI i) = text . show $ i
595 pretty (Fl f) = text . show $ f
596 pretty (Ch c) = text . show $ c
597 pretty (Str s) = text s
598 pretty (AType a) = pretty a
599 pretty StrType = text "String"
600 pretty TheWorld = text "%theWorld"
601 pretty WorldType = text "prim__World"
602 pretty BufferType = text "prim__UnsafeBuffer"
603 pretty PtrType = text "Ptr"
604 pretty ManagedPtrType = text "Ptr"
605 pretty VoidType = text "Void"
606 pretty Forgot = text "Forgot"
607 pretty (B8 w) = text . show $ w
608 pretty (B16 w) = text . show $ w
609 pretty (B32 w) = text . show $ w
610 pretty (B64 w) = text . show $ w
612-- | Determines whether the input constant represents a type
613constIsType :: Const -> Bool
614constIsType (I _) = False
615constIsType (BI _) = False
616constIsType (Fl _) = False
617constIsType (Ch _) = False
618constIsType (Str _) = False
619constIsType (B8 _) = False
620constIsType (B16 _) = False
621constIsType (B32 _) = False
622constIsType (B64 _) = False
623constIsType (B8V _) = False
624constIsType (B16V _) = False
625constIsType (B32V _) = False
626constIsType (B64V _) = False
627constIsType _ = True
629-- | Get the docstring for a Const
630constDocs :: Const -> String
631constDocs c@(AType (ATInt ITBig)) = "Arbitrary-precision integers"
632constDocs c@(AType (ATInt ITNative)) = "Fixed-precision integers of undefined size"
633constDocs c@(AType (ATInt ITChar)) = "Characters in some unspecified encoding"
634constDocs c@(AType ATFloat) = "Double-precision floating-point numbers"
635constDocs StrType = "Strings in some unspecified encoding"
636constDocs PtrType = "Foreign pointers"
637constDocs ManagedPtrType = "Managed pointers"
638constDocs BufferType = "Copy-on-write buffers"
639constDocs c@(AType (ATInt (ITFixed IT8))) = "Eight bits (unsigned)"
640constDocs c@(AType (ATInt (ITFixed IT16))) = "Sixteen bits (unsigned)"
641constDocs c@(AType (ATInt (ITFixed IT32))) = "Thirty-two bits (unsigned)"
642constDocs c@(AType (ATInt (ITFixed IT64))) = "Sixty-four bits (unsigned)"
643constDocs c@(AType (ATInt (ITVec IT8 16))) = "Vectors of sixteen eight-bit values"
644constDocs c@(AType (ATInt (ITVec IT16 8))) = "Vectors of eight sixteen-bit values"
645constDocs c@(AType (ATInt (ITVec IT32 4))) = "Vectors of four thirty-two-bit values"
646constDocs c@(AType (ATInt (ITVec IT64 2))) = "Vectors of two sixty-four-bit values"
647constDocs (Fl f) = "A float"
648constDocs (I i) = "A fixed-precision integer"
649constDocs (BI i) = "An arbitrary-precision integer"
650constDocs (Str s) = "A string of length " ++ show (length s)
651constDocs (Ch c) = "A character"
652constDocs (B8 w) = "The eight-bit value 0x" ++
653 showIntAtBase 16 intToDigit w ""
654constDocs (B16 w) = "The sixteen-bit value 0x" ++
655 showIntAtBase 16 intToDigit w ""
656constDocs (B32 w) = "The thirty-two-bit value 0x" ++
657 showIntAtBase 16 intToDigit w ""
658constDocs (B64 w) = "The sixty-four-bit value 0x" ++
659 showIntAtBase 16 intToDigit w ""
660constDocs (B8V v) = "A vector of eight-bit values"
661constDocs (B16V v) = "A vector of sixteen-bit values"
662constDocs (B32V v) = "A vector of thirty-two-bit values"
663constDocs (B64V v) = "A vector of sixty-four-bit values"
664constDocs prim = "Undocumented"
666data Universe = NullType | UniqueType | AllTypes
667 deriving (Eq, Ord, Data, Typeable)
669instance Show Universe where
670 show UniqueType = "UniqueType"
671 show NullType = "NullType"
672 show AllTypes = "Type*"
674data Raw = Var Name
675 | RBind Name (Binder Raw) Raw
676 | RApp Raw Raw
677 | RType
678 | RUType Universe
679 | RForce Raw
680 | RConstant Const
681 deriving (Show, Eq, Data, Typeable)
683instance Sized Raw where
684 size (Var name) = 1
685 size (RBind name bind right) = 1 + size bind + size right
686 size (RApp left right) = 1 + size left + size right
687 size RType = 1
688 size (RUType _) = 1
689 size (RForce raw) = 1 + size raw
690 size (RConstant const) = size const
692instance Pretty Raw OutputAnnotation where
693 pretty = text . show
695{-!
696deriving instance Binary Raw
697deriving instance NFData Raw
698!-}
700data ImplicitInfo = Impl { tcinstance :: Bool }
701 deriving (Show, Eq, Ord, Data, Typeable)
703{-!
704deriving instance Binary ImplicitInfo
705deriving instance NFData ImplicitInfo
706!-}
708-- The type parameter `b` will normally be something like `TT Name` or just
709-- `Raw`. We do not make a type-level distinction between TT terms that happen
710-- to be TT types and TT terms that are not TT types.
711-- | All binding forms are represented in a uniform fashion. This type only represents
712-- the types of bindings (and their values, if any); the attached identifiers are part
713-- of the 'Bind' constructor for the 'TT' type.
