git.iko.soy/Idris-dev
on 76ec3fe help sign in
Idris-dev/src/Idris/Core/TT.hs
1603 lines 60 kB history raw
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 deriving (Show, Eq, Ord, Data, Typeable)
529intTyName :: IntTy -> String
530intTyName ITNative = "Int"
531intTyName ITBig = "BigInt"
532intTyName (ITFixed sized) = "B" ++ show (nativeTyWidth sized)
533intTyName (ITChar) = "Char"
535data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors https://github.com/idris-lang/Idris-dev/issues/1723
536 deriving (Show, Eq, Ord, Data, Typeable)
537{-!
538deriving instance NFData IntTy
539deriving instance NFData NativeTy
540deriving instance NFData ArithTy
541!-}
543instance Pretty ArithTy OutputAnnotation where
544 pretty (ATInt ITNative) = text "Int"
545 pretty (ATInt ITBig) = text "BigInt"
546 pretty (ATInt ITChar) = text "Char"
547 pretty (ATInt (ITFixed n)) = pretty n
548 pretty ATFloat = text "Float"
550nativeTyWidth :: NativeTy -> Int
551nativeTyWidth IT8 = 8
552nativeTyWidth IT16 = 16
553nativeTyWidth IT32 = 32
554nativeTyWidth IT64 = 64
556{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
557intTyWidth :: IntTy -> Int
558intTyWidth (ITFixed n) = nativeTyWidth n
559intTyWidth ITNative = 8 * sizeOf (0 :: Int)
560intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
561intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
563data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
564 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
565 | AType ArithTy | StrType
566 | WorldType | TheWorld
567 | VoidType | Forgot
568 deriving (Eq, Ord, Data, Typeable)
569{-!
570deriving instance Binary Const
571deriving instance NFData Const
572!-}
574isTypeConst :: Const -> Bool
575isTypeConst (AType _) = True
576isTypeConst StrType = True
577isTypeConst WorldType = True
578isTypeConst VoidType = True
579isTypeConst _ = False
581instance Sized Const where
582 size _ = 1
584instance Pretty Const OutputAnnotation where
585 pretty (I i) = text . show $ i
586 pretty (BI i) = text . show $ i
587 pretty (Fl f) = text . show $ f
588 pretty (Ch c) = text . show $ c
589 pretty (Str s) = text s
590 pretty (AType a) = pretty a
591 pretty StrType = text "String"
592 pretty TheWorld = text "%theWorld"
593 pretty WorldType = text "prim__World"
594 pretty VoidType = text "Void"
595 pretty Forgot = text "Forgot"
596 pretty (B8 w) = text . show $ w
597 pretty (B16 w) = text . show $ w
598 pretty (B32 w) = text . show $ w
599 pretty (B64 w) = text . show $ w
601-- | Determines whether the input constant represents a type
602constIsType :: Const -> Bool
603constIsType (I _) = False
604constIsType (BI _) = False
605constIsType (Fl _) = False
606constIsType (Ch _) = False
607constIsType (Str _) = False
608constIsType (B8 _) = False
609constIsType (B16 _) = False
610constIsType (B32 _) = False
611constIsType (B64 _) = False
612constIsType _ = True
614-- | Get the docstring for a Const
615constDocs :: Const -> String
616constDocs c@(AType (ATInt ITBig)) = "Arbitrary-precision integers"
617constDocs c@(AType (ATInt ITNative)) = "Fixed-precision integers of undefined size"
618constDocs c@(AType (ATInt ITChar)) = "Characters in some unspecified encoding"
619constDocs c@(AType ATFloat) = "Double-precision floating-point numbers"
620constDocs StrType = "Strings in some unspecified encoding"
621constDocs c@(AType (ATInt (ITFixed IT8))) = "Eight bits (unsigned)"
622constDocs c@(AType (ATInt (ITFixed IT16))) = "Sixteen bits (unsigned)"
623constDocs c@(AType (ATInt (ITFixed IT32))) = "Thirty-two bits (unsigned)"
624constDocs c@(AType (ATInt (ITFixed IT64))) = "Sixty-four bits (unsigned)"
625constDocs (Fl f) = "A float"
626constDocs (I i) = "A fixed-precision integer"
627constDocs (BI i) = "An arbitrary-precision integer"
628constDocs (Str s) = "A string of length " ++ show (length s)
629constDocs (Ch c) = "A character"
630constDocs (B8 w) = "The eight-bit value 0x" ++
631 showIntAtBase 16 intToDigit w ""
632constDocs (B16 w) = "The sixteen-bit value 0x" ++
633 showIntAtBase 16 intToDigit w ""
634constDocs (B32 w) = "The thirty-two-bit value 0x" ++
635 showIntAtBase 16 intToDigit w ""
636constDocs (B64 w) = "The sixty-four-bit value 0x" ++
637 showIntAtBase 16 intToDigit w ""
638constDocs prim = "Undocumented"
640data Universe = NullType | UniqueType | AllTypes
641 deriving (Eq, Ord, Data, Typeable)
643instance Show Universe where
644 show UniqueType = "UniqueType"
645 show NullType = "NullType"
646 show AllTypes = "Type*"
648data Raw = Var Name
649 | RBind Name (Binder Raw) Raw
650 | RApp Raw Raw
651 | RType
652 | RUType Universe
653 | RForce Raw
654 | RConstant Const
655 deriving (Show, Eq, Data, Typeable)
657instance Sized Raw where
658 size (Var name) = 1
659 size (RBind name bind right) = 1 + size bind + size right
660 size (RApp left right) = 1 + size left + size right
661 size RType = 1
662 size (RUType _) = 1
663 size (RForce raw) = 1 + size raw
664 size (RConstant const) = size const
666instance Pretty Raw OutputAnnotation where
667 pretty = text . show
669{-!
