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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"
428 showCG' (InstanceCtorN n) = showCG n ++ "_ictor"
429showCG NErased = "_"
432-- |Contexts allow us to map names to things. A root name maps to a collection
433-- of things in different namespaces with that name.
434type Ctxt a = Map.Map Name (Map.Map Name a)
435emptyContext = Map.empty
437mapCtxt :: (a -> b) -> Ctxt a -> Ctxt b
438mapCtxt = fmap . fmap
440-- |Return True if the argument 'Name' should be interpreted as the name of a
441-- typeclass.
442tcname (UN xs) | T.null xs = False
443 | otherwise = T.head xs == '@'
444tcname (NS n _) = tcname n
445tcname (SN (InstanceN _ _)) = True
446tcname (SN (MethodN _)) = True
447tcname (SN (ParentN _ _)) = True
448tcname _ = False
450implicitable (NS n _) = implicitable n
451implicitable (UN xs) | T.null xs = False
452 | otherwise = isLower (T.head xs) || T.head xs == '_'
453implicitable (MN _ x) = not (tnull x) && thead x /= '_'
454implicitable _ = False
456nsroot (NS n _) = n
457nsroot n = n
459-- this will overwrite already existing definitions
460addDef :: Name -> a -> Ctxt a -> Ctxt a
461addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
462 Nothing -> Map.insert (nsroot n)
463 (Map.insert n v Map.empty) ctxt
464 Just xs -> Map.insert (nsroot n)
465 (Map.insert n v xs) ctxt
467{-| Look up a name in the context, given an optional namespace.
468 The name (n) may itself have a (partial) namespace given.
470 Rules for resolution:
472 - if an explicit namespace is given, return the names which match it. If none
473 match, return all names.
475 - if the name has has explicit namespace given, return the names which match it
476 and ignore the given namespace.
478 - otherwise, return all names.
480-}
482lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
483lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
484 Just xs -> filterNS (Map.toList xs)
485 Nothing -> []
486 where
487 filterNS [] = []
488 filterNS ((found, v) : xs)
489 | nsmatch n found = (found, v) : filterNS xs
490 | otherwise = filterNS xs
492 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
493 nsmatch (NS _ _) _ = False
494 nsmatch looking found = True
496lookupCtxt :: Name -> Ctxt a -> [a]
497lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
499lookupCtxtExact :: Name -> Ctxt a -> Maybe a
500lookupCtxtExact n ctxt = listToMaybe [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
502deleteDefExact :: Name -> Ctxt a -> Ctxt a
503deleteDefExact n = Map.adjust (Map.delete n) (nsroot n)
505updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
506updateDef n f ctxt
507 = let ds = lookupCtxtName n ctxt in
508 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
510toAlist :: Ctxt a -> [(Name, a)]
511toAlist ctxt = let allns = map snd (Map.toList ctxt) in
512 concatMap (Map.toList) allns
514addAlist :: [(Name, a)] -> Ctxt a -> Ctxt a
515addAlist [] ctxt = ctxt
516addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
518data NativeTy = IT8 | IT16 | IT32 | IT64
519 deriving (Show, Eq, Ord, Enum, Data, Typeable)
521instance Pretty NativeTy OutputAnnotation where
522 pretty IT8 = text "Bits8"
523 pretty IT16 = text "Bits16"
524 pretty IT32 = text "Bits32"
525 pretty IT64 = text "Bits64"
527data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
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"
536data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors https://github.com/idris-lang/Idris-dev/issues/1723
537 deriving (Show, Eq, Ord, Data, Typeable)
538{-!
539deriving instance NFData IntTy
540deriving instance NFData NativeTy
541deriving instance NFData ArithTy
542!-}
544instance Pretty ArithTy OutputAnnotation where
545 pretty (ATInt ITNative) = text "Int"
546 pretty (ATInt ITBig) = text "BigInt"
547 pretty (ATInt ITChar) = text "Char"
548 pretty (ATInt (ITFixed n)) = pretty n
549 pretty ATFloat = text "Float"
551nativeTyWidth :: NativeTy -> Int
552nativeTyWidth IT8 = 8
553nativeTyWidth IT16 = 16
554nativeTyWidth IT32 = 32
555nativeTyWidth IT64 = 64
557{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
558intTyWidth :: IntTy -> Int
559intTyWidth (ITFixed n) = nativeTyWidth n
560intTyWidth ITNative = 8 * sizeOf (0 :: Int)
561intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
562intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
564data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
565 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
566 | AType ArithTy | StrType
567 | WorldType | TheWorld
568 | VoidType | Forgot
569 deriving (Eq, Ord, Data, Typeable)
570{-!