714data Binder b = Lam { binderTy :: !b {-^ type annotation for bound variable-}}
715 | Pi { binderImpl :: Maybe ImplicitInfo,
716 binderTy :: !b,
717 binderKind :: !b }
718 {-^ A binding that occurs in a function type expression, e.g. @(x:Int) -> ...@
719 The 'binderImpl' flag says whether it was a scoped implicit
720 (i.e. forall bound) in the high level Idris, but otherwise
721 has no relevance in TT. -}
722 | Let { binderTy :: !b,
723 binderVal :: b {-^ value for bound variable-}}
724 -- ^ A binding that occurs in a @let@ expression
725 | NLet { binderTy :: !b,
726 binderVal :: b }
727 | Hole { binderTy :: !b}
728 | GHole { envlen :: Int,
729 binderTy :: !b}
730 | Guess { binderTy :: !b,
731 binderVal :: b }
732 | PVar { binderTy :: !b }
733 -- ^ A pattern variable
734 | PVTy { binderTy :: !b }
735 deriving (Show, Eq, Ord, Functor, Foldable, Traversable, Data, Typeable)
736{-!
737deriving instance Binary Binder
738deriving instance NFData Binder
739!-}
741instance Sized a => Sized (Binder a) where
742 size (Lam ty) = 1 + size ty
743 size (Pi _ ty _) = 1 + size ty
744 size (Let ty val) = 1 + size ty + size val
745 size (NLet ty val) = 1 + size ty + size val
746 size (Hole ty) = 1 + size ty
747 size (GHole _ ty) = 1 + size ty
748 size (Guess ty val) = 1 + size ty + size val
749 size (PVar ty) = 1 + size ty
750 size (PVTy ty) = 1 + size ty
752fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
753fmapMB f (Let t v) = liftM2 Let (f t) (f v)
754fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
755fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
756fmapMB f (Lam t) = liftM Lam (f t)
757fmapMB f (Pi i t k) = liftM2 (Pi i) (f t) (f k)
758fmapMB f (Hole t) = liftM Hole (f t)
759fmapMB f (GHole i t) = liftM (GHole i) (f t)
760fmapMB f (PVar t) = liftM PVar (f t)
761fmapMB f (PVTy t) = liftM PVTy (f t)
763raw_apply :: Raw -> [Raw] -> Raw
764raw_apply f [] = f
765raw_apply f (a : as) = raw_apply (RApp f a) as
767raw_unapply :: Raw -> (Raw, [Raw])
768raw_unapply t = ua [] t where
769 ua args (RApp f a) = ua (a:args) f
770 ua args t = (t, args)
772-- WELL TYPED TERMS ---------------------------------------------------------
774-- | Universe expressions for universe checking
775data UExp = UVar Int -- ^ universe variable
776 | UVal Int -- ^ explicit universe level
777 deriving (Eq, Ord, Data, Typeable)
778{-!
779deriving instance NFData UExp
780!-}
782instance Sized UExp where
783 size _ = 1
785instance Show UExp where
786 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
787 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
788 show (UVal x) = show x
789-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
791-- | Universe constraints
792data UConstraint = ULT UExp UExp -- ^ Strictly less than
793 | ULE UExp UExp -- ^ Less than or equal to
794 deriving (Eq, Ord)
796data ConstraintFC = ConstraintFC { uconstraint :: UConstraint,
797 ufc :: FC }
798 deriving Show
800instance Eq ConstraintFC where
801 x == y = uconstraint x == uconstraint y
803instance Ord ConstraintFC where
804 compare x y = compare (uconstraint x) (uconstraint y)
806instance Show UConstraint where
807 show (ULT x y) = show x ++ " < " ++ show y
808 show (ULE x y) = show x ++ " <= " ++ show y
810type UCs = (Int, [UConstraint])
812data NameType = Bound
813 | Ref
814 | DCon {nt_tag :: Int, nt_arity :: Int, nt_unique :: Bool} -- ^ Data constructor
815 | TCon {nt_tag :: Int, nt_arity :: Int} -- ^ Type constructor
816 deriving (Show, Ord, Data, Typeable)
817{-!
818deriving instance Binary NameType
819deriving instance NFData NameType
820!-}
822instance Sized NameType where
823 size _ = 1
825instance Pretty NameType OutputAnnotation where
826 pretty = text . show
828instance Eq NameType where
829 Bound == Bound = True
830 Ref == Ref = True
831 DCon _ a _ == DCon _ b _ = (a == b) -- ignore tag
832 TCon _ a == TCon _ b = (a == b) -- ignore tag
833 _ == _ = False
835-- | Terms in the core language. The type parameter is the type of
836-- identifiers used for bindings and explicit named references;
837-- usually we use @TT 'Name'@.
838data TT n = P NameType n (TT n) -- ^ named references with type
839 -- (P for "Parameter", motivated by McKinna and Pollack's
840 -- Pure Type Systems Formalized)
841 | V !Int -- ^ a resolved de Bruijn-indexed variable
842 | Bind n !(Binder (TT n)) (TT n) -- ^ a binding
843 | App !(TT n) (TT n) -- ^ function, function type, arg
844 | Constant Const -- ^ constant
845 | Proj (TT n) !Int -- ^ argument projection; runtime only
846 -- (-1) is a special case for 'subtract one from BI'
847 | Erased -- ^ an erased term
848 | Impossible -- ^ special case for totality checking
849 | TType UExp -- ^ the type of types at some level
850 | UType Universe -- ^ Uniqueness type universe (disjoint from TType)
851 deriving (Ord, Functor, Data, Typeable)
852{-!
