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Idris-dev/src/Idris/Core/TT.hs
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1{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, DeriveFunctor #-}
3{-| TT is the core language of Idris. The language has:
5 * Full dependent types
7 * A hierarchy of universes, with cumulativity: Type : Type1, Type1 : Type2, ...
9 * Pattern matching letrec binding
11 * (primitive types defined externally)
13 Some technical stuff:
15 * Typechecker is kept as simple as possible - no unification, just a checker for incomplete terms.
17 * We have a simple collection of tactics which we use to elaborate source
18 programs with implicit syntax into fully explicit terms.
19-}
21module Idris.Core.TT(module Idris.Core.TT, module Idris.Core.TC) where
23import Idris.Core.TC
25import Control.Monad.State.Strict
26import Control.Monad.Trans.Error (Error(..))
27import Debug.Trace
28import qualified Data.Map.Strict as Map
29import Data.Char
30import qualified Data.Text as T
31import Data.List
32import Data.Vector.Unboxed (Vector)
33import qualified Data.Vector.Unboxed as V
34import qualified Data.Binary as B
35import Data.Binary hiding (get, put)
36import Foreign.Storable (sizeOf)
38import Util.Pretty hiding (Str)
40data Option = TTypeInTType
41 | CheckConv
42 deriving Eq
44-- | Source location. These are typically produced by the parser 'Idris.Parser.getFC'
45data FC = FC { fc_fname :: String, -- ^ Filename
46 fc_line :: Int, -- ^ Line number
47 fc_column :: Int -- ^ Column number
48 }
50-- | Ignore source location equality (so deriving classes do not compare FCs)
51instance Eq FC where
52 _ == _ = True
54-- | FC with equality
55newtype FC' = FC' { unwrapFC :: FC }
57instance Eq FC' where
58 FC' fc == FC' fc' = fcEq fc fc'
59 where fcEq (FC n l c) (FC n' l' c') = n == n' && l == l' && c == c'
61-- | Empty source location
62emptyFC :: FC
63emptyFC = fileFC ""
65-- | Source location with file only
66fileFC :: String -> FC
67fileFC s = FC s 0 0
69{-!
70deriving instance Binary FC
71deriving instance NFData FC
72!-}
74instance Sized FC where
75 size (FC f l c) = 1 + length f
77instance Show FC where
78 show (FC f l c) = f ++ ":" ++ show l ++ ":" ++ show c
80-- | Used for error reflection
81data ErrorReportPart = TextPart String
82 | NamePart Name
83 | TermPart Term
84 | SubReport [ErrorReportPart]
85 deriving (Show, Eq)
88-- Please remember to keep Err synchronised with
89-- Language.Reflection.Errors.Err in the stdlib!
91-- | Idris errors. Used as exceptions in the compiler, but reported to users
92-- if they reach the top level.
93data Err' t
94 = Msg String
95 | InternalMsg String
96 | CantUnify Bool t t (Err' t) [(Name, t)] Int
97 -- Int is 'score' - how much we did unify
98 -- Bool indicates recoverability, True indicates more info may make
99 -- unification succeed
100 | InfiniteUnify Name t [(Name, t)]
101 | CantConvert t t [(Name, t)]
102 | CantSolveGoal t [(Name, t)]
103 | UnifyScope Name Name t [(Name, t)]
104 | CantInferType String
105 | NonFunctionType t t
106 | NotEquality t t
107 | TooManyArguments Name
108 | CantIntroduce t
109 | NoSuchVariable Name
110 | NoTypeDecl Name
111 | NotInjective t t t
112 | CantResolve t
113 | CantResolveAlts [String]
114 | IncompleteTerm t
115 | UniverseError
116 | ProgramLineComment
117 | Inaccessible Name
118 | NonCollapsiblePostulate Name
119 | AlreadyDefined Name
120 | ProofSearchFail (Err' t)
121 | NoRewriting t
122 | At FC (Err' t)
123 | Elaborating String Name (Err' t)
124 | ProviderError String
125 | LoadingFailed String (Err' t)
126 | ReflectionError [[ErrorReportPart]] (Err' t)
127 | ReflectionFailed String (Err' t)
128 deriving (Eq, Functor)
130type Err = Err' Term
132{-!