670deriving instance Binary Raw
671deriving instance NFData Raw
672!-}
674data ImplicitInfo = Impl { tcinstance :: Bool }
675 deriving (Show, Eq, Ord, Data, Typeable)
677{-!
678deriving instance Binary ImplicitInfo
679deriving instance NFData ImplicitInfo
680!-}
682-- The type parameter `b` will normally be something like `TT Name` or just
683-- `Raw`. We do not make a type-level distinction between TT terms that happen
684-- to be TT types and TT terms that are not TT types.
685-- | All binding forms are represented in a uniform fashion. This type only represents
686-- the types of bindings (and their values, if any); the attached identifiers are part
687-- of the 'Bind' constructor for the 'TT' type.
688data Binder b = Lam { binderTy :: !b {-^ type annotation for bound variable-}}
689 | Pi { binderImpl :: Maybe ImplicitInfo,
690 binderTy :: !b,
691 binderKind :: !b }
692 {-^ A binding that occurs in a function type expression, e.g. @(x:Int) -> ...@
693 The 'binderImpl' flag says whether it was a scoped implicit
694 (i.e. forall bound) in the high level Idris, but otherwise
695 has no relevance in TT. -}
696 | Let { binderTy :: !b,
697 binderVal :: b {-^ value for bound variable-}}
698 -- ^ A binding that occurs in a @let@ expression
699 | NLet { binderTy :: !b,
700 binderVal :: b }
701 | Hole { binderTy :: !b}
702 | GHole { envlen :: Int,
703 binderTy :: !b}
704 | Guess { binderTy :: !b,
705 binderVal :: b }
706 | PVar { binderTy :: !b }
707 -- ^ A pattern variable
708 | PVTy { binderTy :: !b }
709 deriving (Show, Eq, Ord, Functor, Foldable, Traversable, Data, Typeable)
710{-!
711deriving instance Binary Binder
712deriving instance NFData Binder
713!-}
715instance Sized a => Sized (Binder a) where
716 size (Lam ty) = 1 + size ty
717 size (Pi _ ty _) = 1 + size ty
718 size (Let ty val) = 1 + size ty + size val
719 size (NLet ty val) = 1 + size ty + size val
720 size (Hole ty) = 1 + size ty
721 size (GHole _ ty) = 1 + size ty
722 size (Guess ty val) = 1 + size ty + size val
723 size (PVar ty) = 1 + size ty
724 size (PVTy ty) = 1 + size ty
726fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
727fmapMB f (Let t v) = liftM2 Let (f t) (f v)
728fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
729fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
730fmapMB f (Lam t) = liftM Lam (f t)
731fmapMB f (Pi i t k) = liftM2 (Pi i) (f t) (f k)
732fmapMB f (Hole t) = liftM Hole (f t)
733fmapMB f (GHole i t) = liftM (GHole i) (f t)
734fmapMB f (PVar t) = liftM PVar (f t)
735fmapMB f (PVTy t) = liftM PVTy (f t)
737raw_apply :: Raw -> [Raw] -> Raw
738raw_apply f [] = f
739raw_apply f (a : as) = raw_apply (RApp f a) as
741raw_unapply :: Raw -> (Raw, [Raw])
742raw_unapply t = ua [] t where
743 ua args (RApp f a) = ua (a:args) f
744 ua args t = (t, args)
746-- WELL TYPED TERMS ---------------------------------------------------------
748-- | Universe expressions for universe checking
749data UExp = UVar Int -- ^ universe variable
750 | UVal Int -- ^ explicit universe level
751 deriving (Eq, Ord, Data, Typeable)
752{-!
753deriving instance NFData UExp
754!-}
756instance Sized UExp where
757 size _ = 1
759instance Show UExp where
760 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
761 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
762 show (UVal x) = show x
763-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
765-- | Universe constraints
766data UConstraint = ULT UExp UExp -- ^ Strictly less than
767 | ULE UExp UExp -- ^ Less than or equal to
768 deriving (Eq, Ord)
770data ConstraintFC = ConstraintFC { uconstraint :: UConstraint,
771 ufc :: FC }
772 deriving Show
774instance Eq ConstraintFC where
775 x == y = uconstraint x == uconstraint y
777instance Ord ConstraintFC where
778 compare x y = compare (uconstraint x) (uconstraint y)
780instance Show UConstraint where
781 show (ULT x y) = show x ++ " < " ++ show y
782 show (ULE x y) = show x ++ " <= " ++ show y
784type UCs = (Int, [UConstraint])
786data NameType = Bound
787 | Ref
788 | DCon {nt_tag :: Int, nt_arity :: Int, nt_unique :: Bool} -- ^ Data constructor
789 | TCon {nt_tag :: Int, nt_arity :: Int} -- ^ Type constructor
790 deriving (Show, Ord, Data, Typeable)
791{-!
792deriving instance Binary NameType
793deriving instance NFData NameType
794!-}
796instance Sized NameType where
797 size _ = 1
799instance Pretty NameType OutputAnnotation where
800 pretty = text . show
802instance Eq NameType where
803 Bound == Bound = True
804 Ref == Ref = True
805 DCon _ a _ == DCon _ b _ = (a == b) -- ignore tag
806 TCon _ a == TCon _ b = (a == b) -- ignore tag
807 _ == _ = False
809-- | Terms in the core language. The type parameter is the type of
810-- identifiers used for bindings and explicit named references;
811-- usually we use @TT 'Name'@.
