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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 t
159 | CantResolveAlts [Name]
160 | IncompleteTerm t
161 | UniverseError
162 | UniqueError Universe Name
163 | UniqueKindError Universe Name
164 | ProgramLineComment
165 | Inaccessible Name
166 | CantMatch t
167 | NonCollapsiblePostulate Name
168 | AlreadyDefined Name
169 | ProofSearchFail (Err' t)
170 | NoRewriting t
171 | At FC (Err' t)
172 | Elaborating String Name (Err' t)
173 | ElaboratingArg Name Name [(Name, Name)] (Err' t)
174 | ProviderError String
175 | LoadingFailed String (Err' t)
176 | ReflectionError [[ErrorReportPart]] (Err' t)
177 | ReflectionFailed String (Err' t)
178 | ElabDebug (Maybe String) t [(Name, t, [(Name, Binder t)])]
179 -- ^ User-specified message, proof term, goals with context (first goal is focused)
180 deriving (Eq, Functor, Data, Typeable)
182type Err = Err' Term
184data TC a = OK !a
185 | Error Err
186 deriving (Eq, Functor)
188bindTC :: TC a -> (a -> TC b) -> TC b
189bindTC x k = case x of
190 OK v -> k v
191 Error e -> Error e
192{-# INLINE bindTC #-}
194instance Monad TC where
195 return x = OK x
196 x >>= k = bindTC x k
197 fail e = Error (InternalMsg e)
199instance MonadPlus TC where
200 mzero = fail "Unknown error"
201 (OK x) `mplus` _ = OK x
202 _ `mplus` (OK y) = OK y
203 err `mplus` _ = err
206instance Applicative TC where
207 pure = return
208 (<*>) = ap
210instance Alternative TC where
211 empty = mzero
212 (<|>) = mplus
214{-!
215deriving instance NFData Err
216!-}
218instance Sized ErrorReportPart where
219 size (TextPart msg) = 1 + length msg
220 size (TermPart t) = 1 + size t
221 size (NamePart n) = 1 + size n
222 size (SubReport rs) = 1 + size rs
224instance Sized Err where
225 size (Msg msg) = length msg
226 size (InternalMsg msg) = length msg
227 size (CantUnify _ left right err _ score) = size (fst left) + size (fst right) + size err
228 size (InfiniteUnify _ right _) = size right
229 size (CantConvert left right _) = size left + size right
230 size (UnifyScope _ _ right _) = size right
231 size (NoSuchVariable name) = size name
232 size (NoTypeDecl name) = size name
233 size (NotInjective l c r) = size l + size c + size r
234 size (CantResolve trm) = size trm
235 size (NoRewriting trm) = size trm
236 size (CantResolveAlts _) = 1
237 size (IncompleteTerm trm) = size trm
238 size UniverseError = 1
239 size ProgramLineComment = 1
240 size (At fc err) = size fc + size err
241 size (Elaborating _ n err) = size err
242 size (ElaboratingArg _ _ _ err) = size err
243 size (ProviderError msg) = length msg
244 size (LoadingFailed fn e) = 1 + length fn + size e
245 size _ = 1
247score :: Err -> Int
248score (CantUnify _ _ _ m _ s) = s + score m
249score (CantResolve _) = 20
250score (NoSuchVariable _) = 1000
251score (ProofSearchFail e) = score e
252score (CantSolveGoal _ _) = 100000
253score (InternalMsg _) = -1
254score (At _ e) = score e
255score (ElaboratingArg _ _ _ e) = score e
256score (Elaborating _ _ e) = score e
257score _ = 0
259instance Show Err where
260 show (Msg s) = s
261 show (InternalMsg s) = "Internal error: " ++ show s
262 show (CantUnify rcv l r e sc i) = "CantUnify " ++ show rcv ++ " " ++
263 show l ++ " " ++ show r ++ " " ++
264 show e ++ " in " ++ show sc ++ " " ++ show i
265 show (CantSolveGoal g _) = "CantSolve " ++ show g
266 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
267 show (ProviderError msg) = "Type provider error: " ++ msg
268 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: (TT) " ++ show e
269 show ProgramLineComment = "Program line next to comment"
270 show (At f e) = show f ++ ":" ++ show e
271 show (ElaboratingArg f x prev e) = "Elaborating " ++ show f ++ " arg " ++
272 show x ++ ": " ++ show e
273 show (Elaborating what n e) = "Elaborating " ++ what ++ show n ++ ":" ++ show e
274 show (ProofSearchFail e) = "Proof search fail: " ++ show e
275 show _ = "Error"
277instance Pretty Err OutputAnnotation where
278 pretty (Msg m) = text m
279 pretty (CantUnify _ (l, _) (r, _) e _ i) =
280 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r <+>
281 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
282 pretty (ProviderError msg) = text msg
283 pretty err@(LoadingFailed _ _) = text (show err)
284 pretty _ = text "Error"
286instance (Pretty a OutputAnnotation) => Pretty (TC a) OutputAnnotation where
287 pretty (OK ok) = pretty ok
288 pretty (Error err) =
289 text "Error" <+> colon <+> pretty err
291instance Show a => Show (TC a) where
292 show (OK x) = show x
293 show (Error str) = "Error: " ++ show str
295tfail :: Err -> TC a
296tfail e = Error e
298failMsg :: String -> TC a
299failMsg str = Error (Msg str)
301trun :: FC -> TC a -> TC a
302trun fc (OK a) = OK a
303trun fc (Error e) = Error (At fc e)
305discard :: Monad m => m a -> m ()
306discard f = f >> return ()
308showSep :: String -> [String] -> String
309showSep sep [] = ""
310showSep sep [x] = x
311showSep sep (x:xs) = x ++ sep ++ showSep sep xs
313pmap f (x, y) = (f x, f y)
315traceWhen True msg a = trace msg a
316traceWhen False _ a = a
318-- RAW TERMS ----------------------------------------------------------------
320-- | Names are hierarchies of strings, describing scope (so no danger of
321-- duplicate names, but need to be careful on lookup).
322data Name = UN T.Text -- ^ User-provided name
323 | NS Name [T.Text] -- ^ Root, namespaces
324 | MN Int T.Text -- ^ Machine chosen names
325 | NErased -- ^ Name of something which is never used in scope
326 | SN SpecialName -- ^ Decorated function names
327 | SymRef Int -- ^ Reference to IBC file symbol table (used during serialisation)
328 deriving (Eq, Ord, Data, Typeable)
330txt :: String -> T.Text
331txt = T.pack
333str :: T.Text -> String
334str = T.unpack
336tnull :: T.Text -> Bool
337tnull = T.null
339thead :: T.Text -> Char
340thead = T.head
342-- Smart constructors for names, using old String style
343sUN :: String -> Name
344sUN s = UN (txt s)
346sNS :: Name -> [String] -> Name
347sNS n ss = NS n (map txt ss)
349sMN :: Int -> String -> Name
350sMN i s = MN i (txt s)
352{-!
353deriving instance Binary Name
354deriving instance NFData Name
355!-}
357data SpecialName = WhereN Int Name Name
358 | WithN Int Name
359 | InstanceN Name [T.Text]
360 | ParentN Name T.Text
361 | MethodN Name
362 | CaseN Name
363 | ElimN Name
364 | InstanceCtorN Name
365 deriving (Eq, Ord, Data, Typeable)
366{-!