853deriving instance Binary TT
854deriving instance NFData TT
855!-}
857class TermSize a where
858 termsize :: Name -> a -> Int
860instance TermSize a => TermSize [a] where
861 termsize n [] = 0
862 termsize n (x : xs) = termsize n x + termsize n xs
864instance TermSize (TT Name) where
865 termsize n (P _ n' _)
866 | n' == n = 1000000 -- recursive => really big
867 | otherwise = 1
868 termsize n (V _) = 1
869 -- for `Bind` terms, we can erroneously declare a term
870 -- "recursive => really big" if the name of the bound
871 -- variable is the same as the name we're using
872 -- So generate a different name in that case.
873 termsize n (Bind n' (Let t v) sc)
874 = let rn = if n == n' then sMN 0 "noname" else n in
875 termsize rn v + termsize rn sc
876 termsize n (Bind n' b sc)
877 = let rn = if n == n' then sMN 0 "noname" else n in
878 termsize rn sc
879 termsize n (App f a) = termsize n f + termsize n a
880 termsize n (Proj t i) = termsize n t
881 termsize n _ = 1
883instance Sized a => Sized (TT a) where
884 size (P name n trm) = 1 + size name + size n + size trm
885 size (V v) = 1
886 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
887 size (App l r) = 1 + size l + size r
888 size (Constant c) = size c
889 size Erased = 1
890 size (TType u) = 1 + size u
892instance Pretty a o => Pretty (TT a) o where
893 pretty _ = text "test"
895type EnvTT n = [(n, Binder (TT n))]
897data Datatype n = Data { d_typename :: n,
898 d_typetag :: Int,
899 d_type :: (TT n),
900 d_unique :: Bool,
901 d_cons :: [(n, TT n)] }
902 deriving (Show, Functor, Eq)
904instance Eq n => Eq (TT n) where
905 (==) (P xt x _) (P yt y _) = x == y
906 (==) (V x) (V y) = x == y
907 (==) (Bind _ xb xs) (Bind _ yb ys) = xs == ys && xb == yb
908 (==) (App fx ax) (App fy ay) = ax == ay && fx == fy
909 (==) (TType _) (TType _) = True -- deal with constraints later
910 (==) (Constant x) (Constant y) = x == y
911 (==) (Proj x i) (Proj y j) = x == y && i == j
912 (==) Erased _ = True
913 (==) _ Erased = True
914 (==) _ _ = False
916-- * A few handy operations on well typed terms:
918-- | A term is injective iff it is a data constructor, type constructor,
919-- constant, the type Type, pi-binding, or an application of an injective
920-- term.
921isInjective :: TT n -> Bool
922isInjective (P (DCon _ _ _) _ _) = True
923isInjective (P (TCon _ _) _ _) = True
924isInjective (Constant _) = True
925isInjective (TType x) = True
926isInjective (Bind _ (Pi _ _ _) sc) = True
927isInjective (App f a) = isInjective f
928isInjective _ = False
930-- | Count the number of instances of a de Bruijn index in a term
931vinstances :: Int -> TT n -> Int
932vinstances i (V x) | i == x = 1
933vinstances i (App f a) = vinstances i f + vinstances i a
934vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
935 where instancesB (Let t v) = vinstances i v
936 instancesB _ = 0
937vinstances i t = 0
939-- | Replace the outermost (index 0) de Bruijn variable with the given term
940instantiate :: TT n -> TT n -> TT n
941instantiate e = subst 0 where
942 subst i (P nt x ty) = P nt x (subst i ty)
943 subst i (V x) | i == x = e
944 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
945 subst i (App f a) = App (subst i f) (subst i a)
946 subst i (Proj x idx) = Proj (subst i x) idx
947 subst i t = t
949-- | As 'instantiate', but also decrement the indices of all de Bruijn variables
950-- remaining in the term, so that there are no more references to the variable
951-- that has been substituted.
952substV :: TT n -> TT n -> TT n
953substV x tm = dropV 0 (instantiate x tm) where
954 subst i (P nt x ty) = P nt x (subst i ty)
955 dropV i (V x) | x > i = V (x - 1)
956 | otherwise = V x
957 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
958 dropV i (App f a) = App (dropV i f) (dropV i a)
959 dropV i (Proj x idx) = Proj (dropV i x) idx
960 dropV i t = t
962-- | Replace all non-free de Bruijn references in the given term with references
963-- to the name of their binding.
964explicitNames :: TT n -> TT n
965explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
966 Bind x b'
967 (explicitNames (instantiate
968 (P Bound x (binderTy b')) sc))
969explicitNames (App f a) = App (explicitNames f) (explicitNames a)
970explicitNames (Proj x idx) = Proj (explicitNames x) idx
971explicitNames t = t
973-- | Replace references to the given 'Name'-like id with references to
974-- de Bruijn index 0.
975pToV :: Eq n => n -> TT n -> TT n
976pToV n = pToV' n 0
977pToV' n i (P _ x _) | n == x = V i
978pToV' n i (Bind x b sc)
979-- We can assume the inner scope has been pToVed already, so continue to
980-- resolve names from the *outer* scope which may happen to have the same id.