812data TT n = P NameType n (TT n) -- ^ named references with type
813 -- (P for "Parameter", motivated by McKinna and Pollack's
814 -- Pure Type Systems Formalized)
815 | V !Int -- ^ a resolved de Bruijn-indexed variable
816 | Bind n !(Binder (TT n)) (TT n) -- ^ a binding
817 | App !(TT n) (TT n) -- ^ function, function type, arg
818 | Constant Const -- ^ constant
819 | Proj (TT n) !Int -- ^ argument projection; runtime only
820 -- (-1) is a special case for 'subtract one from BI'
821 | Erased -- ^ an erased term
822 | Impossible -- ^ special case for totality checking
823 | TType UExp -- ^ the type of types at some level
824 | UType Universe -- ^ Uniqueness type universe (disjoint from TType)
825 deriving (Ord, Functor, Data, Typeable)
826{-!
827deriving instance Binary TT
828deriving instance NFData TT
829!-}
831class TermSize a where
832 termsize :: Name -> a -> Int
834instance TermSize a => TermSize [a] where
835 termsize n [] = 0
836 termsize n (x : xs) = termsize n x + termsize n xs
838instance TermSize (TT Name) where
839 termsize n (P _ n' _)
840 | n' == n = 1000000 -- recursive => really big
841 | otherwise = 1
842 termsize n (V _) = 1
843 -- for `Bind` terms, we can erroneously declare a term
844 -- "recursive => really big" if the name of the bound
845 -- variable is the same as the name we're using
846 -- So generate a different name in that case.
847 termsize n (Bind n' (Let t v) sc)
848 = let rn = if n == n' then sMN 0 "noname" else n in
849 termsize rn v + termsize rn sc
850 termsize n (Bind n' b sc)
851 = let rn = if n == n' then sMN 0 "noname" else n in
852 termsize rn sc
853 termsize n (App f a) = termsize n f + termsize n a
854 termsize n (Proj t i) = termsize n t
855 termsize n _ = 1
857instance Sized a => Sized (TT a) where
858 size (P name n trm) = 1 + size name + size n + size trm
859 size (V v) = 1
860 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
861 size (App l r) = 1 + size l + size r
862 size (Constant c) = size c
863 size Erased = 1
864 size (TType u) = 1 + size u
866instance Pretty a o => Pretty (TT a) o where
867 pretty _ = text "test"
869type EnvTT n = [(n, Binder (TT n))]
871data Datatype n = Data { d_typename :: n,
872 d_typetag :: Int,
873 d_type :: (TT n),
874 d_unique :: Bool,
875 d_cons :: [(n, TT n)] }
876 deriving (Show, Functor, Eq)
878instance Eq n => Eq (TT n) where
879 (==) (P xt x _) (P yt y _) = x == y
880 (==) (V x) (V y) = x == y
881 (==) (Bind _ xb xs) (Bind _ yb ys) = xs == ys && xb == yb
882 (==) (App fx ax) (App fy ay) = ax == ay && fx == fy
883 (==) (TType _) (TType _) = True -- deal with constraints later
884 (==) (Constant x) (Constant y) = x == y
885 (==) (Proj x i) (Proj y j) = x == y && i == j
886 (==) Erased _ = True
887 (==) _ Erased = True
888 (==) _ _ = False
890-- * A few handy operations on well typed terms:
892-- | A term is injective iff it is a data constructor, type constructor,
893-- constant, the type Type, pi-binding, or an application of an injective
894-- term.
895isInjective :: TT n -> Bool
896isInjective (P (DCon _ _ _) _ _) = True
897isInjective (P (TCon _ _) _ _) = True
898isInjective (Constant _) = True
899isInjective (TType x) = True
900isInjective (Bind _ (Pi _ _ _) sc) = True
901isInjective (App f a) = isInjective f
902isInjective _ = False
904-- | Count the number of instances of a de Bruijn index in a term
905vinstances :: Int -> TT n -> Int
906vinstances i (V x) | i == x = 1
907vinstances i (App f a) = vinstances i f + vinstances i a
908vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
909 where instancesB (Let t v) = vinstances i v
910 instancesB _ = 0
911vinstances i t = 0
913-- | Replace the outermost (index 0) de Bruijn variable with the given term
914instantiate :: TT n -> TT n -> TT n
915instantiate e = subst 0 where
916 subst i (P nt x ty) = P nt x (subst i ty)
917 subst i (V x) | i == x = e
918 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
919 subst i (App f a) = App (subst i f) (subst i a)
920 subst i (Proj x idx) = Proj (subst i x) idx
921 subst i t = t
923-- | As 'instantiate', but also decrement the indices of all de Bruijn variables
924-- remaining in the term, so that there are no more references to the variable
925-- that has been substituted.
926substV :: TT n -> TT n -> TT n
927substV x tm = dropV 0 (instantiate x tm) where
928 subst i (P nt x ty) = P nt x (subst i ty)
929 dropV i (V x) | x > i = V (x - 1)
930 | otherwise = V x
931 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
932 dropV i (App f a) = App (dropV i f) (dropV i a)
933 dropV i (Proj x idx) = Proj (dropV i x) idx
934 dropV i t = t
936-- | Replace all non-free de Bruijn references in the given term with references
937-- to the name of their binding.
938explicitNames :: TT n -> TT n
939explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
940 Bind x b'
941 (explicitNames (instantiate
942 (P Bound x (binderTy b')) sc))
943explicitNames (App f a) = App (explicitNames f) (explicitNames a)
944explicitNames (Proj x idx) = Proj (explicitNames x) idx
945explicitNames t = t
947-- | Replace references to the given 'Name'-like id with references to
948-- de Bruijn index 0.