367deriving instance Binary SpecialName
368deriving instance NFData SpecialName
369!-}
371sInstanceN :: Name -> [String] -> SpecialName
372sInstanceN n ss = InstanceN n (map T.pack ss)
374sParentN :: Name -> String -> SpecialName
375sParentN n s = ParentN n (T.pack s)
377instance Sized Name where
378 size (UN n) = 1
379 size (NS n els) = 1 + length els
380 size (MN i n) = 1
381 size _ = 1
383instance Pretty Name OutputAnnotation where
384 pretty n@(UN n') = annotate (AnnName n Nothing Nothing Nothing) $ text (T.unpack n')
385 pretty n@(NS un s) = annotate (AnnName n Nothing Nothing Nothing) . noAnnotate $ pretty un
386 pretty n@(MN i s) = annotate (AnnName n Nothing Nothing Nothing) $
387 lbrace <+> text (T.unpack s) <+> (text . show $ i) <+> rbrace
388 pretty n@(SN s) = annotate (AnnName n Nothing Nothing Nothing) $ text (show s)
390instance Pretty [Name] OutputAnnotation where
391 pretty = encloseSep empty empty comma . map pretty
393instance Show Name where
394 show (UN n) = str n
395 show (NS n s) = showSep "." (map T.unpack (reverse s)) ++ "." ++ show n
396 show (MN _ u) | u == txt "underscore" = "_"
397 show (MN i s) = "{" ++ str s ++ show i ++ "}"
398 show (SN s) = show s
399 show NErased = "_"
401instance Show SpecialName where
402 show (WhereN i p c) = show p ++ ", " ++ show c
403 show (WithN i n) = "with block in " ++ show n
404 show (InstanceN cl inst) = showSep ", " (map T.unpack inst) ++ " instance of " ++ show cl
405 show (MethodN m) = "method " ++ show m
406 show (ParentN p c) = show p ++ "#" ++ T.unpack c
407 show (CaseN n) = "case block in " ++ show n
408 show (ElimN n) = "<<" ++ show n ++ " eliminator>>"
409 show (InstanceCtorN n) = "constructor of " ++ show n
411-- Show a name in a way decorated for code generation, not human reading
412showCG :: Name -> String
413showCG (UN n) = T.unpack n
414showCG (NS n s) = showSep "." (map T.unpack (reverse s)) ++ "." ++ showCG n
415showCG (MN _ u) | u == txt "underscore" = "_"
416showCG (MN i s) = "{" ++ T.unpack s ++ show i ++ "}"
417showCG (SN s) = showCG' s
418 where showCG' (WhereN i p c) = showCG p ++ ":" ++ showCG c ++ ":" ++ show i
419 showCG' (WithN i n) = "_" ++ showCG n ++ "_with_" ++ show i
420 showCG' (InstanceN cl inst) = '@':showCG cl ++ '$':showSep ":" (map T.unpack inst)
421 showCG' (MethodN m) = '!':showCG m
422 showCG' (ParentN p c) = showCG p ++ "#" ++ show c
423 showCG' (CaseN c) = showCG c ++ "_case"
424 showCG' (ElimN sn) = showCG sn ++ "_elim"
425showCG NErased = "_"
428-- |Contexts allow us to map names to things. A root name maps to a collection
429-- of things in different namespaces with that name.
430type Ctxt a = Map.Map Name (Map.Map Name a)
431emptyContext = Map.empty
433mapCtxt :: (a -> b) -> Ctxt a -> Ctxt b
434mapCtxt = fmap . fmap
436-- |Return True if the argument 'Name' should be interpreted as the name of a
437-- typeclass.
438tcname (UN xs) | T.null xs = False
439 | otherwise = T.head xs == '@'
440tcname (NS n _) = tcname n
441tcname (SN (InstanceN _ _)) = True
442tcname (SN (MethodN _)) = True
443tcname (SN (ParentN _ _)) = True
444tcname _ = False
446implicitable (NS n _) = implicitable n
447implicitable (UN xs) | T.null xs = False
448 | otherwise = isLower (T.head xs) || T.head xs == '_'
449implicitable (MN _ x) = not (tnull x) && thead x /= '_'
450implicitable _ = False
452nsroot (NS n _) = n
453nsroot n = n
455-- this will overwrite already existing definitions
456addDef :: Name -> a -> Ctxt a -> Ctxt a
457addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
458 Nothing -> Map.insert (nsroot n)
459 (Map.insert n v Map.empty) ctxt
460 Just xs -> Map.insert (nsroot n)
461 (Map.insert n v xs) ctxt
463{-| Look up a name in the context, given an optional namespace.
464 The name (n) may itself have a (partial) namespace given.
466 Rules for resolution:
468 - if an explicit namespace is given, return the names which match it. If none
469 match, return all names.
471 - if the name has has explicit namespace given, return the names which match it
472 and ignore the given namespace.
474 - otherwise, return all names.
476-}
478lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
479lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
480 Just xs -> filterNS (Map.toList xs)
481 Nothing -> []
482 where
483 filterNS [] = []
484 filterNS ((found, v) : xs)
485 | nsmatch n found = (found, v) : filterNS xs
486 | otherwise = filterNS xs
488 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
489 nsmatch (NS _ _) _ = False
490 nsmatch looking found = True
492lookupCtxt :: Name -> Ctxt a -> [a]
493lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
495lookupCtxtExact :: Name -> Ctxt a -> Maybe a
496lookupCtxtExact n ctxt = listToMaybe [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
498deleteDefExact :: Name -> Ctxt a -> Ctxt a
499deleteDefExact n = Map.adjust (Map.delete n) (nsroot n)
501updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
502updateDef n f ctxt
503 = let ds = lookupCtxtName n ctxt in
504 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
506toAlist :: Ctxt a -> [(Name, a)]
507toAlist ctxt = let allns = map snd (Map.toList ctxt) in
508 concatMap (Map.toList) allns
510addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
511addAlist [] ctxt = ctxt
512addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
514data NativeTy = IT8 | IT16 | IT32 | IT64
515 deriving (Show, Eq, Ord, Enum, Data, Typeable)
517instance Pretty NativeTy OutputAnnotation where
518 pretty IT8 = text "Bits8"
519 pretty IT16 = text "Bits16"
520 pretty IT32 = text "Bits32"
521 pretty IT64 = text "Bits64"
523data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
524 | ITVec NativeTy Int
525 deriving (Show, Eq, Ord, Data, Typeable)
527intTyName :: IntTy -> String
528intTyName ITNative = "Int"
529intTyName ITBig = "BigInt"
530intTyName (ITFixed sized) = "B" ++ show (nativeTyWidth sized)
531intTyName (ITChar) = "Char"
532intTyName (ITVec ity count) = "B" ++ show (nativeTyWidth ity) ++ "x" ++ show count
534data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors https://github.com/idris-lang/Idris-dev/issues/1723
535 deriving (Show, Eq, Ord, Data, Typeable)
536{-!
537deriving instance NFData IntTy
538deriving instance NFData NativeTy
539deriving instance NFData ArithTy
540!-}
542instance Pretty ArithTy OutputAnnotation where
543 pretty (ATInt ITNative) = text "Int"
544 pretty (ATInt ITBig) = text "BigInt"
545 pretty (ATInt ITChar) = text "Char"
546 pretty (ATInt (ITFixed n)) = pretty n
547 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
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 | B8V (Vector Word8) | B16V (Vector Word16)
566 | B32V (Vector Word32) | B64V (Vector Word64)
567 | AType ArithTy | StrType
568 | WorldType | TheWorld
569 | PtrType | ManagedPtrType | BufferType | VoidType | Forgot
570 deriving (Eq, Ord, Data, Typeable)
571{-!