981 | n == x = Bind x (fmap (pToV' n i) b) sc
982 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
983pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
984pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
985pToV' n i t = t
987-- increase de Bruijn indices, as if a binder has been added
988addBinder :: TT n -> TT n
989addBinder t = ab 0 t
990 where
991 ab top (V i) | i >= top = V (i + 1)
992 | otherwise = V i
993 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
994 ab top (App f a) = App (ab top f) (ab top a)
995 ab top (Proj t idx) = Proj (ab top t) idx
996 ab top t = t
998-- | Convert several names. First in the list comes out as V 0
999pToVs :: Eq n => [n] -> TT n -> TT n
1000pToVs ns tm = pToVs' ns tm 0 where
1001 pToVs' [] tm i = tm
1002 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
1004-- | Replace de Bruijn indices in the given term with explicit references to
1005-- the names of the bindings they refer to. It is an error if the given term
1006-- contains free de Bruijn indices.
1007vToP :: TT n -> TT n
1008vToP = vToP' [] where
1009 vToP' env (V i) = let (n, b) = (env !! i) in
1010 P Bound n (binderTy b)
1011 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
1012 Bind n b' (vToP' ((n, b'):env) sc)
1013 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
1014 vToP' env t = t
1016-- | Replace every non-free reference to the name of a binding in
1017-- the given term with a de Bruijn index.
1018finalise :: Eq n => TT n -> TT n
1019finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
1020finalise (App f a) = App (finalise f) (finalise a)
1021finalise t = t
1023-- Once we've finished checking everything about a term we no longer need
1024-- the type on the 'P' so erase it so save memory
1026pEraseType :: TT n -> TT n
1027pEraseType (P nt t _) = P nt t Erased
1028pEraseType (App f a) = App (pEraseType f) (pEraseType a)
1029pEraseType (Bind n b sc) = Bind n (fmap pEraseType b) (pEraseType sc)
1030pEraseType t = t
1032-- | As 'instantiate', but in addition to replacing @'V' 0@,
1033-- replace references to the given 'Name'-like id.
1034subst :: Eq n => n {-^ The id to replace -} ->
1035 TT n {-^ The replacement term -} ->
1036 TT n {-^ The term to replace in -} ->
1037 TT n
1038-- subst n v tm = instantiate v (pToV n tm)
1039subst n v tm = fst $ subst' 0 tm
1040 where
1041 -- keep track of updates to save allocations - this is a big win on
1042 -- large terms in particular
1043 -- ('Maybe' would be neater here, but >>= is not the right combinator.
1044 -- Feel free to tidy up, as long as it still saves allocating when no
1045 -- substitution happens...)
1046 subst' i (V x) | i == x = (v, True)
1047 subst' i (P _ x _) | n == x = (v, True)
1048 subst' i t@(P nt x ty)
1049 = let (ty', ut) = subst' i ty in
1050 if ut then (P nt x ty', True) else (t, False)
1051 subst' i t@(Bind x b sc) | x /= n
1052 = let (b', ub) = substB' i b
1053 (sc', usc) = subst' (i+1) sc in
1054 if ub || usc then (Bind x b' sc', True) else (t, False)
1055 subst' i t@(App f a) = let (f', uf) = subst' i f
1056 (a', ua) = subst' i a in
1057 if uf || ua then (App f' a', True) else (t, False)
1058 subst' i t@(Proj x idx) = let (x', u) = subst' i x in
1059 if u then (Proj x' idx, u) else (t, False)
1060 subst' i t = (t, False)
1062 substB' i b@(Let t v) = let (t', ut) = subst' i t
1063 (v', uv) = subst' i v in
1064 if ut || uv then (Let t' v', True)
1065 else (b, False)
1066 substB' i b@(Guess t v) = let (t', ut) = subst' i t
1067 (v', uv) = subst' i v in
1068 if ut || uv then (Guess t' v', True)
1069 else (b, False)
1070 substB' i b = let (ty', u) = subst' i (binderTy b) in
1071 if u then (b { binderTy = ty' }, u) else (b, False)
1073-- If there are no Vs in the term (i.e. in proof state)
1074psubst :: Eq n => n -> TT n -> TT n -> TT n
1075psubst n v tm = s' 0 tm where
1076 s' i (V x) | x > i = V (x - 1)
1077 | x == i = v
1078 | otherwise = V x
1079 s' i (P _ x _) | n == x = v
1080 s' i (Bind x b sc) | n == x = Bind x (fmap (s' i) b) sc
1081 | otherwise = Bind x (fmap (s' i) b) (s' (i+1) sc)
1082 s' i (App f a) = App (s' i f) (s' i a)
1083 s' i (Proj t idx) = Proj (s' i t) idx
1084 s' i t = t
1086-- | As 'subst', but takes a list of (name, substitution) pairs instead
1087-- of a single name and substitution
1088substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
1089substNames [] t = t
1090substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
1092-- | Replaces all terms equal (in the sense of @(==)@) to
1093-- the old term with the new term.