571deriving instance Binary Const
572deriving instance NFData Const
573!-}
575isTypeConst :: Const -> Bool
576isTypeConst (AType _) = True
577isTypeConst StrType = True
578isTypeConst WorldType = True
579isTypeConst VoidType = True
580isTypeConst _ = False
582instance Sized Const where
583 size _ = 1
585instance Pretty Const OutputAnnotation where
586 pretty (I i) = text . show $ i
587 pretty (BI i) = text . show $ i
588 pretty (Fl f) = text . show $ f
589 pretty (Ch c) = text . show $ c
590 pretty (Str s) = text s
591 pretty (AType a) = pretty a
592 pretty StrType = text "String"
593 pretty TheWorld = text "%theWorld"
594 pretty WorldType = text "prim__World"
595 pretty VoidType = text "Void"
596 pretty Forgot = text "Forgot"
597 pretty (B8 w) = text . show $ w
598 pretty (B16 w) = text . show $ w
599 pretty (B32 w) = text . show $ w
600 pretty (B64 w) = text . show $ w
602-- | Determines whether the input constant represents a type
603constIsType :: Const -> Bool
604constIsType (I _) = False
605constIsType (BI _) = False
606constIsType (Fl _) = False
607constIsType (Ch _) = False
608constIsType (Str _) = False
609constIsType (B8 _) = False
610constIsType (B16 _) = False
611constIsType (B32 _) = False
612constIsType (B64 _) = False
613constIsType _ = True
615-- | Get the docstring for a Const
616constDocs :: Const -> String
617constDocs c@(AType (ATInt ITBig)) = "Arbitrary-precision integers"
618constDocs c@(AType (ATInt ITNative)) = "Fixed-precision integers of undefined size"
619constDocs c@(AType (ATInt ITChar)) = "Characters in some unspecified encoding"
620constDocs c@(AType ATFloat) = "Double-precision floating-point numbers"
621constDocs StrType = "Strings in some unspecified encoding"
622constDocs c@(AType (ATInt (ITFixed IT8))) = "Eight bits (unsigned)"
623constDocs c@(AType (ATInt (ITFixed IT16))) = "Sixteen bits (unsigned)"
624constDocs c@(AType (ATInt (ITFixed IT32))) = "Thirty-two bits (unsigned)"
625constDocs c@(AType (ATInt (ITFixed IT64))) = "Sixty-four bits (unsigned)"
626constDocs (Fl f) = "A float"
627constDocs (I i) = "A fixed-precision integer"
628constDocs (BI i) = "An arbitrary-precision integer"
629constDocs (Str s) = "A string of length " ++ show (length s)
630constDocs (Ch c) = "A character"
631constDocs (B8 w) = "The eight-bit value 0x" ++
632 showIntAtBase 16 intToDigit w ""
633constDocs (B16 w) = "The sixteen-bit value 0x" ++
634 showIntAtBase 16 intToDigit w ""
635constDocs (B32 w) = "The thirty-two-bit value 0x" ++
636 showIntAtBase 16 intToDigit w ""
637constDocs (B64 w) = "The sixty-four-bit value 0x" ++
638 showIntAtBase 16 intToDigit w ""
639constDocs prim = "Undocumented"
641data Universe = NullType | UniqueType | AllTypes
642 deriving (Eq, Ord, Data, Typeable)
644instance Show Universe where
645 show UniqueType = "UniqueType"
646 show NullType = "NullType"
647 show AllTypes = "Type*"
649data Raw = Var Name
650 | RBind Name (Binder Raw) Raw
651 | RApp Raw Raw
652 | RType
653 | RUType Universe
654 | RForce Raw
655 | RConstant Const
656 deriving (Show, Eq, Data, Typeable)
658instance Sized Raw where
659 size (Var name) = 1
660 size (RBind name bind right) = 1 + size bind + size right
661 size (RApp left right) = 1 + size left + size right
662 size RType = 1
663 size (RUType _) = 1
664 size (RForce raw) = 1 + size raw
665 size (RConstant const) = size const
667instance Pretty Raw OutputAnnotation where
668 pretty = text . show
670{-!
671deriving instance Binary Raw
672deriving instance NFData Raw
673!-}
675data ImplicitInfo = Impl { tcinstance :: Bool }
676 deriving (Show, Eq, Ord, Data, Typeable)
678{-!
679deriving instance Binary ImplicitInfo
680deriving instance NFData ImplicitInfo
681!-}
683-- The type parameter `b` will normally be something like `TT Name` or just
684-- `Raw`. We do not make a type-level distinction between TT terms that happen
685-- to be TT types and TT terms that are not TT types.
686-- | All binding forms are represented in a uniform fashion. This type only represents
687-- the types of bindings (and their values, if any); the attached identifiers are part
688-- of the 'Bind' constructor for the 'TT' type.
689data Binder b = Lam { binderTy :: !b {-^ type annotation for bound variable-}}
690 | Pi { binderImpl :: Maybe ImplicitInfo,
691 binderTy :: !b,
692 binderKind :: !b }
693 {-^ A binding that occurs in a function type expression, e.g. @(x:Int) -> ...@
694 The 'binderImpl' flag says whether it was a scoped implicit
695 (i.e. forall bound) in the high level Idris, but otherwise
696 has no relevance in TT. -}
697 | Let { binderTy :: !b,
698 binderVal :: b {-^ value for bound variable-}}
699 -- ^ A binding that occurs in a @let@ expression
700 | NLet { binderTy :: !b,
701 binderVal :: b }
702 | Hole { binderTy :: !b}
703 | GHole { envlen :: Int,
704 binderTy :: !b}
705 | Guess { binderTy :: !b,
706 binderVal :: b }
707 | PVar { binderTy :: !b }
708 -- ^ A pattern variable
709 | PVTy { binderTy :: !b }
710 deriving (Show, Eq, Ord, Functor, Foldable, Traversable, Data, Typeable)
711{-!
712deriving instance Binary Binder
713deriving instance NFData Binder
714!-}
716instance Sized a => Sized (Binder a) where
717 size (Lam ty) = 1 + size ty
718 size (Pi _ ty _) = 1 + size ty
719 size (Let ty val) = 1 + size ty + size val
720 size (NLet ty val) = 1 + size ty + size val
721 size (Hole ty) = 1 + size ty
722 size (GHole _ ty) = 1 + size ty
723 size (Guess ty val) = 1 + size ty + size val
724 size (PVar ty) = 1 + size ty
725 size (PVTy ty) = 1 + size ty
727fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
728fmapMB f (Let t v) = liftM2 Let (f t) (f v)
729fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
730fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
731fmapMB f (Lam t) = liftM Lam (f t)
732fmapMB f (Pi i t k) = liftM2 (Pi i) (f t) (f k)
733fmapMB f (Hole t) = liftM Hole (f t)
734fmapMB f (GHole i t) = liftM (GHole i) (f t)
735fmapMB f (PVar t) = liftM PVar (f t)
736fmapMB f (PVTy t) = liftM PVTy (f t)
738raw_apply :: Raw -> [Raw] -> Raw
739raw_apply f [] = f
740raw_apply f (a : as) = raw_apply (RApp f a) as
742raw_unapply :: Raw -> (Raw, [Raw])
743raw_unapply t = ua [] t where
744 ua args (RApp f a) = ua (a:args) f
745 ua args t = (t, args)
747-- WELL TYPED TERMS ---------------------------------------------------------
749-- | Universe expressions for universe checking
750data UExp = UVar Int -- ^ universe variable
751 | UVal Int -- ^ explicit universe level
752 deriving (Eq, Ord, Data, Typeable)
753{-!