572deriving instance Binary Const
573deriving instance NFData Const
574!-}
576isTypeConst :: Const -> Bool
577isTypeConst (AType _) = True
578isTypeConst StrType = True
579isTypeConst ManagedPtrType = True
580isTypeConst BufferType = True
581isTypeConst WorldType = True
582isTypeConst PtrType = True
583isTypeConst VoidType = True
584isTypeConst _ = False
586instance Sized Const where
587 size _ = 1
589instance Pretty Const OutputAnnotation where
590 pretty (I i) = text . show $ i
591 pretty (BI i) = text . show $ i
592 pretty (Fl f) = text . show $ f
593 pretty (Ch c) = text . show $ c
594 pretty (Str s) = text s
595 pretty (AType a) = pretty a
596 pretty StrType = text "String"
597 pretty TheWorld = text "%theWorld"
598 pretty WorldType = text "prim__World"
599 pretty BufferType = text "prim__UnsafeBuffer"
600 pretty PtrType = text "Ptr"
601 pretty ManagedPtrType = text "Ptr"
602 pretty VoidType = text "Void"
603 pretty Forgot = text "Forgot"
604 pretty (B8 w) = text . show $ w
605 pretty (B16 w) = text . show $ w
606 pretty (B32 w) = text . show $ w
607 pretty (B64 w) = text . show $ w
609-- | Determines whether the input constant represents a type
610constIsType :: Const -> Bool
611constIsType (I _) = False
612constIsType (BI _) = False
613constIsType (Fl _) = False
614constIsType (Ch _) = False
615constIsType (Str _) = False
616constIsType (B8 _) = False
617constIsType (B16 _) = False
618constIsType (B32 _) = False
619constIsType (B64 _) = False
620constIsType (B8V _) = False
621constIsType (B16V _) = False
622constIsType (B32V _) = False
623constIsType (B64V _) = False
624constIsType _ = True
626-- | Get the docstring for a Const
627constDocs :: Const -> String
628constDocs c@(AType (ATInt ITBig)) = "Arbitrary-precision integers"
629constDocs c@(AType (ATInt ITNative)) = "Fixed-precision integers of undefined size"
630constDocs c@(AType (ATInt ITChar)) = "Characters in some unspecified encoding"
631constDocs c@(AType ATFloat) = "Double-precision floating-point numbers"
632constDocs StrType = "Strings in some unspecified encoding"
633constDocs PtrType = "Foreign pointers"
634constDocs ManagedPtrType = "Managed pointers"
635constDocs BufferType = "Copy-on-write buffers"
636constDocs c@(AType (ATInt (ITFixed IT8))) = "Eight bits (unsigned)"
637constDocs c@(AType (ATInt (ITFixed IT16))) = "Sixteen bits (unsigned)"
638constDocs c@(AType (ATInt (ITFixed IT32))) = "Thirty-two bits (unsigned)"
639constDocs c@(AType (ATInt (ITFixed IT64))) = "Sixty-four bits (unsigned)"
640constDocs c@(AType (ATInt (ITVec IT8 16))) = "Vectors of sixteen eight-bit values"
641constDocs c@(AType (ATInt (ITVec IT16 8))) = "Vectors of eight sixteen-bit values"
642constDocs c@(AType (ATInt (ITVec IT32 4))) = "Vectors of four thirty-two-bit values"
643constDocs c@(AType (ATInt (ITVec IT64 2))) = "Vectors of two sixty-four-bit values"
644constDocs (Fl f) = "A float"
645constDocs (I i) = "A fixed-precision integer"
646constDocs (BI i) = "An arbitrary-precision integer"
647constDocs (Str s) = "A string of length " ++ show (length s)
648constDocs (Ch c) = "A character"
649constDocs (B8 w) = "The eight-bit value 0x" ++
650 showIntAtBase 16 intToDigit w ""
651constDocs (B16 w) = "The sixteen-bit value 0x" ++
652 showIntAtBase 16 intToDigit w ""
653constDocs (B32 w) = "The thirty-two-bit value 0x" ++
654 showIntAtBase 16 intToDigit w ""
655constDocs (B64 w) = "The sixty-four-bit value 0x" ++
656 showIntAtBase 16 intToDigit w ""
657constDocs (B8V v) = "A vector of eight-bit values"
658constDocs (B16V v) = "A vector of sixteen-bit values"
659constDocs (B32V v) = "A vector of thirty-two-bit values"
660constDocs (B64V v) = "A vector of sixty-four-bit values"
661constDocs prim = "Undocumented"
663data Universe = NullType | UniqueType | AllTypes
664 deriving (Eq, Ord, Data, Typeable)
666instance Show Universe where
667 show UniqueType = "UniqueType"
668 show NullType = "NullType"
669 show AllTypes = "Type*"
671data Raw = Var Name
672 | RBind Name (Binder Raw) Raw
673 | RApp Raw Raw
674 | RType
675 | RUType Universe
676 | RForce Raw
677 | RConstant Const
678 deriving (Show, Eq, Data, Typeable)
680instance Sized Raw where
681 size (Var name) = 1
682 size (RBind name bind right) = 1 + size bind + size right
683 size (RApp left right) = 1 + size left + size right
684 size RType = 1
685 size (RUType _) = 1
686 size (RForce raw) = 1 + size raw
687 size (RConstant const) = size const
689instance Pretty Raw OutputAnnotation where
690 pretty = text . show
692{-!
693deriving instance Binary Raw
694deriving instance NFData Raw
695!-}
697data ImplicitInfo = Impl { tcinstance :: Bool }
698 deriving (Show, Eq, Ord, Data, Typeable)
700{-!
701deriving instance Binary ImplicitInfo
702deriving instance NFData ImplicitInfo
703!-}
705-- The type parameter `b` will normally be something like `TT Name` or just
706-- `Raw`. We do not make a type-level distinction between TT terms that happen
707-- to be TT types and TT terms that are not TT types.
708-- | All binding forms are represented in a uniform fashion. This type only represents
709-- the types of bindings (and their values, if any); the attached identifiers are part
710-- of the 'Bind' constructor for the 'TT' type.
711data Binder b = Lam { binderTy :: !b {-^ type annotation for bound variable-}}
712 | Pi { binderImpl :: Maybe ImplicitInfo,
713 binderTy :: !b,
714 binderKind :: !b }
715 {-^ A binding that occurs in a function type expression, e.g. @(x:Int) -> ...@
716 The 'binderImpl' flag says whether it was a scoped implicit
717 (i.e. forall bound) in the high level Idris, but otherwise
718 has no relevance in TT. -}
719 | Let { binderTy :: !b,
720 binderVal :: b {-^ value for bound variable-}}
721 -- ^ A binding that occurs in a @let@ expression
722 | NLet { binderTy :: !b,
723 binderVal :: b }
724 | Hole { binderTy :: !b}
725 | GHole { envlen :: Int,
726 binderTy :: !b}
727 | Guess { binderTy :: !b,
728 binderVal :: b }
729 | PVar { binderTy :: !b }
730 -- ^ A pattern variable
731 | PVTy { binderTy :: !b }
732 deriving (Show, Eq, Ord, Functor, Foldable, Traversable, Data, Typeable)
733{-!