1094substTerm :: Eq n => TT n {-^ Old term -} ->
1095 TT n {-^ New term -} ->
1096 TT n {-^ template term -}
1097 -> TT n
1098substTerm old new = st where
1099 st t | t == old = new
1100 st (App f a) = App (st f) (st a)
1101 st (Bind x b sc) = Bind x (fmap st b) (st sc)
1102 st t = t
1104-- | Return number of occurrences of V 0 or bound name i the term
1105occurrences :: Eq n => n -> TT n -> Int
1106occurrences n t = execState (no' 0 t) 0
1107 where
1108 no' i (V x) | i == x = do num <- get; put (num + 1)
1109 no' i (P Bound x _) | n == x = do num <- get; put (num + 1)
1110 no' i (Bind n b sc) = do noB' i b; no' (i+1) sc
1111 where noB' i (Let t v) = do no' i t; no' i v
1112 noB' i (Guess t v) = do no' i t; no' i v
1113 noB' i b = no' i (binderTy b)
1114 no' i (App f a) = do no' i f; no' i a
1115 no' i (Proj x _) = no' i x
1116 no' i _ = return ()
1118-- | Returns true if V 0 and bound name n do not occur in the term
1119noOccurrence :: Eq n => n -> TT n -> Bool
1120noOccurrence n t = no' 0 t
1121 where
1122 no' i (V x) = not (i == x)
1123 no' i (P Bound x _) = not (n == x)
1124 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
1125 where noB' i (Let t v) = no' i t && no' i v
1126 noB' i (Guess t v) = no' i t && no' i v
1127 noB' i b = no' i (binderTy b)
1128 no' i (App f a) = no' i f && no' i a
1129 no' i (Proj x _) = no' i x
1130 no' i _ = True
1132-- | Returns all names used free in the term
1133freeNames :: Eq n => TT n -> [n]
1134freeNames t = nub $ freeNames' t
1135 where
1136 freeNames' (P _ n _) = [n]
1137 freeNames' (Bind n (Let t v) sc) = freeNames' v ++ (freeNames' sc \\ [n])
1138 ++ freeNames' t
1139 freeNames' (Bind n b sc) = freeNames' (binderTy b) ++ (freeNames' sc \\ [n])
1140 freeNames' (App f a) = freeNames' f ++ freeNames' a
1141 freeNames' (Proj x i) = freeNames' x
1142 freeNames' _ = []
1144-- | Return the arity of a (normalised) type
1145arity :: TT n -> Int
1146arity (Bind n (Pi _ t _) sc) = 1 + arity sc
1147arity _ = 0
1149-- | Deconstruct an application; returns the function and a list of arguments
1150unApply :: TT n -> (TT n, [TT n])
1151unApply t = ua [] t where
1152 ua args (App f a) = ua (a:args) f
1153 ua args t = (t, args)
1155-- | Returns a term representing the application of the first argument
1156-- (a function) to every element of the second argument.
1157mkApp :: TT n -> [TT n] -> TT n
1158mkApp f [] = f
1159mkApp f (a:as) = mkApp (App f a) as
1161unList :: Term -> Maybe [Term]
1162unList tm = case unApply tm of
1163 (nil, [_]) -> Just []
1164 (cons, ([_, x, xs])) ->
1165 do rest <- unList xs
1166 return $ x:rest
1167 (f, args) -> Nothing
1169-- | Cast a 'TT' term to a 'Raw' value, discarding universe information and
1170-- the types of named references and replacing all de Bruijn indices
1171-- with the corresponding name. It is an error if there are free de
1172-- Bruijn indices.
1173forget :: TT Name -> Raw
1174forget tm = forgetEnv [] tm
1176safeForget :: TT Name -> Maybe Raw
1177safeForget tm = safeForgetEnv [] tm
1179forgetEnv :: [Name] -> TT Name -> Raw
1180forgetEnv env tm = case safeForgetEnv env tm of
1181 Just t' -> t'
1182 Nothing -> error $ "Scope error in " ++ show tm
1185safeForgetEnv :: [Name] -> TT Name -> Maybe Raw
1186safeForgetEnv env (P _ n _) = Just $ Var n
1187safeForgetEnv env (V i) | i < length env = Just $ Var (env !! i)
1188 | otherwise = Nothing
1189safeForgetEnv env (Bind n b sc)
1190 = do let n' = uniqueName n env
1191 b' <- safeForgetEnvB env b
1192 sc' <- safeForgetEnv (n':env) sc
1193 Just $ RBind n' b' sc'
1194 where safeForgetEnvB env (Let t v) = liftM2 Let (safeForgetEnv env t)
1195 (safeForgetEnv env v)
1196 safeForgetEnvB env b = do ty' <- safeForgetEnv env (binderTy b)
1197 Just $ fmap (\_ -> ty') b
1198safeForgetEnv env (App f a) = liftM2 RApp (safeForgetEnv env f) (safeForgetEnv env a)
1199safeForgetEnv env (Constant c) = Just $ RConstant c
1200safeForgetEnv env (TType i) = Just RType
1201safeForgetEnv env (UType u) = Just $ RUType u
1202safeForgetEnv env Erased = Just $ RConstant Forgot
1204-- | Introduce a 'Bind' into the given term for each element of the
1205-- given list of (name, binder) pairs.
1206bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
1207bindAll [] t = t
1208bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
1210-- | Like 'bindAll', but the 'Binder's are 'TT' terms instead.
1211-- The first argument is a function to map @TT@ terms to @Binder@s.
1212-- This function might often be something like 'Lam', which directly
1213-- constructs a @Binder@ from a @TT@ term.
1214bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
1215bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
1217-- | Return a list of pairs of the names of the outermost 'Pi'-bound
1218-- variables in the given term, together with their types.