754deriving instance NFData UExp
755!-}
757instance Sized UExp where
758 size _ = 1
760instance Show UExp where
761 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
762 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
763 show (UVal x) = show x
764-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
766-- | Universe constraints
767data UConstraint = ULT UExp UExp -- ^ Strictly less than
768 | ULE UExp UExp -- ^ Less than or equal to
769 deriving (Eq, Ord)
771data ConstraintFC = ConstraintFC { uconstraint :: UConstraint,
772 ufc :: FC }
773 deriving Show
775instance Eq ConstraintFC where
776 x == y = uconstraint x == uconstraint y
778instance Ord ConstraintFC where
779 compare x y = compare (uconstraint x) (uconstraint y)
781instance Show UConstraint where
782 show (ULT x y) = show x ++ " < " ++ show y
783 show (ULE x y) = show x ++ " <= " ++ show y
785type UCs = (Int, [UConstraint])
787data NameType = Bound
788 | Ref
789 | DCon {nt_tag :: Int, nt_arity :: Int, nt_unique :: Bool} -- ^ Data constructor
790 | TCon {nt_tag :: Int, nt_arity :: Int} -- ^ Type constructor
791 deriving (Show, Ord, Data, Typeable)
792{-!
793deriving instance Binary NameType
794deriving instance NFData NameType
795!-}
797instance Sized NameType where
798 size _ = 1
800instance Pretty NameType OutputAnnotation where
801 pretty = text . show
803instance Eq NameType where
804 Bound == Bound = True
805 Ref == Ref = True
806 DCon _ a _ == DCon _ b _ = (a == b) -- ignore tag
807 TCon _ a == TCon _ b = (a == b) -- ignore tag
808 _ == _ = False
810-- | Terms in the core language. The type parameter is the type of
811-- identifiers used for bindings and explicit named references;
812-- usually we use @TT 'Name'@.
813data TT n = P NameType n (TT n) -- ^ named references with type
814 -- (P for "Parameter", motivated by McKinna and Pollack's
815 -- Pure Type Systems Formalized)
816 | V !Int -- ^ a resolved de Bruijn-indexed variable
817 | Bind n !(Binder (TT n)) (TT n) -- ^ a binding
818 | App !(TT n) (TT n) -- ^ function, function type, arg
819 | Constant Const -- ^ constant
820 | Proj (TT n) !Int -- ^ argument projection; runtime only
821 -- (-1) is a special case for 'subtract one from BI'
822 | Erased -- ^ an erased term
823 | Impossible -- ^ special case for totality checking
824 | TType UExp -- ^ the type of types at some level
825 | UType Universe -- ^ Uniqueness type universe (disjoint from TType)
826 deriving (Ord, Functor, Data, Typeable)
827{-!
828deriving instance Binary TT
829deriving instance NFData TT
830!-}
832class TermSize a where
833 termsize :: Name -> a -> Int
835instance TermSize a => TermSize [a] where
836 termsize n [] = 0
837 termsize n (x : xs) = termsize n x + termsize n xs
839instance TermSize (TT Name) where
840 termsize n (P _ n' _)
841 | n' == n = 1000000 -- recursive => really big
842 | otherwise = 1
843 termsize n (V _) = 1
844 -- for `Bind` terms, we can erroneously declare a term
845 -- "recursive => really big" if the name of the bound
846 -- variable is the same as the name we're using
847 -- So generate a different name in that case.
848 termsize n (Bind n' (Let t v) sc)
849 = let rn = if n == n' then sMN 0 "noname" else n in
850 termsize rn v + termsize rn sc
851 termsize n (Bind n' b sc)
852 = let rn = if n == n' then sMN 0 "noname" else n in
853 termsize rn sc
854 termsize n (App f a) = termsize n f + termsize n a
855 termsize n (Proj t i) = termsize n t
856 termsize n _ = 1
858instance Sized a => Sized (TT a) where
859 size (P name n trm) = 1 + size name + size n + size trm
860 size (V v) = 1
861 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
862 size (App l r) = 1 + size l + size r
863 size (Constant c) = size c
864 size Erased = 1
865 size (TType u) = 1 + size u
867instance Pretty a o => Pretty (TT a) o where
868 pretty _ = text "test"
870type EnvTT n = [(n, Binder (TT n))]
872data Datatype n = Data { d_typename :: n,
873 d_typetag :: Int,
874 d_type :: (TT n),
875 d_unique :: Bool,
876 d_cons :: [(n, TT n)] }
877 deriving (Show, Functor, Eq)
879instance Eq n => Eq (TT n) where
880 (==) (P xt x _) (P yt y _) = x == y
881 (==) (V x) (V y) = x == y
882 (==) (Bind _ xb xs) (Bind _ yb ys) = xs == ys && xb == yb
883 (==) (App fx ax) (App fy ay) = ax == ay && fx == fy
884 (==) (TType _) (TType _) = True -- deal with constraints later
885 (==) (Constant x) (Constant y) = x == y
886 (==) (Proj x i) (Proj y j) = x == y && i == j
887 (==) Erased _ = True
888 (==) _ Erased = True
889 (==) _ _ = False
891-- * A few handy operations on well typed terms:
893-- | A term is injective iff it is a data constructor, type constructor,
894-- constant, the type Type, pi-binding, or an application of an injective
895-- term.