734deriving instance Binary Binder
735deriving instance NFData Binder
736!-}
738instance Sized a => Sized (Binder a) where
739 size (Lam ty) = 1 + size ty
740 size (Pi _ ty _) = 1 + size ty
741 size (Let ty val) = 1 + size ty + size val
742 size (NLet ty val) = 1 + size ty + size val
743 size (Hole ty) = 1 + size ty
744 size (GHole _ ty) = 1 + size ty
745 size (Guess ty val) = 1 + size ty + size val
746 size (PVar ty) = 1 + size ty
747 size (PVTy ty) = 1 + size ty
749fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
750fmapMB f (Let t v) = liftM2 Let (f t) (f v)
751fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
752fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
753fmapMB f (Lam t) = liftM Lam (f t)
754fmapMB f (Pi i t k) = liftM2 (Pi i) (f t) (f k)
755fmapMB f (Hole t) = liftM Hole (f t)
756fmapMB f (GHole i t) = liftM (GHole i) (f t)
757fmapMB f (PVar t) = liftM PVar (f t)
758fmapMB f (PVTy t) = liftM PVTy (f t)
760raw_apply :: Raw -> [Raw] -> Raw
761raw_apply f [] = f
762raw_apply f (a : as) = raw_apply (RApp f a) as
764raw_unapply :: Raw -> (Raw, [Raw])
765raw_unapply t = ua [] t where
766 ua args (RApp f a) = ua (a:args) f
767 ua args t = (t, args)
769-- WELL TYPED TERMS ---------------------------------------------------------
771-- | Universe expressions for universe checking
772data UExp = UVar Int -- ^ universe variable
773 | UVal Int -- ^ explicit universe level
774 deriving (Eq, Ord, Data, Typeable)
775{-!
776deriving instance NFData UExp
777!-}
779instance Sized UExp where
780 size _ = 1
782-- We assume that universe levels have been checked, so anything external
783-- can just have the same universe variable and we won't get any new
784-- cycles.
786instance Binary UExp where
787 put x = return ()
788 get = return (UVar (-1))
790instance Show UExp where
791 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
792 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
793 show (UVal x) = show x
794-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
796-- | Universe constraints
797data UConstraint = ULT UExp UExp -- ^ Strictly less than
798 | ULE UExp UExp -- ^ Less than or equal to
799 deriving (Eq, Ord)
801instance Show UConstraint where
802 show (ULT x y) = show x ++ " < " ++ show y
803 show (ULE x y) = show x ++ " <= " ++ show y
805type UCs = (Int, [UConstraint])
807data NameType = Bound
808 | Ref
809 | DCon {nt_tag :: Int, nt_arity :: Int, nt_unique :: Bool} -- ^ Data constructor
810 | TCon {nt_tag :: Int, nt_arity :: Int} -- ^ Type constructor
811 deriving (Show, Ord, Data, Typeable)
812{-!
813deriving instance Binary NameType
814deriving instance NFData NameType
815!-}
817instance Sized NameType where
818 size _ = 1
820instance Pretty NameType OutputAnnotation where
821 pretty = text . show
823instance Eq NameType where
824 Bound == Bound = True
825 Ref == Ref = True
826 DCon _ a _ == DCon _ b _ = (a == b) -- ignore tag
827 TCon _ a == TCon _ b = (a == b) -- ignore tag
828 _ == _ = False
830-- | Terms in the core language. The type parameter is the type of
831-- identifiers used for bindings and explicit named references;
832-- usually we use @TT 'Name'@.
833data TT n = P NameType n (TT n) -- ^ named references with type
834 -- (P for "Parameter", motivated by McKinna and Pollack's
835 -- Pure Type Systems Formalized)
836 | V !Int -- ^ a resolved de Bruijn-indexed variable
837 | Bind n !(Binder (TT n)) (TT n) -- ^ a binding
838 | App !(TT n) (TT n) -- ^ function, function type, arg
839 | Constant Const -- ^ constant
840 | Proj (TT n) !Int -- ^ argument projection; runtime only
841 -- (-1) is a special case for 'subtract one from BI'
842 | Erased -- ^ an erased term
843 | Impossible -- ^ special case for totality checking
844 | TType UExp -- ^ the type of types at some level
845 | UType Universe -- ^ Uniqueness type universe (disjoint from TType)
846 deriving (Ord, Functor, Data, Typeable)
847{-!
848deriving instance Binary TT
849deriving instance NFData TT
850!-}
852class TermSize a where
853 termsize :: Name -> a -> Int
855instance TermSize a => TermSize [a] where
856 termsize n [] = 0
857 termsize n (x : xs) = termsize n x + termsize n xs
859instance TermSize (TT Name) where
860 termsize n (P _ n' _)
861 | n' == n = 1000000 -- recursive => really big
862 | otherwise = 1
863 termsize n (V _) = 1
864 -- for `Bind` terms, we can erroneously declare a term
865 -- "recursive => really big" if the name of the bound
866 -- variable is the same as the name we're using
867 -- So generate a different name in that case.
868 termsize n (Bind n' (Let t v) sc)
869 = let rn = if n == n' then sMN 0 "noname" else n in
870 termsize rn v + termsize rn sc
871 termsize n (Bind n' b sc)
872 = let rn = if n == n' then sMN 0 "noname" else n in
873 termsize rn sc
874 termsize n (App f a) = termsize n f + termsize n a
875 termsize n (Proj t i) = termsize n t
876 termsize n _ = 1
878instance Sized a => Sized (TT a) where
879 size (P name n trm) = 1 + size name + size n + size trm
880 size (V v) = 1
881 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
882 size (App l r) = 1 + size l + size r
883 size (Constant c) = size c
884 size Erased = 1
885 size (TType u) = 1 + size u
887instance Pretty a o => Pretty (TT a) o where
888 pretty _ = text "test"
890type EnvTT n = [(n, Binder (TT n))]
892data Datatype n = Data { d_typename :: n,
893 d_typetag :: Int,
894 d_type :: (TT n),
895 d_unique :: Bool,
896 d_cons :: [(n, TT n)] }
897 deriving (Show, Functor, Eq)
899instance Eq n => Eq (TT n) where
900 (==) (P xt x _) (P yt y _) = x == y
901 (==) (V x) (V y) = x == y
902 (==) (Bind _ xb xs) (Bind _ yb ys) = xs == ys && xb == yb
903 (==) (App fx ax) (App fy ay) = ax == ay && fx == fy
904 (==) (TType _) (TType _) = True -- deal with constraints later
905 (==) (Constant x) (Constant y) = x == y
906 (==) (Proj x i) (Proj y j) = x == y && i == j
907 (==) Erased _ = True
908 (==) _ Erased = True
909 (==) _ _ = False
911-- * A few handy operations on well typed terms:
913-- | A term is injective iff it is a data constructor, type constructor,
914-- constant, the type Type, pi-binding, or an application of an injective
915-- term.