949pToV :: Eq n => n -> TT n -> TT n
950pToV n = pToV' n 0
951pToV' n i (P _ x _) | n == x = V i
952pToV' n i (Bind x b sc)
953-- We can assume the inner scope has been pToVed already, so continue to
954-- resolve names from the *outer* scope which may happen to have the same id.
955 | n == x = Bind x (fmap (pToV' n i) b) sc
956 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
957pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
958pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
959pToV' n i t = t
961-- increase de Bruijn indices, as if a binder has been added
962addBinder :: TT n -> TT n
963addBinder t = ab 0 t
964 where
965 ab top (V i) | i >= top = V (i + 1)
966 | otherwise = V i
967 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
968 ab top (App f a) = App (ab top f) (ab top a)
969 ab top (Proj t idx) = Proj (ab top t) idx
970 ab top t = t
972-- | Convert several names. First in the list comes out as V 0
973pToVs :: Eq n => [n] -> TT n -> TT n
974pToVs ns tm = pToVs' ns tm 0 where
975 pToVs' [] tm i = tm
976 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
978-- | Replace de Bruijn indices in the given term with explicit references to
979-- the names of the bindings they refer to. It is an error if the given term
980-- contains free de Bruijn indices.
981vToP :: TT n -> TT n
982vToP = vToP' [] where
983 vToP' env (V i) = let (n, b) = (env !! i) in
984 P Bound n (binderTy b)
985 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
986 Bind n b' (vToP' ((n, b'):env) sc)
987 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
988 vToP' env t = t
990-- | Replace every non-free reference to the name of a binding in
991-- the given term with a de Bruijn index.
992finalise :: Eq n => TT n -> TT n
993finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
994finalise (App f a) = App (finalise f) (finalise a)
995finalise t = t
997-- Once we've finished checking everything about a term we no longer need
998-- the type on the 'P' so erase it so save memory
1000pEraseType :: TT n -> TT n
1001pEraseType (P nt t _) = P nt t Erased
1002pEraseType (App f a) = App (pEraseType f) (pEraseType a)
1003pEraseType (Bind n b sc) = Bind n (fmap pEraseType b) (pEraseType sc)
1004pEraseType t = t
1006-- | As 'instantiate', but in addition to replacing @'V' 0@,
1007-- replace references to the given 'Name'-like id.
1008subst :: Eq n => n {-^ The id to replace -} ->
1009 TT n {-^ The replacement term -} ->
1010 TT n {-^ The term to replace in -} ->
1011 TT n
1012-- subst n v tm = instantiate v (pToV n tm)
1013subst n v tm = fst $ subst' 0 tm
1014 where
1015 -- keep track of updates to save allocations - this is a big win on
1016 -- large terms in particular
1017 -- ('Maybe' would be neater here, but >>= is not the right combinator.
1018 -- Feel free to tidy up, as long as it still saves allocating when no
1019 -- substitution happens...)
1020 subst' i (V x) | i == x = (v, True)
1021 subst' i (P _ x _) | n == x = (v, True)
1022 subst' i t@(P nt x ty)
1023 = let (ty', ut) = subst' i ty in
1024 if ut then (P nt x ty', True) else (t, False)
1025 subst' i t@(Bind x b sc) | x /= n
1026 = let (b', ub) = substB' i b
1027 (sc', usc) = subst' (i+1) sc in
1028 if ub || usc then (Bind x b' sc', True) else (t, False)
1029 subst' i t@(App f a) = let (f', uf) = subst' i f
1030 (a', ua) = subst' i a in
1031 if uf || ua then (App f' a', True) else (t, False)
1032 subst' i t@(Proj x idx) = let (x', u) = subst' i x in
1033 if u then (Proj x' idx, u) else (t, False)
1034 subst' i t = (t, False)
1036 substB' i b@(Let t v) = let (t', ut) = subst' i t
1037 (v', uv) = subst' i v in
1038 if ut || uv then (Let t' v', True)
1039 else (b, False)
1040 substB' i b@(Guess t v) = let (t', ut) = subst' i t
1041 (v', uv) = subst' i v in
1042 if ut || uv then (Guess t' v', True)
1043 else (b, False)
1044 substB' i b = let (ty', u) = subst' i (binderTy b) in
1045 if u then (b { binderTy = ty' }, u) else (b, False)
1047-- If there are no Vs in the term (i.e. in proof state)
1048psubst :: Eq n => n -> TT n -> TT n -> TT n
1049psubst n v tm = s' 0 tm where
1050 s' i (V x) | x > i = V (x - 1)
1051 | x == i = v
1052 | otherwise = V x
1053 s' i (P _ x _) | n == x = v
1054 s' i (Bind x b sc) | n == x = Bind x (fmap (s' i) b) sc
1055 | otherwise = Bind x (fmap (s' i) b) (s' (i+1) sc)
1056 s' i (App f a) = App (s' i f) (s' i a)
1057 s' i (Proj t idx) = Proj (s' i t) idx
1058 s' i t = t
1060-- | As 'subst', but takes a list of (name, substitution) pairs instead
1061-- of a single name and substitution
1062substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
1063substNames [] t = t
1064substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
1066-- | Replaces all terms equal (in the sense of @(==)@) to
1067-- the old term with the new term.