896isInjective :: TT n -> Bool
897isInjective (P (DCon _ _ _) _ _) = True
898isInjective (P (TCon _ _) _ _) = True
899isInjective (Constant _) = True
900isInjective (TType x) = True
901isInjective (Bind _ (Pi _ _ _) sc) = True
902isInjective (App f a) = isInjective f
903isInjective _ = False
905-- | Count the number of instances of a de Bruijn index in a term
906vinstances :: Int -> TT n -> Int
907vinstances i (V x) | i == x = 1
908vinstances i (App f a) = vinstances i f + vinstances i a
909vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
910 where instancesB (Let t v) = vinstances i v
911 instancesB _ = 0
912vinstances i t = 0
914-- | Replace the outermost (index 0) de Bruijn variable with the given term
915instantiate :: TT n -> TT n -> TT n
916instantiate e = subst 0 where
917 subst i (P nt x ty) = P nt x (subst i ty)
918 subst i (V x) | i == x = e
919 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
920 subst i (App f a) = App (subst i f) (subst i a)
921 subst i (Proj x idx) = Proj (subst i x) idx
922 subst i t = t
924-- | As 'instantiate', but also decrement the indices of all de Bruijn variables
925-- remaining in the term, so that there are no more references to the variable
926-- that has been substituted.
927substV :: TT n -> TT n -> TT n
928substV x tm = dropV 0 (instantiate x tm) where
929 subst i (P nt x ty) = P nt x (subst i ty)
930 dropV i (V x) | x > i = V (x - 1)
931 | otherwise = V x
932 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
933 dropV i (App f a) = App (dropV i f) (dropV i a)
934 dropV i (Proj x idx) = Proj (dropV i x) idx
935 dropV i t = t
937-- | Replace all non-free de Bruijn references in the given term with references
938-- to the name of their binding.
939explicitNames :: TT n -> TT n
940explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
941 Bind x b'
942 (explicitNames (instantiate
943 (P Bound x (binderTy b')) sc))
944explicitNames (App f a) = App (explicitNames f) (explicitNames a)
945explicitNames (Proj x idx) = Proj (explicitNames x) idx
946explicitNames t = t
948-- | Replace references to the given 'Name'-like id with references to
949-- de Bruijn index 0.
950pToV :: Eq n => n -> TT n -> TT n
951pToV n = pToV' n 0
952pToV' n i (P _ x _) | n == x = V i
953pToV' n i (Bind x b sc)
954-- We can assume the inner scope has been pToVed already, so continue to
955-- resolve names from the *outer* scope which may happen to have the same id.
956 | n == x = Bind x (fmap (pToV' n i) b) sc
957 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
958pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
959pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
960pToV' n i t = t
962-- increase de Bruijn indices, as if a binder has been added
963addBinder :: TT n -> TT n
964addBinder t = ab 0 t
965 where
966 ab top (V i) | i >= top = V (i + 1)
967 | otherwise = V i
968 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
969 ab top (App f a) = App (ab top f) (ab top a)
970 ab top (Proj t idx) = Proj (ab top t) idx
971 ab top t = t
973-- | Convert several names. First in the list comes out as V 0
974pToVs :: Eq n => [n] -> TT n -> TT n
975pToVs ns tm = pToVs' ns tm 0 where
976 pToVs' [] tm i = tm
977 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
979-- | Replace de Bruijn indices in the given term with explicit references to
980-- the names of the bindings they refer to. It is an error if the given term
981-- contains free de Bruijn indices.
982vToP :: TT n -> TT n
983vToP = vToP' [] where
984 vToP' env (V i) = let (n, b) = (env !! i) in
985 P Bound n (binderTy b)
986 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
987 Bind n b' (vToP' ((n, b'):env) sc)
988 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
989 vToP' env t = t
991-- | Replace every non-free reference to the name of a binding in
992-- the given term with a de Bruijn index.
993finalise :: Eq n => TT n -> TT n
994finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
995finalise (App f a) = App (finalise f) (finalise a)
996finalise t = t
998-- Once we've finished checking everything about a term we no longer need
999-- the type on the 'P' so erase it so save memory
1001pEraseType :: TT n -> TT n
1002pEraseType (P nt t _) = P nt t Erased
1003pEraseType (App f a) = App (pEraseType f) (pEraseType a)
1004pEraseType (Bind n b sc) = Bind n (fmap pEraseType b) (pEraseType sc)
1005pEraseType t = t
1007-- | As 'instantiate', but in addition to replacing @'V' 0@,
1008-- replace references to the given 'Name'-like id.
1009subst :: Eq n => n {-^ The id to replace -} ->
1010 TT n {-^ The replacement term -} ->
1011 TT n {-^ The term to replace in -} ->
1012 TT n
1013-- subst n v tm = instantiate v (pToV n tm)
1014subst n v tm = fst $ subst' 0 tm
1015 where
1016 -- keep track of updates to save allocations - this is a big win on
1017 -- large terms in particular
1018 -- ('Maybe' would be neater here, but >>= is not the right combinator.
1019 -- Feel free to tidy up, as long as it still saves allocating when no
1020 -- substitution happens...)
1021 subst' i (V x) | i == x = (v, True)
1022 subst' i (P _ x _) | n == x = (v, True)
1023 subst' i t@(P nt x ty)
1024 = let (ty', ut) = subst' i ty in
1025 if ut then (P nt x ty', True) else (t, False)
1026 subst' i t@(Bind x b sc) | x /= n
1027 = let (b', ub) = substB' i b
1028 (sc', usc) = subst' (i+1) sc in
1029 if ub || usc then (Bind x b' sc', True) else (t, False)
1030 subst' i t@(App f a) = let (f', uf) = subst' i f
1031 (a', ua) = subst' i a in
1032 if uf || ua then (App f' a', True) else (t, False)
1033 subst' i t@(Proj x idx) = let (x', u) = subst' i x in
1034 if u then (Proj x' idx, u) else (t, False)
1035 subst' i t = (t, False)
1037 substB' i b@(Let t v) = let (t', ut) = subst' i t
1038 (v', uv) = subst' i v in
1039 if ut || uv then (Let t' v', True)
1040 else (b, False)
1041 substB' i b@(Guess t v) = let (t', ut) = subst' i t
1042 (v', uv) = subst' i v in
1043 if ut || uv then (Guess t' v', True)
1044 else (b, False)
1045 substB' i b = let (ty', u) = subst' i (binderTy b) in
1046 if u then (b { binderTy = ty' }, u) else (b, False)
1048-- If there are no Vs in the term (i.e. in proof state)
1049psubst :: Eq n => n -> TT n -> TT n -> TT n
1050psubst n v tm = s' 0 tm where
1051 s' i (V x) | x > i = V (x - 1)
1052 | x == i = v
1053 | otherwise = V x
1054 s' i (P _ x _) | n == x = v
1055 s' i (Bind x b sc) | n == x = Bind x (fmap (s' i) b) sc
1056 | otherwise = Bind x (fmap (s' i) b) (s' (i+1) sc)
1057 s' i (App f a) = App (s' i f) (s' i a)
1058 s' i (Proj t idx) = Proj (s' i t) idx
1059 s' i t = t
1061-- | As 'subst', but takes a list of (name, substitution) pairs instead
1062-- of a single name and substitution
1063substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
1064substNames [] t = t
1065substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
1067-- | Replaces all terms equal (in the sense of @(==)@) to
1068-- the old term with the new term.