133deriving instance NFData Err
134!-}
136instance Sized Err where
137 size (Msg msg) = length msg
138 size (InternalMsg msg) = length msg
139 size (CantUnify _ left right err _ score) = size left + size right + size err
140 size (InfiniteUnify _ right _) = size right
141 size (CantConvert left right _) = size left + size right
142 size (UnifyScope _ _ right _) = size right
143 size (NoSuchVariable name) = size name
144 size (NoTypeDecl name) = size name
145 size (NotInjective l c r) = size l + size c + size r
146 size (CantResolve trm) = size trm
147 size (NoRewriting trm) = size trm
148 size (CantResolveAlts _) = 1
149 size (IncompleteTerm trm) = size trm
150 size UniverseError = 1
151 size ProgramLineComment = 1
152 size (At fc err) = size fc + size err
153 size (Elaborating _ n err) = size err
154 size (ProviderError msg) = length msg
155 size (LoadingFailed fn e) = 1 + length fn + size e
156 size _ = 1
158score :: Err -> Int
159score (CantUnify _ _ _ m _ s) = s + score m
160score (CantResolve _) = 20
161score (NoSuchVariable _) = 1000
162score (ProofSearchFail _) = 10000
163score (CantSolveGoal _ _) = 10000
164score (InternalMsg _) = -1
165score _ = 0
167instance Show Err where
168 show (Msg s) = s
169 show (InternalMsg s) = "Internal error: " ++ show s
170 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
171 ++ show e ++ " in " ++ show sc ++ " " ++ show i
172 show (CantSolveGoal g _) = "CantSolve " ++ show g
173 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
174 show (ProviderError msg) = "Type provider error: " ++ msg
175 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: (TT) " ++ show e
176 show ProgramLineComment = "Program line next to comment"
177 show (At f e) = show f ++ ":" ++ show e
178 show _ = "Error"
180instance Pretty Err where
181 pretty (Msg m) = text m
182 pretty (CantUnify _ l r e _ i) =
183 if size l + size r > breakingSize then
184 text "Cannot unify" <+> colon $$
185 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
186 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
187 else
188 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
189 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
190 pretty (ProviderError msg) = text msg
191 pretty err@(LoadingFailed _ _) = text (show err)
192 pretty _ = text "Error"
194instance Error Err where
195 strMsg = InternalMsg
197type TC = TC' Err
199instance (Pretty a) => Pretty (TC a) where
200 pretty (OK ok) = pretty ok
201 pretty (Error err) =
202 if size err > breakingSize then
203 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
204 else
205 text "Error" <+> colon <+> pretty err
207instance Show a => Show (TC a) where
208 show (OK x) = show x
209 show (Error str) = "Error: " ++ show str
211tfail :: Err -> TC a
212tfail e = Error e
214failMsg :: String -> TC a
215failMsg str = Error (Msg str)
217trun :: FC -> TC a -> TC a
218trun fc (OK a) = OK a
219trun fc (Error e) = Error (At fc e)
221discard :: Monad m => m a -> m ()
222discard f = f >> return ()
224showSep :: String -> [String] -> String
225showSep sep [] = ""
226showSep sep [x] = x
227showSep sep (x:xs) = x ++ sep ++ showSep sep xs
229pmap f (x, y) = (f x, f y)
231traceWhen True msg a = trace msg a
232traceWhen False _ a = a
234-- RAW TERMS ----------------------------------------------------------------
236-- | Names are hierarchies of strings, describing scope (so no danger of
237-- duplicate names, but need to be careful on lookup).