916isInjective :: TT n -> Bool
917isInjective (P (DCon _ _ _) _ _) = True
918isInjective (P (TCon _ _) _ _) = True
919isInjective (Constant _) = True
920isInjective (TType x) = True
921isInjective (Bind _ (Pi _ _ _) sc) = True
922isInjective (App f a) = isInjective f
923isInjective _ = False
925-- | Count the number of instances of a de Bruijn index in a term
926vinstances :: Int -> TT n -> Int
927vinstances i (V x) | i == x = 1
928vinstances i (App f a) = vinstances i f + vinstances i a
929vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
930 where instancesB (Let t v) = vinstances i v
931 instancesB _ = 0
932vinstances i t = 0
934-- | Replace the outermost (index 0) de Bruijn variable with the given term
935instantiate :: TT n -> TT n -> TT n
936instantiate e = subst 0 where
937 subst i (V x) | i == x = e
938 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
939 subst i (App f a) = App (subst i f) (subst i a)
940 subst i (Proj x idx) = Proj (subst i x) idx
941 subst i t = t
943-- | As 'instantiate', but also decrement the indices of all de Bruijn variables
944-- remaining in the term, so that there are no more references to the variable
945-- that has been substituted.
946substV :: TT n -> TT n -> TT n
947substV x tm = dropV 0 (instantiate x tm) where
948 dropV i (V x) | x > i = V (x - 1)
949 | otherwise = V x
950 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
951 dropV i (App f a) = App (dropV i f) (dropV i a)
952 dropV i (Proj x idx) = Proj (dropV i x) idx
953 dropV i t = t
955-- | Replace all non-free de Bruijn references in the given term with references
956-- to the name of their binding.
957explicitNames :: TT n -> TT n
958explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
959 Bind x b'
960 (explicitNames (instantiate
961 (P Bound x (binderTy b')) sc))
962explicitNames (App f a) = App (explicitNames f) (explicitNames a)
963explicitNames (Proj x idx) = Proj (explicitNames x) idx
964explicitNames t = t
966-- | Replace references to the given 'Name'-like id with references to
967-- de Bruijn index 0.
968pToV :: Eq n => n -> TT n -> TT n
969pToV n = pToV' n 0
970pToV' n i (P _ x _) | n == x = V i
971pToV' n i (Bind x b sc)
972-- We can assume the inner scope has been pToVed already, so continue to
973-- resolve names from the *outer* scope which may happen to have the same id.
974 | n == x = Bind x (fmap (pToV' n i) b) sc
975 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
976pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
977pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
978pToV' n i t = t
980-- increase de Bruijn indices, as if a binder has been added
981addBinder :: TT n -> TT n
982addBinder t = ab 0 t
983 where
984 ab top (V i) | i >= top = V (i + 1)
985 | otherwise = V i
986 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
987 ab top (App f a) = App (ab top f) (ab top a)
988 ab top (Proj t idx) = Proj (ab top t) idx
989 ab top t = t
991-- | Convert several names. First in the list comes out as V 0
992pToVs :: Eq n => [n] -> TT n -> TT n
993pToVs ns tm = pToVs' ns tm 0 where
994 pToVs' [] tm i = tm
995 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
997-- | Replace de Bruijn indices in the given term with explicit references to
998-- the names of the bindings they refer to. It is an error if the given term
999-- contains free de Bruijn indices.
1000vToP :: TT n -> TT n
1001vToP = vToP' [] where
1002 vToP' env (V i) = let (n, b) = (env !! i) in
1003 P Bound n (binderTy b)
1004 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
1005 Bind n b' (vToP' ((n, b'):env) sc)
1006 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
1007 vToP' env t = t
1009-- | Replace every non-free reference to the name of a binding in
1010-- the given term with a de Bruijn index.
1011finalise :: Eq n => TT n -> TT n
1012finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
1013finalise (App f a) = App (finalise f) (finalise a)
1014finalise t = t
1016-- Once we've finished checking everything about a term we no longer need
1017-- the type on the 'P' so erase it so save memory
1019pEraseType :: TT n -> TT n
1020pEraseType (P nt t _) = P nt t Erased
1021pEraseType (App f a) = App (pEraseType f) (pEraseType a)
1022pEraseType (Bind n b sc) = Bind n (fmap pEraseType b) (pEraseType sc)
1023pEraseType t = t
1025-- | As 'instantiate', but in addition to replacing @'V' 0@,
1026-- replace references to the given 'Name'-like id.
1027subst :: Eq n => n {-^ The id to replace -} ->
1028 TT n {-^ The replacement term -} ->
1029 TT n {-^ The term to replace in -} ->
1030 TT n
1031-- subst n v tm = instantiate v (pToV n tm)
1032subst n v tm = fst $ subst' 0 tm
1033 where
1034 -- keep track of updates to save allocations - this is a big win on
1035 -- large terms in particular
1036 -- ('Maybe' would be neater here, but >>= is not the right combinator.
1037 -- Feel free to tidy up, as long as it still saves allocating when no
1038 -- substitution happens...)
1039 subst' i (V x) | i == x = (v, True)
1040 subst' i (P _ x _) | n == x = (v, True)
1041 subst' i t@(Bind x b sc) | x /= n
1042 = let (b', ub) = substB' i b
1043 (sc', usc) = subst' (i+1) sc in
1044 if ub || usc then (Bind x b' sc', True) else (t, False)
1045 subst' i t@(App f a) = let (f', uf) = subst' i f
1046 (a', ua) = subst' i a in
1047 if uf || ua then (App f' a', True) else (t, False)
1048 subst' i t@(Proj x idx) = let (x', u) = subst' i x in
1049 if u then (Proj x' idx, u) else (t, False)
1050 subst' i t = (t, False)
1052 substB' i b@(Let t v) = let (t', ut) = subst' i t
1053 (v', uv) = subst' i v in
1054 if ut || uv then (Let t' v', True)
1055 else (b, False)
1056 substB' i b@(Guess t v) = let (t', ut) = subst' i t
1057 (v', uv) = subst' i v in
1058 if ut || uv then (Guess t' v', True)
1059 else (b, False)
1060 substB' i b = let (ty', u) = subst' i (binderTy b) in
1061 if u then (b { binderTy = ty' }, u) else (b, False)
1063-- If there are no Vs in the term (i.e. in proof state)
1064psubst :: Eq n => n -> TT n -> TT n -> TT n
1065psubst n v tm = s' 0 tm where
1066 s' i (V x) | x > i = V (x - 1)
1067 | x == i = v
1068 | otherwise = V x
1069 s' i (P _ x _) | n == x = v
1070 s' i (Bind x b sc) | n == x = Bind x (fmap (s' i) b) sc
1071 | otherwise = Bind x (fmap (s' i) b) (s' (i+1) sc)
1072 s' i (App f a) = App (s' i f) (s' i a)
1073 s' i (Proj t idx) = Proj (s' i t) idx
1074 s' i t = t
1076-- | As 'subst', but takes a list of (name, substitution) pairs instead
1077-- of a single name and substitution
1078substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
1079substNames [] t = t
1080substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
1082-- | Replaces all terms equal (in the sense of @(==)@) to
1083-- the old term with the new term.