1068substTerm :: Eq n => TT n {-^ Old term -} ->
1069 TT n {-^ New term -} ->
1070 TT n {-^ template term -}
1071 -> TT n
1072substTerm old new = st where
1073 st t | t == old = new
1074 st (App f a) = App (st f) (st a)
1075 st (Bind x b sc) = Bind x (fmap st b) (st sc)
1076 st t = t
1078-- | Return number of occurrences of V 0 or bound name i the term
1079occurrences :: Eq n => n -> TT n -> Int
1080occurrences n t = execState (no' 0 t) 0
1081 where
1082 no' i (V x) | i == x = do num <- get; put (num + 1)
1083 no' i (P Bound x _) | n == x = do num <- get; put (num + 1)
1084 no' i (Bind n b sc) = do noB' i b; no' (i+1) sc
1085 where noB' i (Let t v) = do no' i t; no' i v
1086 noB' i (Guess t v) = do no' i t; no' i v
1087 noB' i b = no' i (binderTy b)
1088 no' i (App f a) = do no' i f; no' i a
1089 no' i (Proj x _) = no' i x
1090 no' i _ = return ()
1092-- | Returns true if V 0 and bound name n do not occur in the term
1093noOccurrence :: Eq n => n -> TT n -> Bool
1094noOccurrence n t = no' 0 t
1095 where
1096 no' i (V x) = not (i == x)
1097 no' i (P Bound x _) = not (n == x)
1098 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
1099 where noB' i (Let t v) = no' i t && no' i v
1100 noB' i (Guess t v) = no' i t && no' i v
1101 noB' i b = no' i (binderTy b)
1102 no' i (App f a) = no' i f && no' i a
1103 no' i (Proj x _) = no' i x
1104 no' i _ = True
1106-- | Returns all names used free in the term
1107freeNames :: Eq n => TT n -> [n]
1108freeNames t = nub $ freeNames' t
1109 where
1110 freeNames' (P _ n _) = [n]
1111 freeNames' (Bind n (Let t v) sc) = freeNames' v ++ (freeNames' sc \\ [n])
1112 ++ freeNames' t
1113 freeNames' (Bind n b sc) = freeNames' (binderTy b) ++ (freeNames' sc \\ [n])
1114 freeNames' (App f a) = freeNames' f ++ freeNames' a
1115 freeNames' (Proj x i) = freeNames' x
1116 freeNames' _ = []
1118-- | Return the arity of a (normalised) type
1119arity :: TT n -> Int
1120arity (Bind n (Pi _ t _) sc) = 1 + arity sc
1121arity _ = 0
1123-- | Deconstruct an application; returns the function and a list of arguments
1124unApply :: TT n -> (TT n, [TT n])
1125unApply t = ua [] t where
1126 ua args (App f a) = ua (a:args) f
1127 ua args t = (t, args)
1129-- | Returns a term representing the application of the first argument
1130-- (a function) to every element of the second argument.
1131mkApp :: TT n -> [TT n] -> TT n
1132mkApp f [] = f
1133mkApp f (a:as) = mkApp (App f a) as
1135unList :: Term -> Maybe [Term]
1136unList tm = case unApply tm of
1137 (nil, [_]) -> Just []
1138 (cons, ([_, x, xs])) ->
1139 do rest <- unList xs
1140 return $ x:rest
1141 (f, args) -> Nothing
1143-- | Cast a 'TT' term to a 'Raw' value, discarding universe information and
1144-- the types of named references and replacing all de Bruijn indices
1145-- with the corresponding name. It is an error if there are free de
1146-- Bruijn indices.
1147forget :: TT Name -> Raw
1148forget tm = forgetEnv [] tm
1150safeForget :: TT Name -> Maybe Raw
1151safeForget tm = safeForgetEnv [] tm
1153forgetEnv :: [Name] -> TT Name -> Raw
1154forgetEnv env tm = case safeForgetEnv env tm of
1155 Just t' -> t'
1156 Nothing -> error $ "Scope error in " ++ show tm
1159safeForgetEnv :: [Name] -> TT Name -> Maybe Raw
1160safeForgetEnv env (P _ n _) = Just $ Var n
1161safeForgetEnv env (V i) | i < length env = Just $ Var (env !! i)
1162 | otherwise = Nothing
1163safeForgetEnv env (Bind n b sc)
1164 = do let n' = uniqueName n env
1165 b' <- safeForgetEnvB env b
1166 sc' <- safeForgetEnv (n':env) sc
1167 Just $ RBind n' b' sc'
1168 where safeForgetEnvB env (Let t v) = liftM2 Let (safeForgetEnv env t)
1169 (safeForgetEnv env v)
1170 safeForgetEnvB env (Guess t v) = liftM2 Guess (safeForgetEnv env t)
1171 (safeForgetEnv env v)
1172 safeForgetEnvB env b = do ty' <- safeForgetEnv env (binderTy b)
1173 Just $ fmap (\_ -> ty') b
1174safeForgetEnv env (App f a) = liftM2 RApp (safeForgetEnv env f) (safeForgetEnv env a)
1175safeForgetEnv env (Constant c) = Just $ RConstant c
1176safeForgetEnv env (TType i) = Just RType
1177safeForgetEnv env (UType u) = Just $ RUType u
1178safeForgetEnv env Erased = Just $ RConstant Forgot
1180-- | Introduce a 'Bind' into the given term for each element of the
1181-- given list of (name, binder) pairs.
1182bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
1183bindAll [] t = t
1184bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
1186-- | Like 'bindAll', but the 'Binder's are 'TT' terms instead.
1187-- The first argument is a function to map @TT@ terms to @Binder@s.
1188-- This function might often be something like 'Lam', which directly
1189-- constructs a @Binder@ from a @TT@ term.
1190bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
1191bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
1193-- | Return a list of pairs of the names of the outermost 'Pi'-bound
1194-- variables in the given term, together with their types.