238data Name = UN T.Text -- ^ User-provided name
239 | NS Name [T.Text] -- ^ Root, namespaces
240 | MN Int T.Text -- ^ Machine chosen names
241 | NErased -- ^ Name of somethng which is never used in scope
242 | SN SpecialName -- ^ Decorated function names
243 | SymRef Int -- ^ Reference to IBC file symbol table (used during serialisation)
244 deriving (Eq, Ord)
246txt :: String -> T.Text
247txt = T.pack
249str :: T.Text -> String
250str = T.unpack
252tnull :: T.Text -> Bool
253tnull = T.null
255thead :: T.Text -> Char
256thead = T.head
258-- Smart constructors for names, using old String style
259sUN :: String -> Name
260sUN s = UN (txt s)
262sNS :: Name -> [String] -> Name
263sNS n ss = NS n (map txt ss)
265sMN :: Int -> String -> Name
266sMN i s = MN i (txt s)
268{-!
269deriving instance Binary Name
270deriving instance NFData Name
271!-}
273data SpecialName = WhereN Int Name Name
274 | InstanceN Name [T.Text]
275 | ParentN Name T.Text
276 | MethodN Name
277 | CaseN Name
278 | ElimN Name
279 deriving (Eq, Ord)
280{-!
281deriving instance Binary SpecialName
282deriving instance NFData SpecialName
283!-}
285sInstanceN :: Name -> [String] -> SpecialName
286sInstanceN n ss = InstanceN n (map T.pack ss)
288sParentN :: Name -> String -> SpecialName
289sParentN n s = ParentN n (T.pack s)
291instance Sized Name where
292 size (UN n) = 1
293 size (NS n els) = 1 + length els
294 size (MN i n) = 1
295 size _ = 1
297instance Pretty Name where
298 pretty (UN n) = text (T.unpack n)
299 pretty (NS n s) = pretty n
300 pretty (MN i s) = lbrace <+> text (T.unpack s) <+> (text . show $ i) <+> rbrace
301 pretty (SN s) = text (show s)
303instance Show Name where
304 show (UN n) = str n
305 show (NS n s) = showSep "." (map T.unpack (reverse s)) ++ "." ++ show n
306 show (MN _ u) | u == txt "underscore" = "_"
307 show (MN i s) = "{" ++ str s ++ show i ++ "}"
308 show (SN s) = show s
309 show NErased = "_"
311instance Show SpecialName where
312 show (WhereN i p c) = show p ++ ", " ++ show c
313 show (InstanceN cl inst) = showSep ", " (map T.unpack inst) ++ " instance of " ++ show cl
314 show (MethodN m) = "method " ++ show m
315 show (ParentN p c) = show p ++ "#" ++ T.unpack c
316 show (CaseN n) = "case block in " ++ show n
317 show (ElimN n) = "<<" ++ show n ++ " eliminator>>"
319-- Show a name in a way decorated for code generation, not human reading
320showCG :: Name -> String
321showCG (UN n) = T.unpack n
322showCG (NS n s) = showSep "." (map T.unpack (reverse s)) ++ "." ++ showCG n
323showCG (MN _ u) | u == txt "underscore" = "_"
324showCG (MN i s) = "{" ++ T.unpack s ++ show i ++ "}"
325showCG (SN s) = showCG' s
326 where showCG' (WhereN i p c) = showCG p ++ ":" ++ showCG c ++ ":" ++ show i
327 showCG' (InstanceN cl inst) = '@':showCG cl ++ '$':showSep ":" (map T.unpack inst)
328 showCG' (MethodN m) = '!':showCG m
329 showCG' (ParentN p c) = showCG p ++ "#" ++ show c
330 showCG' (CaseN c) = showCG c ++ "_case"
331 showCG' (ElimN sn) = showCG sn ++ "_elim"
332showCG NErased = "_"
335-- |Contexts allow us to map names to things. A root name maps to a collection
336-- of things in different namespaces with that name.