1084substTerm :: Eq n => TT n {-^ Old term -} ->
1085 TT n {-^ New term -} ->
1086 TT n {-^ template term -}
1087 -> TT n
1088substTerm old new = st where
1089 st t | t == old = new
1090 st (App f a) = App (st f) (st a)
1091 st (Bind x b sc) = Bind x (fmap st b) (st sc)
1092 st t = t
1094-- | Return number of occurrences of V 0 or bound name i the term
1095occurrences :: Eq n => n -> TT n -> Int
1096occurrences n t = execState (no' 0 t) 0
1097 where
1098 no' i (V x) | i == x = do num <- get; put (num + 1)
1099 no' i (P Bound x _) | n == x = do num <- get; put (num + 1)
1100 no' i (Bind n b sc) = do noB' i b; no' (i+1) sc
1101 where noB' i (Let t v) = do no' i t; no' i v
1102 noB' i (Guess t v) = do no' i t; no' i v
1103 noB' i b = no' i (binderTy b)
1104 no' i (App f a) = do no' i f; no' i a
1105 no' i (Proj x _) = no' i x
1106 no' i _ = return ()
1108-- | Returns true if V 0 and bound name n do not occur in the term
1109noOccurrence :: Eq n => n -> TT n -> Bool
1110noOccurrence n t = no' 0 t
1111 where
1112 no' i (V x) = not (i == x)
1113 no' i (P Bound x _) = not (n == x)
1114 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
1115 where noB' i (Let t v) = no' i t && no' i v
1116 noB' i (Guess t v) = no' i t && no' i v
1117 noB' i b = no' i (binderTy b)
1118 no' i (App f a) = no' i f && no' i a
1119 no' i (Proj x _) = no' i x
1120 no' i _ = True
1122-- | Returns all names used free in the term
1123freeNames :: Eq n => TT n -> [n]
1124freeNames t = nub $ freeNames' t
1125 where
1126 freeNames' (P _ n _) = [n]
1127 freeNames' (Bind n (Let t v) sc) = freeNames' v ++ (freeNames' sc \\ [n])
1128 ++ freeNames' t
1129 freeNames' (Bind n b sc) = freeNames' (binderTy b) ++ (freeNames' sc \\ [n])
1130 freeNames' (App f a) = freeNames' f ++ freeNames' a
1131 freeNames' (Proj x i) = freeNames' x
1132 freeNames' _ = []
1134-- | Return the arity of a (normalised) type
1135arity :: TT n -> Int
1136arity (Bind n (Pi _ t _) sc) = 1 + arity sc
1137arity _ = 0
1139-- | Deconstruct an application; returns the function and a list of arguments
1140unApply :: TT n -> (TT n, [TT n])
1141unApply t = ua [] t where
1142 ua args (App f a) = ua (a:args) f
1143 ua args t = (t, args)
1145-- | Returns a term representing the application of the first argument
1146-- (a function) to every element of the second argument.
1147mkApp :: TT n -> [TT n] -> TT n
1148mkApp f [] = f
1149mkApp f (a:as) = mkApp (App f a) as
1151unList :: Term -> Maybe [Term]
1152unList tm = case unApply tm of
1153 (nil, [_]) -> Just []
1154 (cons, ([_, x, xs])) ->
1155 do rest <- unList xs
1156 return $ x:rest
1157 (f, args) -> Nothing
1159-- | Cast a 'TT' term to a 'Raw' value, discarding universe information and
1160-- the types of named references and replacing all de Bruijn indices
1161-- with the corresponding name. It is an error if there are free de
1162-- Bruijn indices.
1163forget :: TT Name -> Raw
1164forget tm = forgetEnv [] tm
1166forgetEnv :: [Name] -> TT Name -> Raw
1167forgetEnv env (P _ n _) = Var n
1168forgetEnv env (V i) = Var (env !! i)
1169forgetEnv env (Bind n b sc) = let n' = uniqueName n env in
1170 RBind n' (fmap (forgetEnv env) b)
1171 (forgetEnv (n':env) sc)
1172forgetEnv env (App f a) = RApp (forgetEnv env f) (forgetEnv env a)
1173forgetEnv env (Constant c) = RConstant c
1174forgetEnv env (TType i) = RType
1175forgetEnv env (UType u) = RUType u
1176forgetEnv env Erased = RConstant Forgot
1178-- | Introduce a 'Bind' into the given term for each element of the
1179-- given list of (name, binder) pairs.
1180bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
1181bindAll [] t = t
1182bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
1184-- | Like 'bindAll', but the 'Binder's are 'TT' terms instead.
1185-- The first argument is a function to map @TT@ terms to @Binder@s.
1186-- This function might often be something like 'Lam', which directly
1187-- constructs a @Binder@ from a @TT@ term.
1188bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
1189bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
1191-- | Return a list of pairs of the names of the outermost 'Pi'-bound
1192-- variables in the given term, together with their types.
1193getArgTys :: TT n -> [(n, TT n)]
1194getArgTys (Bind n (PVar _) sc) = getArgTys sc
1195getArgTys (Bind n (PVTy _) sc) = getArgTys sc
1196getArgTys (Bind n (Pi _ t _) sc) = (n, t) : getArgTys sc
1197getArgTys _ = []
1199getRetTy :: TT n -> TT n
1200getRetTy (Bind n (PVar _) sc) = getRetTy sc
1201getRetTy (Bind n (PVTy _) sc) = getRetTy sc
1202getRetTy (Bind n (Pi _ _ _) sc) = getRetTy sc
1203getRetTy sc = sc
1205uniqueNameFrom :: [Name] -> [Name] -> Name
1206uniqueNameFrom [] hs = uniqueName (nextName (sUN "x")) hs
1207uniqueNameFrom (s : supply) hs
1208 | s `elem` hs = uniqueNameFrom supply hs
1209 | otherwise = s
1211uniqueName :: Name -> [Name] -> Name
1212uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
1213 | otherwise = n
1215uniqueNameSet :: Name -> Set Name -> Name
1216uniqueNameSet n hs | n `member` hs = uniqueNameSet (nextName n) hs
1217 | otherwise = n
1219uniqueBinders :: [Name] -> TT Name -> TT Name
1220uniqueBinders ns = ubSet (fromList ns) where
1221 ubSet ns (Bind n b sc)
1222 = let n' = uniqueNameSet n ns
1223 ns' = insert n' ns in
1224 Bind n' (fmap (ubSet ns') b) (ubSet ns' sc)
1225 ubSet ns (App f a) = App (ubSet ns f) (ubSet ns a)
1226 ubSet ns t = t
1229nextName (NS x s) = NS (nextName x) s
1230nextName (MN i n) = MN (i+1) n
1231nextName (UN x) = let (num', nm') = T.span isDigit (T.reverse x)
1232 nm = T.reverse nm'
1233 num = readN (T.reverse num') in
1234 UN (nm `T.append` txt (show (num+1)))
1235 where
1236 readN x | not (T.null x) = read (T.unpack x)
1237 readN x = 0
1238nextName (SN x) = SN (nextName' x)
1239 where
1240 nextName' (WhereN i f x) = WhereN i f (nextName x)
1241 nextName' (WithN i n) = WithN i (nextName n)
1242 nextName' (InstanceN n ns) = InstanceN (nextName n) ns
1243 nextName' (ParentN n ns) = ParentN (nextName n) ns
1244 nextName' (CaseN n) = CaseN (nextName n)
1245 nextName' (ElimN n) = ElimN (nextName n)
1246 nextName' (MethodN n) = MethodN (nextName n)
1247 nextName' (InstanceCtorN n) = InstanceCtorN (nextName n)
1249type Term = TT Name
1250type Type = Term
1252type Env = EnvTT Name
1254-- | an environment with de Bruijn indices 'normalised' so that they all refer to
1255-- this environment
1257newtype WkEnvTT n = Wk (EnvTT n)
1258type WkEnv = WkEnvTT Name
1260instance (Eq n, Show n) => Show (TT n) where
1261 show t = showEnv [] t