1195getArgTys :: TT n -> [(n, TT n)]
1196getArgTys (Bind n (PVar _) sc) = getArgTys sc
1197getArgTys (Bind n (PVTy _) sc) = getArgTys sc
1198getArgTys (Bind n (Pi _ t _) sc) = (n, t) : getArgTys sc
1199getArgTys _ = []
1201getRetTy :: TT n -> TT n
1202getRetTy (Bind n (PVar _) sc) = getRetTy sc
1203getRetTy (Bind n (PVTy _) sc) = getRetTy sc
1204getRetTy (Bind n (Pi _ _ _) sc) = getRetTy sc
1205getRetTy sc = sc
1207uniqueNameFrom :: [Name] -> [Name] -> Name
1208uniqueNameFrom [] hs = uniqueName (nextName (sUN "x")) hs
1209uniqueNameFrom (s : supply) hs
1210 | s `elem` hs = uniqueNameFrom supply hs
1211 | otherwise = s
1213uniqueName :: Name -> [Name] -> Name
1214uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
1215 | otherwise = n
1217uniqueNameSet :: Name -> Set Name -> Name
1218uniqueNameSet n hs | n `member` hs = uniqueNameSet (nextName n) hs
1219 | otherwise = n
1221uniqueBinders :: [Name] -> TT Name -> TT Name
1222uniqueBinders ns = ubSet (fromList ns) where
1223 ubSet ns (Bind n b sc)
1224 = let n' = uniqueNameSet n ns
1225 ns' = insert n' ns in
1226 Bind n' (fmap (ubSet ns') b) (ubSet ns' sc)
1227 ubSet ns (App f a) = App (ubSet ns f) (ubSet ns a)
1228 ubSet ns t = t
1231nextName (NS x s) = NS (nextName x) s
1232nextName (MN i n) = MN (i+1) n
1233nextName (UN x) = let (num', nm') = T.span isDigit (T.reverse x)
1234 nm = T.reverse nm'
1235 num = readN (T.reverse num') in
1236 UN (nm `T.append` txt (show (num+1)))
1237 where
1238 readN x | not (T.null x) = read (T.unpack x)
1239 readN x = 0
1240nextName (SN x) = SN (nextName' x)
1241 where
1242 nextName' (WhereN i f x) = WhereN i f (nextName x)
1243 nextName' (WithN i n) = WithN i (nextName n)
1244 nextName' (InstanceN n ns) = InstanceN (nextName n) ns
1245 nextName' (ParentN n ns) = ParentN (nextName n) ns
1246 nextName' (CaseN n) = CaseN (nextName n)
1247 nextName' (ElimN n) = ElimN (nextName n)
1248 nextName' (MethodN n) = MethodN (nextName n)
1249 nextName' (InstanceCtorN n) = InstanceCtorN (nextName n)
1251type Term = TT Name
1252type Type = Term
1254type Env = EnvTT Name
1256-- | an environment with de Bruijn indices 'normalised' so that they all refer to
1257-- this environment
1259newtype WkEnvTT n = Wk (EnvTT n)
1260type WkEnv = WkEnvTT Name
1262instance (Eq n, Show n) => Show (TT n) where
1263 show t = showEnv [] t
1265itBitsName IT8 = "Bits8"
1266itBitsName IT16 = "Bits16"
1267itBitsName IT32 = "Bits32"
1268itBitsName IT64 = "Bits64"
1270instance Show Const where
1271 show (I i) = show i
1272 show (BI i) = show i
1273 show (Fl f) = show f
1274 show (Ch c) = show c
1275 show (Str s) = show s
1276 show (B8 x) = show x
1277 show (B16 x) = show x
1278 show (B32 x) = show x
1279 show (B64 x) = show x
1280 show (AType ATFloat) = "Float"
1281 show (AType (ATInt ITBig)) = "Integer"
1282 show (AType (ATInt ITNative)) = "Int"
1283 show (AType (ATInt ITChar)) = "Char"
1284 show (AType (ATInt (ITFixed it))) = itBitsName it
1285 show TheWorld = "prim__TheWorld"
1286 show WorldType = "prim__WorldType"
1287 show StrType = "String"
1288 show VoidType = "Void"
1290showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String
1291showEnv env t = showEnv' env t False
1292showEnvDbg env t = showEnv' env t True
1294prettyEnv env t = prettyEnv' env t False
1295 where
1296 prettyEnv' env t dbg = prettySe 10 env t dbg
1298 bracket outer inner p
1299 | inner > outer = lparen <> p <> rparen
1300 | otherwise = p
1302 prettySe p env (P nt n t) debug =
1303 pretty n <+>
1304 if debug then
1305 lbracket <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbracket
1306 else
1307 empty
1308 prettySe p env (V i) debug
1309 | i < length env =
1310 if debug then
1311 text . show . fst $ env!!i
1312 else
1313 lbracket <+> text (show i) <+> rbracket
1314 | otherwise = text "unbound" <+> text (show i) <+> text "!"
1315 prettySe p env (Bind n b@(Pi _ t _) sc) debug
1316 | noOccurrence n sc && not debug =
1317 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1318 prettySe p env (Bind n b sc) debug =
1319 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1320 prettySe p env (App f a) debug =
1321 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
1322 prettySe p env (Proj x i) debug =
1323 prettySe 1 env x debug <+> text ("!" ++ show i)
1324 prettySe p env (Constant c) debug = pretty c
1325 prettySe p env Erased debug = text "[_]"
1326 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
1328 -- Render a `Binder` and its name
1329 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
1330 prettySb env n (Hole t) = prettyB env "?defer" "." n t
1331 prettySb env n (Pi _ t _) = prettyB env "(" ") ->" n t
1332 prettySb env n (PVar t) = prettyB env "pat" "." n t
1333 prettySb env n (PVTy t) = prettyB env "pty" "." n t
1334 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
1335 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
1337 -- Use `op` and `sc` to delimit `n` (a binding name) and its type
1338 -- declaration
1339 -- e.g. "λx : Int =>" for the Lam case
1340 prettyB env op sc n t debug =
1341 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
1343 -- Like `prettyB`, but handle the bindings that have values in addition
1344 -- to names and types
1345 prettyBv env op sc n t v debug =
1346 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
1347 prettySe 10 env v debug <> text sc
1350showEnv' env t dbg = se 10 env t where
1351 se p env (P nt n t) = show n
1352 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
1353 se p env (V i) | i < length env && i >= 0
1354 = (show $ fst $ env!!i) ++
1355 if dbg then "{" ++ show i ++ "}" else ""
1356 | otherwise = "!!V " ++ show i ++ "!!"