1069substTerm :: Eq n => TT n {-^ Old term -} ->
1070 TT n {-^ New term -} ->
1071 TT n {-^ template term -}
1072 -> TT n
1073substTerm old new = st where
1074 st t | t == old = new
1075 st (App f a) = App (st f) (st a)
1076 st (Bind x b sc) = Bind x (fmap st b) (st sc)
1077 st t = t
1079-- | Return number of occurrences of V 0 or bound name i the term
1080occurrences :: Eq n => n -> TT n -> Int
1081occurrences n t = execState (no' 0 t) 0
1082 where
1083 no' i (V x) | i == x = do num <- get; put (num + 1)
1084 no' i (P Bound x _) | n == x = do num <- get; put (num + 1)
1085 no' i (Bind n b sc) = do noB' i b; no' (i+1) sc
1086 where noB' i (Let t v) = do no' i t; no' i v
1087 noB' i (Guess t v) = do no' i t; no' i v
1088 noB' i b = no' i (binderTy b)
1089 no' i (App f a) = do no' i f; no' i a
1090 no' i (Proj x _) = no' i x
1091 no' i _ = return ()
1093-- | Returns true if V 0 and bound name n do not occur in the term
1094noOccurrence :: Eq n => n -> TT n -> Bool
1095noOccurrence n t = no' 0 t
1096 where
1097 no' i (V x) = not (i == x)
1098 no' i (P Bound x _) = not (n == x)
1099 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
1100 where noB' i (Let t v) = no' i t && no' i v
1101 noB' i (Guess t v) = no' i t && no' i v
1102 noB' i b = no' i (binderTy b)
1103 no' i (App f a) = no' i f && no' i a
1104 no' i (Proj x _) = no' i x
1105 no' i _ = True
1107-- | Returns all names used free in the term
1108freeNames :: Eq n => TT n -> [n]
1109freeNames t = nub $ freeNames' t
1110 where
1111 freeNames' (P _ n _) = [n]
1112 freeNames' (Bind n (Let t v) sc) = freeNames' v ++ (freeNames' sc \\ [n])
1113 ++ freeNames' t
1114 freeNames' (Bind n b sc) = freeNames' (binderTy b) ++ (freeNames' sc \\ [n])
1115 freeNames' (App f a) = freeNames' f ++ freeNames' a
1116 freeNames' (Proj x i) = freeNames' x
1117 freeNames' _ = []
1119-- | Return the arity of a (normalised) type
1120arity :: TT n -> Int
1121arity (Bind n (Pi _ t _) sc) = 1 + arity sc
1122arity _ = 0
1124-- | Deconstruct an application; returns the function and a list of arguments
1125unApply :: TT n -> (TT n, [TT n])
1126unApply t = ua [] t where
1127 ua args (App f a) = ua (a:args) f
1128 ua args t = (t, args)
1130-- | Returns a term representing the application of the first argument
1131-- (a function) to every element of the second argument.
1132mkApp :: TT n -> [TT n] -> TT n
1133mkApp f [] = f
1134mkApp f (a:as) = mkApp (App f a) as
1136unList :: Term -> Maybe [Term]
1137unList tm = case unApply tm of
1138 (nil, [_]) -> Just []
1139 (cons, ([_, x, xs])) ->
1140 do rest <- unList xs
1141 return $ x:rest
1142 (f, args) -> Nothing
1144-- | Cast a 'TT' term to a 'Raw' value, discarding universe information and
1145-- the types of named references and replacing all de Bruijn indices
1146-- with the corresponding name. It is an error if there are free de
1147-- Bruijn indices.
1148forget :: TT Name -> Raw
1149forget tm = forgetEnv [] tm
1151safeForget :: TT Name -> Maybe Raw
1152safeForget tm = safeForgetEnv [] tm
1154forgetEnv :: [Name] -> TT Name -> Raw
1155forgetEnv env tm = case safeForgetEnv env tm of
1156 Just t' -> t'
1157 Nothing -> error $ "Scope error in " ++ show tm
1160safeForgetEnv :: [Name] -> TT Name -> Maybe Raw
1161safeForgetEnv env (P _ n _) = Just $ Var n
1162safeForgetEnv env (V i) | i < length env = Just $ Var (env !! i)
1163 | otherwise = Nothing
1164safeForgetEnv env (Bind n b sc)
1165 = do let n' = uniqueName n env
1166 b' <- safeForgetEnvB env b
1167 sc' <- safeForgetEnv (n':env) sc
1168 Just $ RBind n' b' sc'
1169 where safeForgetEnvB env (Let t v) = liftM2 Let (safeForgetEnv env t)
1170 (safeForgetEnv env v)
1171 safeForgetEnvB env (Guess t v) = liftM2 Guess (safeForgetEnv env t)
1172 (safeForgetEnv env v)
1173 safeForgetEnvB env b = do ty' <- safeForgetEnv env (binderTy b)
1174 Just $ fmap (\_ -> ty') b
1175safeForgetEnv env (App f a) = liftM2 RApp (safeForgetEnv env f) (safeForgetEnv env a)
1176safeForgetEnv env (Constant c) = Just $ RConstant c
1177safeForgetEnv env (TType i) = Just RType
1178safeForgetEnv env (UType u) = Just $ RUType u
1179safeForgetEnv env Erased = Just $ RConstant Forgot
1181-- | Introduce a 'Bind' into the given term for each element of the
1182-- given list of (name, binder) pairs.