1219getArgTys :: TT n -> [(n, TT n)]
1220getArgTys (Bind n (PVar _) sc) = getArgTys sc
1221getArgTys (Bind n (PVTy _) sc) = getArgTys sc
1222getArgTys (Bind n (Pi _ t _) sc) = (n, t) : getArgTys sc
1223getArgTys _ = []
1225getRetTy :: TT n -> TT n
1226getRetTy (Bind n (PVar _) sc) = getRetTy sc
1227getRetTy (Bind n (PVTy _) sc) = getRetTy sc
1228getRetTy (Bind n (Pi _ _ _) sc) = getRetTy sc
1229getRetTy sc = sc
1231uniqueNameFrom :: [Name] -> [Name] -> Name
1232uniqueNameFrom [] hs = uniqueName (nextName (sUN "x")) hs
1233uniqueNameFrom (s : supply) hs
1234 | s `elem` hs = uniqueNameFrom supply hs
1235 | otherwise = s
1237uniqueName :: Name -> [Name] -> Name
1238uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
1239 | otherwise = n
1241uniqueNameSet :: Name -> Set Name -> Name
1242uniqueNameSet n hs | n `member` hs = uniqueNameSet (nextName n) hs
1243 | otherwise = n
1245uniqueBinders :: [Name] -> TT Name -> TT Name
1246uniqueBinders ns = ubSet (fromList ns) where
1247 ubSet ns (Bind n b sc)
1248 = let n' = uniqueNameSet n ns
1249 ns' = insert n' ns in
1250 Bind n' (fmap (ubSet ns') b) (ubSet ns' sc)
1251 ubSet ns (App f a) = App (ubSet ns f) (ubSet ns a)
1252 ubSet ns t = t
1255nextName (NS x s) = NS (nextName x) s
1256nextName (MN i n) = MN (i+1) n
1257nextName (UN x) = let (num', nm') = T.span isDigit (T.reverse x)
1258 nm = T.reverse nm'
1259 num = readN (T.reverse num') in
1260 UN (nm `T.append` txt (show (num+1)))
1261 where
1262 readN x | not (T.null x) = read (T.unpack x)
1263 readN x = 0
1264nextName (SN x) = SN (nextName' x)
1265 where
1266 nextName' (WhereN i f x) = WhereN i f (nextName x)
1267 nextName' (WithN i n) = WithN i (nextName n)
1268 nextName' (InstanceN n ns) = InstanceN (nextName n) ns
1269 nextName' (ParentN n ns) = ParentN (nextName n) ns
1270 nextName' (CaseN n) = CaseN (nextName n)
1271 nextName' (ElimN n) = ElimN (nextName n)
1272 nextName' (MethodN n) = MethodN (nextName n)
1273 nextName' (InstanceCtorN n) = InstanceCtorN (nextName n)
1275type Term = TT Name
1276type Type = Term
1278type Env = EnvTT Name
1280-- | an environment with de Bruijn indices 'normalised' so that they all refer to
1281-- this environment
1283newtype WkEnvTT n = Wk (EnvTT n)
1284type WkEnv = WkEnvTT Name
1286instance (Eq n, Show n) => Show (TT n) where
1287 show t = showEnv [] t
1289itBitsName IT8 = "Bits8"
1290itBitsName IT16 = "Bits16"
1291itBitsName IT32 = "Bits32"
1292itBitsName IT64 = "Bits64"
1294instance Show Const where
1295 show (I i) = show i
1296 show (BI i) = show i
1297 show (Fl f) = show f
1298 show (Ch c) = show c
1299 show (Str s) = show s
1300 show (B8 x) = show x
1301 show (B16 x) = show x
1302 show (B32 x) = show x
1303 show (B64 x) = show x
1304 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1305 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1306 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1307 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1308 show (AType ATFloat) = "Float"
1309 show (AType (ATInt ITBig)) = "Integer"
1310 show (AType (ATInt ITNative)) = "Int"
1311 show (AType (ATInt ITChar)) = "Char"
1312 show (AType (ATInt (ITFixed it))) = itBitsName it
1313 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
1314 show TheWorld = "prim__TheWorld"
1315 show WorldType = "prim__WorldType"
1316 show StrType = "String"
1317 show BufferType = "prim__UnsafeBuffer"
1318 show PtrType = "Ptr"
1319 show ManagedPtrType = "ManagedPtr"
1320 show VoidType = "Void"
1322showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String
1323showEnv env t = showEnv' env t False
1324showEnvDbg env t = showEnv' env t True
1326prettyEnv env t = prettyEnv' env t False
1327 where
1328 prettyEnv' env t dbg = prettySe 10 env t dbg
1330 bracket outer inner p
1331 | inner > outer = lparen <> p <> rparen
1332 | otherwise = p
1334 prettySe p env (P nt n t) debug =
1335 pretty n <+>
1336 if debug then
1337 lbracket <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbracket
1338 else
1339 empty
1340 prettySe p env (V i) debug
1341 | i < length env =
1342 if debug then
1343 text . show . fst $ env!!i
1344 else
1345 lbracket <+> text (show i) <+> rbracket
1346 | otherwise = text "unbound" <+> text (show i) <+> text "!"
1347 prettySe p env (Bind n b@(Pi _ t _) sc) debug
1348 | noOccurrence n sc && not debug =
1349 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1350 prettySe p env (Bind n b sc) debug =
1351 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1352 prettySe p env (App f a) debug =
1353 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
1354 prettySe p env (Proj x i) debug =
1355 prettySe 1 env x debug <+> text ("!" ++ show i)
1356 prettySe p env (Constant c) debug = pretty c
1357 prettySe p env Erased debug = text "[_]"
1358 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
1360 -- Render a `Binder` and its name
1361 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
1362 prettySb env n (Hole t) = prettyB env "?defer" "." n t
1363 prettySb env n (Pi _ t _) = prettyB env "(" ") ->" n t
1364 prettySb env n (PVar t) = prettyB env "pat" "." n t
1365 prettySb env n (PVTy t) = prettyB env "pty" "." n t
1366 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
1367 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
1369 -- Use `op` and `sc` to delimit `n` (a binding name) and its type
1370 -- declaration
1371 -- e.g. "λx : Int =>" for the Lam case
1372 prettyB env op sc n t debug =
1373 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
1375 -- Like `prettyB`, but handle the bindings that have values in addition
1376 -- to names and types
1377 prettyBv env op sc n t v debug =
1378 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
1379 prettySe 10 env v debug <> text sc
1382showEnv' env t dbg = se 10 env t where
1383 se p env (P nt n t) = show n
1384 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
1385 se p env (V i) | i < length env && i >= 0
1386 = (show $ fst $ env!!i) ++
1387 if dbg then "{" ++ show i ++ "}" else ""
1388 | otherwise = "!!V " ++ show i ++ "!!"