337type Ctxt a = Map.Map Name (Map.Map Name a)
338emptyContext = Map.empty
340mapCtxt :: (a -> b) -> Ctxt a -> Ctxt b
341mapCtxt = fmap . fmap
343-- |Return True if the argument 'Name' should be interpreted as the name of a
344-- typeclass.
345tcname (UN xs) | T.null xs = False
346 | otherwise = T.head xs == '@'
347tcname (NS n _) = tcname n
348tcname (SN (InstanceN _ _)) = True
349tcname (SN (MethodN _)) = True
350tcname (SN (ParentN _ _)) = True
351tcname _ = False
353implicitable (NS n _) = implicitable n
354implicitable (UN xs) | T.null xs = False
355 | otherwise = isLower (T.head xs)
356implicitable (MN _ _) = True
357implicitable _ = False
359nsroot (NS n _) = n
360nsroot n = n
362addDef :: Name -> a -> Ctxt a -> Ctxt a
363addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
364 Nothing -> Map.insert (nsroot n)
365 (Map.insert n v Map.empty) ctxt
366 Just xs -> Map.insert (nsroot n)
367 (Map.insert n v xs) ctxt
369{-| Look up a name in the context, given an optional namespace.
370 The name (n) may itself have a (partial) namespace given.
372 Rules for resolution:
374 - if an explicit namespace is given, return the names which match it. If none
375 match, return all names.
377 - if the name has has explicit namespace given, return the names which match it
378 and ignore the given namespace.
380 - otherwise, return all names.
382-}
384lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
385lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
386 Just xs -> filterNS (Map.toList xs)
387 Nothing -> []
388 where
389 filterNS [] = []
390 filterNS ((found, v) : xs)
391 | nsmatch n found = (found, v) : filterNS xs
392 | otherwise = filterNS xs
394 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
395 nsmatch (NS _ _) _ = False
396 nsmatch looking found = True
398lookupCtxt :: Name -> Ctxt a -> [a]
399lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
401lookupCtxtExact :: Name -> Ctxt a -> [a]
402lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
404updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
405updateDef n f ctxt
406 = let ds = lookupCtxtName n ctxt in
407 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
409toAlist :: Ctxt a -> [(Name, a)]
410toAlist ctxt = let allns = map snd (Map.toList ctxt) in
411 concat (map (Map.toList) allns)
413addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
414addAlist [] ctxt = ctxt
415addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
417data NativeTy = IT8 | IT16 | IT32 | IT64
418 deriving (Show, Eq, Ord, Enum)
420instance Pretty NativeTy where
421 pretty IT8 = text "Bits8"
422 pretty IT16 = text "Bits16"
423 pretty IT32 = text "Bits32"
424 pretty IT64 = text "Bits64"
426data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
427 | ITVec NativeTy Int
428 deriving (Show, Eq, Ord)
430data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
431 deriving (Show, Eq, Ord)
432{-!
433deriving instance NFData IntTy
434deriving instance NFData NativeTy
435deriving instance NFData ArithTy
436!-}
438instance Pretty ArithTy where
439 pretty (ATInt ITNative) = text "Int"
440 pretty (ATInt ITBig) = text "BigInt"
441 pretty (ATInt ITChar) = text "Char"
442 pretty (ATInt (ITFixed n)) = pretty n
443 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
444 pretty ATFloat = text "Float"
446nativeTyWidth :: NativeTy -> Int
447nativeTyWidth IT8 = 8
448nativeTyWidth IT16 = 16
449nativeTyWidth IT32 = 32
450nativeTyWidth IT64 = 64
452{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
453intTyWidth :: IntTy -> Int
454intTyWidth (ITFixed n) = nativeTyWidth n
455intTyWidth ITNative = 8 * sizeOf (0 :: Int)
456intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
457intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
459data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
460 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
461 | B8V (Vector Word8) | B16V (Vector Word16)
462 | B32V (Vector Word32) | B64V (Vector Word64)
463 | AType ArithTy | StrType
464 | PtrType | VoidType | Forgot
465 deriving (Eq, Ord)
466{-!