1183bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
1184bindAll [] t = t
1185bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
1187-- | Like 'bindAll', but the 'Binder's are 'TT' terms instead.
1188-- The first argument is a function to map @TT@ terms to @Binder@s.
1189-- This function might often be something like 'Lam', which directly
1190-- constructs a @Binder@ from a @TT@ term.
1191bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
1192bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
1194-- | Return a list of pairs of the names of the outermost 'Pi'-bound
1195-- variables in the given term, together with their types.
1196getArgTys :: TT n -> [(n, TT n)]
1197getArgTys (Bind n (PVar _) sc) = getArgTys sc
1198getArgTys (Bind n (PVTy _) sc) = getArgTys sc
1199getArgTys (Bind n (Pi _ t _) sc) = (n, t) : getArgTys sc
1200getArgTys _ = []
1202getRetTy :: TT n -> TT n
1203getRetTy (Bind n (PVar _) sc) = getRetTy sc
1204getRetTy (Bind n (PVTy _) sc) = getRetTy sc
1205getRetTy (Bind n (Pi _ _ _) sc) = getRetTy sc
1206getRetTy sc = sc
1208uniqueNameFrom :: [Name] -> [Name] -> Name
1209uniqueNameFrom [] hs = uniqueName (nextName (sUN "x")) hs
1210uniqueNameFrom (s : supply) hs
1211 | s `elem` hs = uniqueNameFrom supply hs
1212 | otherwise = s
1214uniqueName :: Name -> [Name] -> Name
1215uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
1216 | otherwise = n
1218uniqueNameSet :: Name -> Set Name -> Name
1219uniqueNameSet n hs | n `member` hs = uniqueNameSet (nextName n) hs
1220 | otherwise = n
1222uniqueBinders :: [Name] -> TT Name -> TT Name
1223uniqueBinders ns = ubSet (fromList ns) where
1224 ubSet ns (Bind n b sc)
1225 = let n' = uniqueNameSet n ns
1226 ns' = insert n' ns in
1227 Bind n' (fmap (ubSet ns') b) (ubSet ns' sc)
1228 ubSet ns (App f a) = App (ubSet ns f) (ubSet ns a)
1229 ubSet ns t = t
1232nextName (NS x s) = NS (nextName x) s
1233nextName (MN i n) = MN (i+1) n
1234nextName (UN x) = let (num', nm') = T.span isDigit (T.reverse x)
1235 nm = T.reverse nm'
1236 num = readN (T.reverse num') in
1237 UN (nm `T.append` txt (show (num+1)))
1238 where
1239 readN x | not (T.null x) = read (T.unpack x)
1240 readN x = 0
1241nextName (SN x) = SN (nextName' x)
1242 where
1243 nextName' (WhereN i f x) = WhereN i f (nextName x)
1244 nextName' (WithN i n) = WithN i (nextName n)
1245 nextName' (InstanceN n ns) = InstanceN (nextName n) ns
1246 nextName' (ParentN n ns) = ParentN (nextName n) ns
1247 nextName' (CaseN n) = CaseN (nextName n)
1248 nextName' (ElimN n) = ElimN (nextName n)
1249 nextName' (MethodN n) = MethodN (nextName n)
1250 nextName' (InstanceCtorN n) = InstanceCtorN (nextName n)
1252type Term = TT Name
1253type Type = Term
1255type Env = EnvTT Name
1257-- | an environment with de Bruijn indices 'normalised' so that they all refer to
1258-- this environment
1260newtype WkEnvTT n = Wk (EnvTT n)
1261type WkEnv = WkEnvTT Name
1263instance (Eq n, Show n) => Show (TT n) where
1264 show t = showEnv [] t
1266itBitsName IT8 = "Bits8"
1267itBitsName IT16 = "Bits16"
1268itBitsName IT32 = "Bits32"
1269itBitsName IT64 = "Bits64"
1271instance Show Const where
1272 show (I i) = show i
1273 show (BI i) = show i
1274 show (Fl f) = show f
1275 show (Ch c) = show c
1276 show (Str s) = show s
1277 show (B8 x) = show x
1278 show (B16 x) = show x
1279 show (B32 x) = show x
1280 show (B64 x) = show x
1281 show (AType ATFloat) = "Float"
1282 show (AType (ATInt ITBig)) = "Integer"
1283 show (AType (ATInt ITNative)) = "Int"
1284 show (AType (ATInt ITChar)) = "Char"
1285 show (AType (ATInt (ITFixed it))) = itBitsName it
1286 show TheWorld = "prim__TheWorld"
1287 show WorldType = "prim__WorldType"
1288 show StrType = "String"
1289 show VoidType = "Void"
1291showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String
1292showEnv env t = showEnv' env t False
1293showEnvDbg env t = showEnv' env t True
1295prettyEnv env t = prettyEnv' env t False
1296 where
1297 prettyEnv' env t dbg = prettySe 10 env t dbg
1299 bracket outer inner p
1300 | inner > outer = lparen <> p <> rparen
1301 | otherwise = p
1303 prettySe p env (P nt n t) debug =
1304 pretty n <+>
1305 if debug then
1306 lbracket <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbracket
1307 else
1308 empty
1309 prettySe p env (V i) debug
1310 | i < length env =
1311 if debug then
1312 text . show . fst $ env!!i
1313 else
1314 lbracket <+> text (show i) <+> rbracket
1315 | otherwise = text "unbound" <+> text (show i) <+> text "!"