1357 se p env (Bind n b@(Pi (Just _) t k) sc)
1358 = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1359 se p env (Bind n b@(Pi _ t k) sc)
1360 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ arrow k ++ se 10 ((n,b):env) sc
1361 where arrow (TType _) = " -> "
1362 arrow u = " [" ++ show u ++ "] -> "
1363 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1364 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
1365 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
1366 se p env (Constant c) = show c
1367 se p env Erased = "[__]"
1368 se p env Impossible = "[impossible]"
1369 se p env (TType i) = "Type " ++ show i
1370 se p env (UType u) = show u
1372 sb env n (Lam t) = showb env "\\ " " => " n t
1373 sb env n (Hole t) = showb env "? " ". " n t
1374 sb env n (GHole i t) = showb env "?defer " ". " n t
1375 sb env n (Pi (Just _) t _) = showb env "{" "} -> " n t
1376 sb env n (Pi _ t _) = showb env "(" ") -> " n t
1377 sb env n (PVar t) = showb env "pat " ". " n t
1378 sb env n (PVTy t) = showb env "pty " ". " n t
1379 sb env n (Let t v) = showbv env "let " " in " n t v
1380 sb env n (Guess t v) = showbv env "?? " " in " n t v
1382 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
1383 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
1384 se 10 env v ++ sc
1386 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
1387 | otherwise = str
1389-- | Check whether a term has any holes in it - impure if so
1390pureTerm :: TT Name -> Bool
1391pureTerm (App f a) = pureTerm f && pureTerm a
1392pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
1393 pureBinder (Hole _) = False
1394 pureBinder (Guess _ _) = False
1395 pureBinder (Let t v) = pureTerm t && pureTerm v
1396 pureBinder t = pureTerm (binderTy t)
1398 notClassName (MN _ c) | c == txt "class" = False
1399 notClassName _ = True
1401pureTerm _ = True
1403-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1404weakenTm :: Int -> TT n -> TT n
1405weakenTm i t = wk i 0 t
1406 where wk i min (V x) | x >= min = V (i + x)
1407 wk i m (App f a) = App (wk i m f) (wk i m a)
1408 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1409 wk i m t = t
1410 wkb i m t = fmap (wk i m) t
1412-- | Weaken an environment so that all the de Bruijn indices are correct according
1413-- to the latest bound variable
1415weakenEnv :: EnvTT n -> EnvTT n
1416weakenEnv env = wk (length env - 1) env
1417 where wk i [] = []
1418 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1419 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1420 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1421 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1423-- | Weaken every term in the environment by the given amount
1424weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1425weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1427-- | Gather up all the outer 'PVar's and 'Hole's in an expression and reintroduce
1428-- them in a canonical order
1429orderPats :: Term -> Term
1430orderPats tm = op [] tm
1431 where
1432 op [] (App f a) = App f (op [] a) -- for Infer terms
1434 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1435 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1436 op ps (Bind n (Pi i t k) sc) = op ((n, Pi i t k) : ps) sc
1437 op ps sc = bindAll (sortP ps) sc
1439 sortP ps = pick [] (reverse ps)
1441 pick acc [] = reverse acc
1442 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1444 insert n t [] = [(n, t)]
1445 insert n t ((n',t') : ps)
1446 | n `elem` (refsIn (binderTy t') ++
1447 concatMap refsIn (map (binderTy . snd) ps))
1448 = (n', t') : insert n t ps
1449 | otherwise = (n,t):(n',t'):ps
1451refsIn :: TT Name -> [Name]
1452refsIn (P _ n _) = [n]
1453refsIn (Bind n b t) = nub $ nb b ++ refsIn t
1454 where nb (Let t v) = nub (refsIn t) ++ nub (refsIn v)
1455 nb (Guess t v) = nub (refsIn t) ++ nub (refsIn v)
1456 nb t = refsIn (binderTy t)
1457refsIn (App f a) = nub (refsIn f ++ refsIn a)
1458refsIn _ = []
1460-- Make sure all the pattern bindings are as far out as possible
1461liftPats :: Term -> Term
1462liftPats tm = let (tm', ps) = runState (getPats tm) [] in
1463 orderPats $ bindPats (reverse ps) tm'
1464 where
1465 bindPats [] tm = tm
1466 bindPats ((n, t):ps) tm
1467 | n `notElem` map fst ps = Bind n (PVar t) (bindPats ps tm)
1468 | otherwise = bindPats ps tm
1470 getPats :: Term -> State [(Name, Type)] Term
1471 getPats (Bind n (PVar t) sc) = do ps <- get
1472 put ((n, t) : ps)
1473 getPats sc
1474 getPats (Bind n (Guess t v) sc) = do t' <- getPats t
1475 v' <- getPats v
1476 sc' <- getPats sc
1477 return (Bind n (Guess t' v') sc')
1478 getPats (Bind n (Let t v) sc) = do t' <- getPats t