467deriving instance Binary Const
468deriving instance NFData Const
469!-}
471instance Sized Const where
472 size _ = 1
474instance Pretty Const where
475 pretty (I i) = text . show $ i
476 pretty (BI i) = text . show $ i
477 pretty (Fl f) = text . show $ f
478 pretty (Ch c) = text . show $ c
479 pretty (Str s) = text s
480 pretty (AType a) = pretty a
481 pretty StrType = text "String"
482 pretty PtrType = text "Ptr"
483 pretty VoidType = text "Void"
484 pretty Forgot = text "Forgot"
485 pretty (B8 w) = text . show $ w
486 pretty (B16 w) = text . show $ w
487 pretty (B32 w) = text . show $ w
488 pretty (B64 w) = text . show $ w
490data Raw = Var Name
491 | RBind Name (Binder Raw) Raw
492 | RApp Raw Raw
493 | RType
494 | RForce Raw
495 | RConstant Const
496 deriving (Show, Eq)
498instance Sized Raw where
499 size (Var name) = 1
500 size (RBind name bind right) = 1 + size bind + size right
501 size (RApp left right) = 1 + size left + size right
502 size RType = 1
503 size (RForce raw) = 1 + size raw
504 size (RConstant const) = size const
506instance Pretty Raw where
507 pretty = text . show
509{-!
510deriving instance Binary Raw
511deriving instance NFData Raw
512!-}
514-- The type parameter `b` will normally be something like `TT Name` or just
515-- `Raw`. We do not make a type-level distinction between TT terms that happen
516-- to be TT types and TT terms that are not TT types.
517-- | All binding forms are represented in a uniform fashion. This type only represents
518-- the types of bindings (and their values, if any); the attached identifiers are part
519-- of the 'Bind' constructor for the 'TT' type.
520data Binder b = Lam { binderTy :: !b {-^ type annotation for bound variable-}}
521 | Pi { binderTy :: !b }
522 {-^ A binding that occurs in a function type expression, e.g. @(x:Int) -> ...@ -}
523 | Let { binderTy :: !b,
524 binderVal :: b {-^ value for bound variable-}}
525 -- ^ A binding that occurs in a @let@ expression
526 | NLet { binderTy :: !b,
527 binderVal :: b }
528 | Hole { binderTy :: !b}
529 | GHole { envlen :: Int,
530 binderTy :: !b}
531 | Guess { binderTy :: !b,
532 binderVal :: b }
533 | PVar { binderTy :: !b }
534 -- ^ A pattern variable
535 | PVTy { binderTy :: !b }
536 deriving (Show, Eq, Ord, Functor)
537{-!
538deriving instance Binary Binder
539deriving instance NFData Binder
540!-}
542instance Sized a => Sized (Binder a) where
543 size (Lam ty) = 1 + size ty
544 size (Pi ty) = 1 + size ty
545 size (Let ty val) = 1 + size ty + size val
546 size (NLet ty val) = 1 + size ty + size val
547 size (Hole ty) = 1 + size ty
548 size (GHole _ ty) = 1 + size ty
549 size (Guess ty val) = 1 + size ty + size val
550 size (PVar ty) = 1 + size ty
551 size (PVTy ty) = 1 + size ty
553fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
554fmapMB f (Let t v) = liftM2 Let (f t) (f v)
555fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
556fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
557fmapMB f (Lam t) = liftM Lam (f t)
558fmapMB f (Pi t) = liftM Pi (f t)
559fmapMB f (Hole t) = liftM Hole (f t)
560fmapMB f (GHole i t) = liftM (GHole i) (f t)
561fmapMB f (PVar t) = liftM PVar (f t)
562fmapMB f (PVTy t) = liftM PVTy (f t)
564raw_apply :: Raw -> [Raw] -> Raw
565raw_apply f [] = f
566raw_apply f (a : as) = raw_apply (RApp f a) as
568raw_unapply :: Raw -> (Raw, [Raw])
569raw_unapply t = ua [] t where
570 ua args (RApp f a) = ua (a:args) f
571 ua args t = (t, args)
573-- WELL TYPED TERMS ---------------------------------------------------------
575-- | Universe expressions for universe checking
576data UExp = UVar Int -- ^ universe variable
577 | UVal Int -- ^ explicit universe level
578 deriving (Eq, Ord)
579{-!