1263itBitsName IT8 = "Bits8"
1264itBitsName IT16 = "Bits16"
1265itBitsName IT32 = "Bits32"
1266itBitsName IT64 = "Bits64"
1268instance Show Const where
1269 show (I i) = show i
1270 show (BI i) = show i
1271 show (Fl f) = show f
1272 show (Ch c) = show c
1273 show (Str s) = show s
1274 show (B8 x) = show x
1275 show (B16 x) = show x
1276 show (B32 x) = show x
1277 show (B64 x) = show x
1278 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1279 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1280 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1281 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1282 show (AType ATFloat) = "Float"
1283 show (AType (ATInt ITBig)) = "Integer"
1284 show (AType (ATInt ITNative)) = "Int"
1285 show (AType (ATInt ITChar)) = "Char"
1286 show (AType (ATInt (ITFixed it))) = itBitsName it
1287 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
1288 show TheWorld = "prim__TheWorld"
1289 show WorldType = "prim__WorldType"
1290 show StrType = "String"
1291 show BufferType = "prim__UnsafeBuffer"
1292 show PtrType = "Ptr"
1293 show ManagedPtrType = "ManagedPtr"
1294 show VoidType = "Void"
1296showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String
1297showEnv env t = showEnv' env t False
1298showEnvDbg env t = showEnv' env t True
1300prettyEnv env t = prettyEnv' env t False
1301 where
1302 prettyEnv' env t dbg = prettySe 10 env t dbg
1304 bracket outer inner p
1305 | inner > outer = lparen <> p <> rparen
1306 | otherwise = p
1308 prettySe p env (P nt n t) debug =
1309 pretty n <+>
1310 if debug then
1311 lbracket <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbracket
1312 else
1313 empty
1314 prettySe p env (V i) debug
1315 | i < length env =
1316 if debug then
1317 text . show . fst $ env!!i
1318 else
1319 lbracket <+> text (show i) <+> rbracket
1320 | otherwise = text "unbound" <+> text (show i) <+> text "!"
1321 prettySe p env (Bind n b@(Pi _ t _) sc) debug
1322 | noOccurrence n sc && not debug =
1323 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1324 prettySe p env (Bind n b sc) debug =
1325 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1326 prettySe p env (App f a) debug =
1327 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
1328 prettySe p env (Proj x i) debug =
1329 prettySe 1 env x debug <+> text ("!" ++ show i)
1330 prettySe p env (Constant c) debug = pretty c
1331 prettySe p env Erased debug = text "[_]"
1332 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
1334 -- Render a `Binder` and its name
1335 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
1336 prettySb env n (Hole t) = prettyB env "?defer" "." n t
1337 prettySb env n (Pi _ t _) = prettyB env "(" ") ->" n t
1338 prettySb env n (PVar t) = prettyB env "pat" "." n t
1339 prettySb env n (PVTy t) = prettyB env "pty" "." n t
1340 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
1341 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
1343 -- Use `op` and `sc` to delimit `n` (a binding name) and its type
1344 -- declaration
1345 -- e.g. "λx : Int =>" for the Lam case
1346 prettyB env op sc n t debug =
1347 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
1349 -- Like `prettyB`, but handle the bindings that have values in addition
1350 -- to names and types
1351 prettyBv env op sc n t v debug =
1352 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
1353 prettySe 10 env v debug <> text sc
1356showEnv' env t dbg = se 10 env t where
1357 se p env (P nt n t) = show n
1358 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
1359 se p env (V i) | i < length env && i >= 0
1360 = (show $ fst $ env!!i) ++
1361 if dbg then "{" ++ show i ++ "}" else ""
1362 | otherwise = "!!V " ++ show i ++ "!!"
1363 se p env (Bind n b@(Pi (Just _) t k) sc)
1364 = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1365 se p env (Bind n b@(Pi _ t k) sc)
1366 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ arrow k ++ se 10 ((n,b):env) sc
1367 where arrow (TType _) = " -> "
1368 arrow u = " [" ++ show u ++ "] -> "
1369 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1370 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
1371 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
1372 se p env (Constant c) = show c
1373 se p env Erased = "[__]"
1374 se p env Impossible = "[impossible]"
1375 se p env (TType i) = "Type " ++ show i
1376 se p env (UType u) = show u
1378 sb env n (Lam t) = showb env "\\ " " => " n t
1379 sb env n (Hole t) = showb env "? " ". " n t
1380 sb env n (GHole i t) = showb env "?defer " ". " n t
1381 sb env n (Pi (Just _) t _) = showb env "{" "} -> " n t
1382 sb env n (Pi _ t _) = showb env "(" ") -> " n t
1383 sb env n (PVar t) = showb env "pat " ". " n t
1384 sb env n (PVTy t) = showb env "pty " ". " n t
1385 sb env n (Let t v) = showbv env "let " " in " n t v
1386 sb env n (Guess t v) = showbv env "?? " " in " n t v
1388 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
1389 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
1390 se 10 env v ++ sc
1392 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
1393 | otherwise = str
1395-- | Check whether a term has any holes in it - impure if so
1396pureTerm :: TT Name -> Bool
1397pureTerm (App f a) = pureTerm f && pureTerm a
1398pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
1399 pureBinder (Hole _) = False
1400 pureBinder (Guess _ _) = False
1401 pureBinder (Let t v) = pureTerm t && pureTerm v
1402 pureBinder t = pureTerm (binderTy t)
1404 notClassName (MN _ c) | c == txt "class" = False
1405 notClassName _ = True
1407pureTerm _ = True
1409-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1410weakenTm :: Int -> TT n -> TT n
1411weakenTm i t = wk i 0 t
1412 where wk i min (V x) | x >= min = V (i + x)
1413 wk i m (App f a) = App (wk i m f) (wk i m a)
1414 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1415 wk i m t = t
1416 wkb i m t = fmap (wk i m) t
1418-- | Weaken an environment so that all the de Bruijn indices are correct according
1419-- to the latest bound variable
1421weakenEnv :: EnvTT n -> EnvTT n
1422weakenEnv env = wk (length env - 1) env
1423 where wk i [] = []
1424 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1425 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1426 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1427 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1429-- | Weaken every term in the environment by the given amount