1479 v' <- getPats v
1480 sc' <- getPats sc
1481 return (Bind n (Let t' v') sc')
1482 getPats (Bind n (Pi i t k) sc) = do t' <- getPats t
1483 k' <- getPats k
1484 sc' <- getPats sc
1485 return (Bind n (Pi i t' k') sc')
1486 getPats (Bind n (Lam t) sc) = do t' <- getPats t
1487 sc' <- getPats sc
1488 return (Bind n (Lam t') sc')
1489 getPats (Bind n (Hole t) sc) = do t' <- getPats t
1490 sc' <- getPats sc
1491 return (Bind n (Hole t') sc')
1494 getPats (App f a) = do f' <- getPats f
1495 a' <- getPats a
1496 return (App f' a')
1497 getPats t = return t
1499allTTNames :: Eq n => TT n -> [n]
1500allTTNames = nub . allNamesIn
1501 where allNamesIn (P _ n _) = [n]
1502 allNamesIn (Bind n b t) = [n] ++ nb b ++ allNamesIn t
1503 where nb (Let t v) = allNamesIn t ++ allNamesIn v
1504 nb (Guess t v) = allNamesIn t ++ allNamesIn v
1505 nb t = allNamesIn (binderTy t)
1506 allNamesIn (App f a) = allNamesIn f ++ allNamesIn a
1507 allNamesIn _ = []
1510-- | Pretty-print a term
1511pprintTT :: [Name] -- ^ The bound names (for highlighting and de Bruijn indices)
1512 -> TT Name -- ^ The term to be printed
1513 -> Doc OutputAnnotation
1514pprintTT bound tm = pp startPrec bound tm
1516 where
1517 startPrec = 0
1518 appPrec = 10
1520 pp p bound (P Bound n ty) = annotate (AnnBoundName n False) (text $ show n)
1521 pp p bound (P nt n ty) = annotate (AnnName n Nothing Nothing Nothing)
1522 (text $ show n)
1523 pp p bound (V i)
1524 | i < length bound = let n = bound !! i
1525 in annotate (AnnBoundName n False) (text $ show n)
1526 | otherwise = text ("{{{V" ++ show i ++ "}}}")
1527 pp p bound (Bind n b sc) = ppb p bound n b $
1528 pp startPrec (n:bound) sc
1529 pp p bound (App tm1 tm2) =
1530 bracket p appPrec . group . hang 2 $
1531 pp appPrec bound tm1 <> line <>
1532 pp (appPrec + 1) bound tm2
1533 pp p bound (Constant c) = annotate (AnnConst c) (text (show c))
1534 pp p bound (Proj tm i) =
1535 lparen <> pp startPrec bound tm <> rparen <>
1536 text "!" <> text (show i)
1537 pp p bound Erased = text "<<<erased>>>"
1538 pp p bound Impossible = text "<<<impossible>>>"
1539 pp p bound (TType ue) = annotate (AnnType "Type" "The type of types") $
1540 text "Type"
1541 pp p bound (UType u) = text (show u)
1543 ppb p bound n (Lam ty) sc =
1544 bracket p startPrec . group . align . hang 2 $
1545 text "λ" <+> bindingOf n False <+> text "." <> line <> sc
1546 ppb p bound n (Pi _ ty k) sc =
1547 bracket p startPrec . group . align $
1548 lparen <> (bindingOf n False) <+> colon <+>
1549 (group . align) (pp startPrec bound ty) <>
1550 rparen <+> mkArrow k <> line <> sc
1551 where mkArrow (UType UniqueType) = text "⇴"
1552 mkArrow (UType NullType) = text "⥛"
1553 mkArrow _ = text "→"
1554 ppb p bound n (Let ty val) sc =
1555 bracket p startPrec . group . align $
1556 (group . hang 2) (annotate AnnKeyword (text "let") <+>
1557 bindingOf n False <+> colon <+>
1558 pp startPrec bound ty <+>
1559 text "=" <> line <>
1560 pp startPrec bound val) <> line <>
1561 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1562 ppb p bound n (NLet ty val) sc =
1563 bracket p startPrec . group . align $
1564 (group . hang 2) (annotate AnnKeyword (text "nlet") <+>
1565 bindingOf n False <+> colon <+>
1566 pp startPrec bound ty <+>
1567 text "=" <> line <>
1568 pp startPrec bound val) <> line <>
1569 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1570 ppb p bound n (Hole ty) sc =
1571 bracket p startPrec . group . align . hang 2 $
1572 text "?" <+> bindingOf n False <+> text "." <> line <> sc
1573 ppb p bound n (GHole _ ty) sc =
1574 bracket p startPrec . group . align . hang 2 $
1575 text "¿" <+> bindingOf n False <+> text "." <> line <> sc
1576 ppb p bound n (Guess ty val) sc =
1577 bracket p startPrec . group . align . hang 2 $
1578 text "?" <> bindingOf n False <+>
1579 text "≈" <+> pp startPrec bound val <+>
1580 text "." <> line <> sc
1581 ppb p bound n (PVar ty) sc =
1582 bracket p startPrec . group . align . hang 2 $
1583 annotate AnnKeyword (text "pat") <+>
1584 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1585 text "." <> line <>
1586 sc
1587 ppb p bound n (PVTy ty) sc =
1588 bracket p startPrec . group . align . hang 2 $
1589 annotate AnnKeyword (text "patTy") <+>
1590 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1591 text "." <> line <>
1592 sc
1594 bracket outer inner doc
1595 | outer > inner = lparen <> doc <> rparen
1596 | otherwise = doc
1599-- | Pretty-printer helper for the binding site of a name
1600bindingOf :: Name -- ^^ the bound name
1601 -> Bool -- ^^ whether the name is implicit
1602 -> Doc OutputAnnotation
1603bindingOf n imp = annotate (AnnBoundName n imp) (text (show n))