580deriving instance NFData UExp
581!-}
583instance Sized UExp where
584 size _ = 1
586-- We assume that universe levels have been checked, so anything external
587-- can just have the same universe variable and we won't get any new
588-- cycles.
590instance Binary UExp where
591 put x = return ()
592 get = return (UVar (-1))
594instance Show UExp where
595 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
596 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
597 show (UVal x) = show x
598-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
600-- | Universe constraints
601data UConstraint = ULT UExp UExp -- ^ Strictly less than
602 | ULE UExp UExp -- ^ Less than or equal to
603 deriving Eq
605instance Show UConstraint where
606 show (ULT x y) = show x ++ " < " ++ show y
607 show (ULE x y) = show x ++ " <= " ++ show y
609type UCs = (Int, [UConstraint])
611data NameType = Bound
612 | Ref
613 | DCon {nt_tag :: Int, nt_arity :: Int} -- ^ Data constructor
614 | TCon {nt_tag :: Int, nt_arity :: Int} -- ^ Type constructor
615 deriving (Show, Ord)
616{-!
617deriving instance Binary NameType
618deriving instance NFData NameType
619!-}
621instance Sized NameType where
622 size _ = 1
624instance Pretty NameType where
625 pretty = text . show
627instance Eq NameType where
628 Bound == Bound = True
629 Ref == Ref = True
630 DCon _ a == DCon _ b = (a == b) -- ignore tag
631 TCon _ a == TCon _ b = (a == b) -- ignore tag
632 _ == _ = False
634-- | Terms in the core language. The type parameter is the type of
635-- identifiers used for bindings and explicit named references;
636-- usually we use @TT 'Name'@.
637data TT n = P NameType n (TT n) -- ^ named references with type
638 -- (P for "Parameter", motivated by McKinna and Pollack's
639 -- Pure Type Systems Formalized)
640 | V !Int -- ^ a resolved de Bruijn-indexed variable
641 | Bind n !(Binder (TT n)) (TT n) -- ^ a binding
642 | App !(TT n) (TT n) -- ^ function, function type, arg
643 | Constant Const -- ^ constant
644 | Proj (TT n) !Int -- ^ argument projection; runtime only
645 -- (-1) is a special case for 'subtract one from BI'
646 | Erased -- ^ an erased term
647 | Impossible -- ^ special case for totality checking
648 | TType UExp -- ^ the type of types at some level
649 deriving (Ord, Functor)
650{-!
651deriving instance Binary TT
652deriving instance NFData TT
653!-}
655class TermSize a where
656 termsize :: Name -> a -> Int
658instance TermSize a => TermSize [a] where
659 termsize n [] = 0
660 termsize n (x : xs) = termsize n x + termsize n xs
662instance TermSize (TT Name) where
663 termsize n (P _ n' _)
664 | n' == n = 1000000 -- recursive => really big
665 | otherwise = 1
666 termsize n (V _) = 1
667 -- for `Bind` terms, we can erroneously declare a term
668 -- "recursive => really big" if the name of the bound
669 -- variable is the same as the name we're using
670 -- So generate a different name in that case.