1389 se p env (Bind n b@(Pi (Just _) t k) sc)
1390 = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1391 se p env (Bind n b@(Pi _ t k) sc)
1392 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ arrow k ++ se 10 ((n,b):env) sc
1393 where arrow (TType _) = " -> "
1394 arrow u = " [" ++ show u ++ "] -> "
1395 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1396 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
1397 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
1398 se p env (Constant c) = show c
1399 se p env Erased = "[__]"
1400 se p env Impossible = "[impossible]"
1401 se p env (TType i) = "Type " ++ show i
1402 se p env (UType u) = show u
1404 sb env n (Lam t) = showb env "\\ " " => " n t
1405 sb env n (Hole t) = showb env "? " ". " n t
1406 sb env n (GHole i t) = showb env "?defer " ". " n t
1407 sb env n (Pi (Just _) t _) = showb env "{" "} -> " n t
1408 sb env n (Pi _ t _) = showb env "(" ") -> " n t
1409 sb env n (PVar t) = showb env "pat " ". " n t
1410 sb env n (PVTy t) = showb env "pty " ". " n t
1411 sb env n (Let t v) = showbv env "let " " in " n t v
1412 sb env n (Guess t v) = showbv env "?? " " in " n t v
1414 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
1415 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
1416 se 10 env v ++ sc
1418 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
1419 | otherwise = str
1421-- | Check whether a term has any holes in it - impure if so
1422pureTerm :: TT Name -> Bool
1423pureTerm (App f a) = pureTerm f && pureTerm a
1424pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
1425 pureBinder (Hole _) = False
1426 pureBinder (Guess _ _) = False
1427 pureBinder (Let t v) = pureTerm t && pureTerm v
1428 pureBinder t = pureTerm (binderTy t)
1430 notClassName (MN _ c) | c == txt "class" = False
1431 notClassName _ = True
1433pureTerm _ = True
1435-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1436weakenTm :: Int -> TT n -> TT n
1437weakenTm i t = wk i 0 t
1438 where wk i min (V x) | x >= min = V (i + x)
1439 wk i m (App f a) = App (wk i m f) (wk i m a)
1440 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1441 wk i m t = t
1442 wkb i m t = fmap (wk i m) t
1444-- | Weaken an environment so that all the de Bruijn indices are correct according
1445-- to the latest bound variable
1447weakenEnv :: EnvTT n -> EnvTT n
1448weakenEnv env = wk (length env - 1) env
1449 where wk i [] = []
1450 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1451 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1452 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1453 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1455-- | Weaken every term in the environment by the given amount
1456weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1457weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1459-- | Gather up all the outer 'PVar's and 'Hole's in an expression and reintroduce
1460-- them in a canonical order
1461orderPats :: Term -> Term
1462orderPats tm = op [] tm
1463 where
1464 op [] (App f a) = App f (op [] a) -- for Infer terms
1466 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1467 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1468 op ps (Bind n (Pi i t k) sc) = op ((n, Pi i t k) : ps) sc
1469 op ps sc = bindAll (sortP ps) sc
1471 sortP ps = pick [] (reverse ps)
1473 pick acc [] = reverse acc
1474 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1476 insert n t [] = [(n, t)]
1477 insert n t ((n',t') : ps)
1478 | n `elem` (refsIn (binderTy t') ++
1479 concatMap refsIn (map (binderTy . snd) ps))
1480 = (n', t') : insert n t ps
1481 | otherwise = (n,t):(n',t'):ps
1483refsIn :: TT Name -> [Name]
1484refsIn (P _ n _) = [n]
1485refsIn (Bind n b t) = nub $ nb b ++ refsIn t
1486 where nb (Let t v) = nub (refsIn t) ++ nub (refsIn v)
1487 nb (Guess t v) = nub (refsIn t) ++ nub (refsIn v)
1488 nb t = refsIn (binderTy t)
1489refsIn (App f a) = nub (refsIn f ++ refsIn a)
1490refsIn _ = []
1492-- Make sure all the pattern bindings are as far out as possible
1493liftPats :: Term -> Term
1494liftPats tm = let (tm', ps) = runState (getPats tm) [] in
1495 orderPats $ bindPats (reverse ps) tm'
1496 where
1497 bindPats [] tm = tm
1498 bindPats ((n, t):ps) tm
1499 | n `notElem` map fst ps = Bind n (PVar t) (bindPats ps tm)
1500 | otherwise = bindPats ps tm
1502 getPats :: Term -> State [(Name, Type)] Term
1503 getPats (Bind n (PVar t) sc) = do ps <- get
1504 put ((n, t) : ps)
1505 getPats sc
1506 getPats (Bind n (Guess t v) sc) = do t' <- getPats t
1507 v' <- getPats v
1508 sc' <- getPats sc
1509 return (Bind n (Guess t' v') sc')
1510 getPats (Bind n (Let t v) sc) = do t' <- getPats t