1316 prettySe p env (Bind n b@(Pi _ t _) sc) debug
1317 | noOccurrence n sc && not debug =
1318 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1319 prettySe p env (Bind n b sc) debug =
1320 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1321 prettySe p env (App f a) debug =
1322 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
1323 prettySe p env (Proj x i) debug =
1324 prettySe 1 env x debug <+> text ("!" ++ show i)
1325 prettySe p env (Constant c) debug = pretty c
1326 prettySe p env Erased debug = text "[_]"
1327 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
1329 -- Render a `Binder` and its name
1330 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
1331 prettySb env n (Hole t) = prettyB env "?defer" "." n t
1332 prettySb env n (Pi _ t _) = prettyB env "(" ") ->" n t
1333 prettySb env n (PVar t) = prettyB env "pat" "." n t
1334 prettySb env n (PVTy t) = prettyB env "pty" "." n t
1335 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
1336 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
1338 -- Use `op` and `sc` to delimit `n` (a binding name) and its type
1339 -- declaration
1340 -- e.g. "λx : Int =>" for the Lam case
1341 prettyB env op sc n t debug =
1342 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
1344 -- Like `prettyB`, but handle the bindings that have values in addition
1345 -- to names and types
1346 prettyBv env op sc n t v debug =
1347 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
1348 prettySe 10 env v debug <> text sc
1351showEnv' env t dbg = se 10 env t where
1352 se p env (P nt n t) = show n
1353 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
1354 se p env (V i) | i < length env && i >= 0
1355 = (show $ fst $ env!!i) ++
1356 if dbg then "{" ++ show i ++ "}" else ""
1357 | otherwise = "!!V " ++ show i ++ "!!"
1358 se p env (Bind n b@(Pi (Just _) t k) sc)
1359 = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1360 se p env (Bind n b@(Pi _ t k) sc)
1361 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ arrow k ++ se 10 ((n,b):env) sc
1362 where arrow (TType _) = " -> "
1363 arrow u = " [" ++ show u ++ "] -> "
1364 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1365 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
1366 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
1367 se p env (Constant c) = show c
1368 se p env Erased = "[__]"
1369 se p env Impossible = "[impossible]"
1370 se p env (TType i) = "Type " ++ show i
1371 se p env (UType u) = show u
1373 sb env n (Lam t) = showb env "\\ " " => " n t
1374 sb env n (Hole t) = showb env "? " ". " n t
1375 sb env n (GHole i t) = showb env "?defer " ". " n t
1376 sb env n (Pi (Just _) t _) = showb env "{" "} -> " n t
1377 sb env n (Pi _ t _) = showb env "(" ") -> " n t
1378 sb env n (PVar t) = showb env "pat " ". " n t
1379 sb env n (PVTy t) = showb env "pty " ". " n t
1380 sb env n (Let t v) = showbv env "let " " in " n t v
1381 sb env n (Guess t v) = showbv env "?? " " in " n t v
1383 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
1384 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
1385 se 10 env v ++ sc
1387 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
1388 | otherwise = str
1390-- | Check whether a term has any holes in it - impure if so
1391pureTerm :: TT Name -> Bool
1392pureTerm (App f a) = pureTerm f && pureTerm a
1393pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
1394 pureBinder (Hole _) = False
1395 pureBinder (Guess _ _) = False
1396 pureBinder (Let t v) = pureTerm t && pureTerm v
1397 pureBinder t = pureTerm (binderTy t)
1399 notClassName (MN _ c) | c == txt "class" = False
1400 notClassName _ = True
1402pureTerm _ = True
1404-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1405weakenTm :: Int -> TT n -> TT n
1406weakenTm i t = wk i 0 t
1407 where wk i min (V x) | x >= min = V (i + x)
1408 wk i m (App f a) = App (wk i m f) (wk i m a)
1409 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1410 wk i m t = t
1411 wkb i m t = fmap (wk i m) t
1413-- | Weaken an environment so that all the de Bruijn indices are correct according
1414-- to the latest bound variable
1416weakenEnv :: EnvTT n -> EnvTT n
1417weakenEnv env = wk (length env - 1) env
1418 where wk i [] = []
1419 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1420 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1421 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1422 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1424-- | Weaken every term in the environment by the given amount
1425weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1426weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1428-- | Gather up all the outer 'PVar's and 'Hole's in an expression and reintroduce
1429-- them in a canonical order
1430orderPats :: Term -> Term
1431orderPats tm = op [] tm
1432 where
1433 op [] (App f a) = App f (op [] a) -- for Infer terms
1435 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1436 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1437 op ps (Bind n (Pi i t k) sc) = op ((n, Pi i t k) : ps) sc
1438 op ps sc = bindAll (sortP ps) sc
1440 sortP ps = pick [] (reverse ps)
1442 pick acc [] = reverse acc
1443 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1445 insert n t [] = [(n, t)]
1446 insert n t ((n',t') : ps)
1447 | n `elem` (refsIn (binderTy t') ++
1448 concatMap refsIn (map (binderTy . snd) ps))
1449 = (n', t') : insert n t ps
1450 | otherwise = (n,t):(n',t'):ps
1452refsIn :: TT Name -> [Name]
1453refsIn (P _ n _) = [n]
1454refsIn (Bind n b t) = nub $ nb b ++ refsIn t