1430weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1431weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1433-- | Gather up all the outer 'PVar's and 'Hole's in an expression and reintroduce
1434-- them in a canonical order
1435orderPats :: Term -> Term
1436orderPats tm = op [] tm
1437 where
1438 op [] (App f a) = App f (op [] a) -- for Infer terms
1440 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1441 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1442 op ps (Bind n (Pi i t k) sc) = op ((n, Pi i t k) : ps) sc
1443 op ps sc = bindAll (sortP ps) sc
1445 sortP ps = pick [] (reverse ps)
1447 pick acc [] = reverse acc
1448 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1450 insert n t [] = [(n, t)]
1451 insert n t ((n',t') : ps)
1452 | n `elem` (refsIn (binderTy t') ++
1453 concatMap refsIn (map (binderTy . snd) ps))
1454 = (n', t') : insert n t ps
1455 | otherwise = (n,t):(n',t'):ps
1457refsIn :: TT Name -> [Name]
1458refsIn (P _ n _) = [n]
1459refsIn (Bind n b t) = nub $ nb b ++ refsIn t
1460 where nb (Let t v) = nub (refsIn t) ++ nub (refsIn v)
1461 nb (Guess t v) = nub (refsIn t) ++ nub (refsIn v)
1462 nb t = refsIn (binderTy t)
1463refsIn (App f a) = nub (refsIn f ++ refsIn a)
1464refsIn _ = []
1466-- Make sure all the pattern bindings are as far out as possible
1467liftPats :: Term -> Term
1468liftPats tm = let (tm', ps) = runState (getPats tm) [] in
1469 orderPats $ bindPats (reverse ps) tm'
1470 where
1471 bindPats [] tm = tm
1472 bindPats ((n, t):ps) tm
1473 | n `notElem` map fst ps = Bind n (PVar t) (bindPats ps tm)
1474 | otherwise = bindPats ps tm
1476 getPats :: Term -> State [(Name, Type)] Term
1477 getPats (Bind n (PVar t) sc) = do ps <- get
1478 put ((n, t) : ps)
1479 getPats sc
1480 getPats (Bind n (Guess t v) sc) = do t' <- getPats t
1481 v' <- getPats v
1482 sc' <- getPats sc
1483 return (Bind n (Guess t' v') sc')
1484 getPats (Bind n (Let t v) sc) = do t' <- getPats t
1485 v' <- getPats v
1486 sc' <- getPats sc
1487 return (Bind n (Let t' v') sc')
1488 getPats (Bind n (Pi i t k) sc) = do t' <- getPats t
1489 k' <- getPats k
1490 sc' <- getPats sc
1491 return (Bind n (Pi i t' k') sc')
1492 getPats (Bind n (Lam t) sc) = do t' <- getPats t
1493 sc' <- getPats sc
1494 return (Bind n (Lam t') sc')
1495 getPats (Bind n (Hole t) sc) = do t' <- getPats t
1496 sc' <- getPats sc
1497 return (Bind n (Hole t') sc')
1500 getPats (App f a) = do f' <- getPats f
1501 a' <- getPats a
1502 return (App f' a')
1503 getPats t = return t
1505allTTNames :: Eq n => TT n -> [n]
1506allTTNames = nub . allNamesIn
1507 where allNamesIn (P _ n _) = [n]
1508 allNamesIn (Bind n b t) = [n] ++ nb b ++ allNamesIn t
1509 where nb (Let t v) = allNamesIn t ++ allNamesIn v
1510 nb (Guess t v) = allNamesIn t ++ allNamesIn v
1511 nb t = allNamesIn (binderTy t)
1512 allNamesIn (App f a) = allNamesIn f ++ allNamesIn a
1513 allNamesIn _ = []
1516-- | Pretty-print a term
1517pprintTT :: [Name] -- ^ The bound names (for highlighting and de Bruijn indices)
1518 -> TT Name -- ^ The term to be printed
1519 -> Doc OutputAnnotation
1520pprintTT bound tm = pp startPrec bound tm
1522 where
1523 startPrec = 0
1524 appPrec = 10
1526 pp p bound (P Bound n ty) = annotate (AnnBoundName n False) (text $ show n)
1527 pp p bound (P nt n ty) = annotate (AnnName n Nothing Nothing Nothing)
1528 (text $ show n)
1529 pp p bound (V i)
1530 | i < length bound = let n = bound !! i
1531 in annotate (AnnBoundName n False) (text $ show n)
1532 | otherwise = text ("{{{V" ++ show i ++ "}}}")
1533 pp p bound (Bind n b sc) = ppb p bound n b $
1534 pp startPrec (n:bound) sc
1535 pp p bound (App tm1 tm2) =
1536 bracket p appPrec . group . hang 2 $
1537 pp appPrec bound tm1 <> line <>
1538 pp (appPrec + 1) bound tm2
1539 pp p bound (Constant c) = annotate (AnnConst c) (text (show c))
1540 pp p bound (Proj tm i) =
1541 lparen <> pp startPrec bound tm <> rparen <>
1542 text "!" <> text (show i)
1543 pp p bound Erased = text "<<<erased>>>"
1544 pp p bound Impossible = text "<<<impossible>>>"
1545 pp p bound (TType ue) = annotate (AnnType "Type" "The type of types") $
1546 text "Type"
1547 pp p bound (UType u) = text (show u)
1549 ppb p bound n (Lam ty) sc =
1550 bracket p startPrec . group . align . hang 2 $
1551 text "λ" <+> bindingOf n False <+> text "." <> line <> sc
1552 ppb p bound n (Pi _ ty k) sc =
1553 bracket p startPrec . group . align $
1554 lparen <> (bindingOf n False) <+> colon <+>
1555 (group . align) (pp startPrec bound ty) <>
1556 rparen <+> mkArrow k <> line <> sc
1557 where mkArrow (UType UniqueType) = text "⇴"
1558 mkArrow (UType NullType) = text "⥛"
1559 mkArrow _ = text "→"
1560 ppb p bound n (Let ty val) sc =
1561 bracket p startPrec . group . align $
1562 (group . hang 2) (annotate AnnKeyword (text "let") <+>
1563 bindingOf n False <+> colon <+>
1564 pp startPrec bound ty <+>
1565 text "=" <> line <>
1566 pp startPrec bound val) <> line <>
1567 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1568 ppb p bound n (NLet ty val) sc =
1569 bracket p startPrec . group . align $
1570 (group . hang 2) (annotate AnnKeyword (text "nlet") <+>
1571 bindingOf n False <+> colon <+>
1572 pp startPrec bound ty <+>
1573 text "=" <> line <>
1574 pp startPrec bound val) <> line <>
1575 (group . hang 2) (annotate AnnKeyword (text "in") <+> sc)
1576 ppb p bound n (Hole ty) sc =
1577 bracket p startPrec . group . align . hang 2 $
1578 text "?" <+> bindingOf n False <+> text "." <> line <> sc
1579 ppb p bound n (GHole _ ty) sc =
1580 bracket p startPrec . group . align . hang 2 $
1581 text "¿" <+> bindingOf n False <+> text "." <> line <> sc
1582 ppb p bound n (Guess ty val) sc =
1583 bracket p startPrec . group . align . hang 2 $
1584 text "?" <> bindingOf n False <+>
1585 text "≈" <+> pp startPrec bound val <+>
1586 text "." <> line <> sc
1587 ppb p bound n (PVar ty) sc =
1588 bracket p startPrec . group . align . hang 2 $
1589 annotate AnnKeyword (text "pat") <+>
1590 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1591 text "." <> line <>
1592 sc
1593 ppb p bound n (PVTy ty) sc =
1594 bracket p startPrec . group . align . hang 2 $
1595 annotate AnnKeyword (text "patTy") <+>
1596 bindingOf n False <+> colon <+> pp startPrec bound ty <+>
1597 text "." <> line <>
1598 sc
1600 bracket outer inner doc
1601 | outer > inner = lparen <> doc <> rparen
1602 | otherwise = doc
1605-- | Pretty-printer helper for the binding site of a name
1606bindingOf :: Name -- ^^ the bound name
1607 -> Bool -- ^^ whether the name is implicit
1608 -> Doc OutputAnnotation
1609bindingOf n imp = annotate (AnnBoundName n imp) (text (show n))