1511 v' <- getPats v
1512 sc' <- getPats sc
1513 return (Bind n (Let t' v') sc')
1514 getPats (Bind n (Pi i t k) sc) = do t' <- getPats t
1515 k' <- getPats k
1516 sc' <- getPats sc
1517 return (Bind n (Pi i t' k') sc')
1518 getPats (Bind n (Lam t) sc) = do t' <- getPats t
1519 sc' <- getPats sc
1520 return (Bind n (Lam t') sc')
1521 getPats (Bind n (Hole t) sc) = do t' <- getPats t
1522 sc' <- getPats sc
1523 return (Bind n (Hole t') sc')
1526 getPats (App f a) = do f' <- getPats f
1527 a' <- getPats a
1528 return (App f' a')
1529 getPats t = return t
1531allTTNames :: Eq n => TT n -> [n]
1532allTTNames = nub . allNamesIn
1533 where allNamesIn (P _ n _) = [n]
1534 allNamesIn (Bind n b t) = [n] ++ nb b ++ allNamesIn t
1535 where nb (Let t v) = allNamesIn t ++ allNamesIn v
1536 nb (Guess t v) = allNamesIn t ++ allNamesIn v
1537 nb t = allNamesIn (binderTy t)
1538 allNamesIn (App f a) = allNamesIn f ++ allNamesIn a
1539 allNamesIn _ = []
1542-- | Pretty-print a term
1543pprintTT :: [Name] -- ^ The bound names (for highlighting and de Bruijn indices)
1544 -> TT Name -- ^ The term to be printed
1545 -> Doc OutputAnnotation
1546pprintTT bound tm = pp startPrec bound tm
1548 where
1549 startPrec = 0
1550 appPrec = 10
1552 pp p bound (P Bound n ty) = annotate (AnnBoundName n False) (text $ show n)
1553 pp p bound (P nt n ty) = annotate (AnnName n Nothing Nothing Nothing)
1554 (text $ show n)
1555 pp p bound (V i)
1556 | i < length bound = let n = bound !! i
1557 in annotate (AnnBoundName n False) (text $ show n)
1558 | otherwise = text ("{{{V" ++ show i ++ "}}}")
1559 pp p bound (Bind n b sc) = ppb p bound n b $
1560 pp startPrec (n:bound) sc
1561 pp p bound (App tm1 tm2) =
1562 bracket p appPrec . group . hang 2 $
1563 pp appPrec bound tm1 <> line <>
1564 pp (appPrec + 1) bound tm2
1565 pp p bound (Constant c) = annotate (AnnConst c) (text (show c))
1566 pp p bound (Proj tm i) =
1567 lparen <> pp startPrec bound tm <> rparen <>
1568 text "!" <> text (show i)
1569 pp p bound Erased = text "<<<erased>>>"
1570 pp p bound Impossible = text "<<<impossible>>>"
1571 pp p bound (TType ue) = annotate (AnnType "Type" "The type of types") $
1572 text "Type"
1573 pp p bound (UType u) = text (show u)
1575 ppb p bound n (Lam ty) sc =
1576 bracket p startPrec . group . align . hang 2 $
1577 text "λ" <+> bindingOf n False <+> text "." <> line <> sc
1578 ppb p bound n (Pi _ ty k) sc =
1579 bracket p startPrec . group . align $
1580 lparen <> (bindingOf n False) <+> colon <+>
1581 (group . align) (pp startPrec bound ty) <>
1582 rparen <+> mkArrow k <> line <> sc
1583 where mkArrow (UType UniqueType) = text "⇴"
1584 mkArrow (UType NullType) = text "⥛"
1585 mkArrow _ = text "→"
1586 ppb p bound n (Let ty val) sc =
1587 bracket p startPrec . group . align $
1588 (group . hang 2) (annotate AnnKeyword (text "let") <+>
1589 bindingOf n False <+> colon <+>
1590 pp startPrec bound ty <+>
1591 text "=" <> line <>
1592 pp startPrec bound val) <> line <>
1593 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1594 ppb p bound n (NLet ty val) sc =
1595 bracket p startPrec . group . align $
1596 (group . hang 2) (annotate AnnKeyword (text "nlet") <+>
1597 bindingOf n False <+> colon <+>
1598 pp startPrec bound ty <+>
1599 text "=" <> line <>
1600 pp startPrec bound val) <> line <>
1601 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1602 ppb p bound n (Hole ty) sc =
1603 bracket p startPrec . group . align . hang 2 $
1604 text "?" <+> bindingOf n False <+> text "." <> line <> sc
1605 ppb p bound n (GHole _ ty) sc =
1606 bracket p startPrec . group . align . hang 2 $
1607 text "¿" <+> bindingOf n False <+> text "." <> line <> sc
1608 ppb p bound n (Guess ty val) sc =
1609 bracket p startPrec . group . align . hang 2 $
1610 text "?" <> bindingOf n False <+>
1611 text "≈" <+> pp startPrec bound val <+>
1612 text "." <> line <> sc
1613 ppb p bound n (PVar ty) sc =
1614 bracket p startPrec . group . align . hang 2 $
1615 annotate AnnKeyword (text "pat") <+>
1616 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1617 text "." <> line <>
1618 sc
1619 ppb p bound n (PVTy ty) sc =
1620 bracket p startPrec . group . align . hang 2 $
1621 annotate AnnKeyword (text "patTy") <+>
1622 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1623 text "." <> line <>
1624 sc
1626 bracket outer inner doc
1627 | outer > inner = lparen <> doc <> rparen
1628 | otherwise = doc
1631-- | Pretty-printer helper for the binding site of a name
1632bindingOf :: Name -- ^^ the bound name
1633 -> Bool -- ^^ whether the name is implicit
1634 -> Doc OutputAnnotation
1635bindingOf n imp = annotate (AnnBoundName n imp) (text (show n))