1455 where nb (Let t v) = nub (refsIn t) ++ nub (refsIn v)
1456 nb (Guess t v) = nub (refsIn t) ++ nub (refsIn v)
1457 nb t = refsIn (binderTy t)
1458refsIn (App f a) = nub (refsIn f ++ refsIn a)
1459refsIn _ = []
1461-- Make sure all the pattern bindings are as far out as possible
1462liftPats :: Term -> Term
1463liftPats tm = let (tm', ps) = runState (getPats tm) [] in
1464 orderPats $ bindPats (reverse ps) tm'
1465 where
1466 bindPats [] tm = tm
1467 bindPats ((n, t):ps) tm
1468 | n `notElem` map fst ps = Bind n (PVar t) (bindPats ps tm)
1469 | otherwise = bindPats ps tm
1471 getPats :: Term -> State [(Name, Type)] Term
1472 getPats (Bind n (PVar t) sc) = do ps <- get
1473 put ((n, t) : ps)
1474 getPats sc
1475 getPats (Bind n (Guess t v) sc) = do t' <- getPats t
1476 v' <- getPats v
1477 sc' <- getPats sc
1478 return (Bind n (Guess t' v') sc')
1479 getPats (Bind n (Let t v) sc) = do t' <- getPats t
1480 v' <- getPats v
1481 sc' <- getPats sc
1482 return (Bind n (Let t' v') sc')
1483 getPats (Bind n (Pi i t k) sc) = do t' <- getPats t
1484 k' <- getPats k
1485 sc' <- getPats sc
1486 return (Bind n (Pi i t' k') sc')
1487 getPats (Bind n (Lam t) sc) = do t' <- getPats t
1488 sc' <- getPats sc
1489 return (Bind n (Lam t') sc')
1490 getPats (Bind n (Hole t) sc) = do t' <- getPats t
1491 sc' <- getPats sc
1492 return (Bind n (Hole t') sc')
1495 getPats (App f a) = do f' <- getPats f
1496 a' <- getPats a
1497 return (App f' a')
1498 getPats t = return t
1500allTTNames :: Eq n => TT n -> [n]
1501allTTNames = nub . allNamesIn
1502 where allNamesIn (P _ n _) = [n]
1503 allNamesIn (Bind n b t) = [n] ++ nb b ++ allNamesIn t
1504 where nb (Let t v) = allNamesIn t ++ allNamesIn v
1505 nb (Guess t v) = allNamesIn t ++ allNamesIn v
1506 nb t = allNamesIn (binderTy t)
1507 allNamesIn (App f a) = allNamesIn f ++ allNamesIn a
1508 allNamesIn _ = []
1511-- | Pretty-print a term
1512pprintTT :: [Name] -- ^ The bound names (for highlighting and de Bruijn indices)
1513 -> TT Name -- ^ The term to be printed
1514 -> Doc OutputAnnotation
1515pprintTT bound tm = pp startPrec bound tm
1517 where
1518 startPrec = 0
1519 appPrec = 10
1521 pp p bound (P Bound n ty) = annotate (AnnBoundName n False) (text $ show n)
1522 pp p bound (P nt n ty) = annotate (AnnName n Nothing Nothing Nothing)
1523 (text $ show n)
1524 pp p bound (V i)
1525 | i < length bound = let n = bound !! i
1526 in annotate (AnnBoundName n False) (text $ show n)
1527 | otherwise = text ("{{{V" ++ show i ++ "}}}")
1528 pp p bound (Bind n b sc) = ppb p bound n b $
1529 pp startPrec (n:bound) sc
1530 pp p bound (App tm1 tm2) =
1531 bracket p appPrec . group . hang 2 $
1532 pp appPrec bound tm1 <> line <>
1533 pp (appPrec + 1) bound tm2
1534 pp p bound (Constant c) = annotate (AnnConst c) (text (show c))
1535 pp p bound (Proj tm i) =
1536 lparen <> pp startPrec bound tm <> rparen <>
1537 text "!" <> text (show i)
1538 pp p bound Erased = text "<<<erased>>>"
1539 pp p bound Impossible = text "<<<impossible>>>"
1540 pp p bound (TType ue) = annotate (AnnType "Type" "The type of types") $
1541 text "Type"
1542 pp p bound (UType u) = text (show u)
1544 ppb p bound n (Lam ty) sc =
1545 bracket p startPrec . group . align . hang 2 $
1546 text "λ" <+> bindingOf n False <+> text "." <> line <> sc
1547 ppb p bound n (Pi _ ty k) sc =
1548 bracket p startPrec . group . align $
1549 lparen <> (bindingOf n False) <+> colon <+>
1550 (group . align) (pp startPrec bound ty) <>
1551 rparen <+> mkArrow k <> line <> sc
1552 where mkArrow (UType UniqueType) = text "⇴"
1553 mkArrow (UType NullType) = text "⥛"
1554 mkArrow _ = text "→"
1555 ppb p bound n (Let ty val) sc =
1556 bracket p startPrec . group . align $
1557 (group . hang 2) (annotate AnnKeyword (text "let") <+>
1558 bindingOf n False <+> colon <+>
1559 pp startPrec bound ty <+>
1560 text "=" <> line <>
1561 pp startPrec bound val) <> line <>
1562 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1563 ppb p bound n (NLet ty val) sc =
1564 bracket p startPrec . group . align $
1565 (group . hang 2) (annotate AnnKeyword (text "nlet") <+>
1566 bindingOf n False <+> colon <+>
1567 pp startPrec bound ty <+>
1568 text "=" <> line <>
1569 pp startPrec bound val) <> line <>
1570 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1571 ppb p bound n (Hole ty) sc =
1572 bracket p startPrec . group . align . hang 2 $
1573 text "?" <+> bindingOf n False <+> text "." <> line <> sc
1574 ppb p bound n (GHole _ ty) sc =
1575 bracket p startPrec . group . align . hang 2 $
1576 text "¿" <+> bindingOf n False <+> text "." <> line <> sc
1577 ppb p bound n (Guess ty val) sc =
1578 bracket p startPrec . group . align . hang 2 $
1579 text "?" <> bindingOf n False <+>
1580 text "≈" <+> pp startPrec bound val <+>
1581 text "." <> line <> sc
1582 ppb p bound n (PVar ty) sc =
1583 bracket p startPrec . group . align . hang 2 $
1584 annotate AnnKeyword (text "pat") <+>
1585 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1586 text "." <> line <>
1587 sc
1588 ppb p bound n (PVTy ty) sc =
1589 bracket p startPrec . group . align . hang 2 $
1590 annotate AnnKeyword (text "patTy") <+>
1591 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1592 text "." <> line <>
1593 sc
1595 bracket outer inner doc
1596 | outer > inner = lparen <> doc <> rparen
1597 | otherwise = doc
1600-- | Pretty-printer helper for the binding site of a name
1601bindingOf :: Name -- ^^ the bound name
1602 -> Bool -- ^^ whether the name is implicit
1603 -> Doc OutputAnnotation
1604bindingOf n imp = annotate (AnnBoundName n imp) (text (show n))