671 termsize n (Bind n' (Let t v) sc)
672 = let rn = if n == n' then sMN 0 "noname" else n in
673 termsize rn v + termsize rn sc
674 termsize n (Bind n' b sc)
675 = let rn = if n == n' then sMN 0 "noname" else n in
676 termsize rn sc
677 termsize n (App f a) = termsize n f + termsize n a
678 termsize n (Proj t i) = termsize n t
679 termsize n _ = 1
681instance Sized a => Sized (TT a) where
682 size (P name n trm) = 1 + size name + size n + size trm
683 size (V v) = 1
684 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
685 size (App l r) = 1 + size l + size r
686 size (Constant c) = size c
687 size Erased = 1
688 size (TType u) = 1 + size u
690instance Pretty a => Pretty (TT a) where
691 pretty _ = text "test"
693type EnvTT n = [(n, Binder (TT n))]
695data Datatype n = Data { d_typename :: n,
696 d_typetag :: Int,
697 d_type :: (TT n),
698 d_cons :: [(n, TT n)] }
699 deriving (Show, Functor, Eq)
701instance Eq n => Eq (TT n) where
702 (==) (P xt x _) (P yt y _) = x == y
703 (==) (V x) (V y) = x == y
704 (==) (Bind _ xb xs) (Bind _ yb ys) = xs == ys && xb == yb
705 (==) (App fx ax) (App fy ay) = ax == ay && fx == fy
706 (==) (TType _) (TType _) = True -- deal with constraints later
707 (==) (Constant x) (Constant y) = x == y
708 (==) (Proj x i) (Proj y j) = x == y && i == j
709 (==) Erased _ = True
710 (==) _ Erased = True
711 (==) _ _ = False
713-- * A few handy operations on well typed terms:
715-- | A term is injective iff it is a data constructor, type constructor,
716-- constant, the type Type, pi-binding, or an application of an injective
717-- term.
718isInjective :: TT n -> Bool
719isInjective (P (DCon _ _) _ _) = True
720isInjective (P (TCon _ _) _ _) = True
721isInjective (Constant _) = True
722isInjective (TType x) = True
723isInjective (Bind _ (Pi _) sc) = True
724isInjective (App f a) = isInjective f
725isInjective _ = False
727-- | Count the number of instances of a de Bruijn index in a term
728vinstances :: Int -> TT n -> Int
729vinstances i (V x) | i == x = 1
730vinstances i (App f a) = vinstances i f + vinstances i a
731vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
732 where instancesB (Let t v) = vinstances i v
733 instancesB _ = 0
734vinstances i t = 0
736-- | Replace the outermost (index 0) de Bruijn variable with the given term
737instantiate :: TT n -> TT n -> TT n
738instantiate e = subst 0 where
739 subst i (V x) | i == x = e
740 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
741 subst i (App f a) = App (subst i f) (subst i a)
742 subst i (Proj x idx) = Proj (subst i x) idx
743 subst i t = t
745-- | As 'instantiate', but also decrement the indices of all de Bruijn variables
746-- remaining in the term, so that there are no more references to the variable
747-- that has been substituted.
748substV :: TT n -> TT n -> TT n
749substV x tm = dropV 0 (instantiate x tm) where
750 dropV i (V x) | x > i = V (x - 1)
751 | otherwise = V x
752 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
753 dropV i (App f a) = App (dropV i f) (dropV i a)
754 dropV i (Proj x idx) = Proj (dropV i x) idx
755 dropV i t = t
757-- | Replace all non-free de Bruijn references in the given term with references
758-- to the name of their binding.
759explicitNames :: TT n -> TT n
760explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
761 Bind x b'
762 (explicitNames (instantiate
763 (P Bound x (binderTy b')) sc))
764explicitNames (App f a) = App (explicitNames f) (explicitNames a)
765explicitNames (Proj x idx) = Proj (explicitNames x) idx
766explicitNames t = t
768-- | Replace references to the given 'Name'-like id with references to
769-- de Bruijn index 0.
770pToV :: Eq n => n -> TT n -> TT n
771pToV n = pToV' n 0
772pToV' n i (P _ x _) | n == x = V i
773pToV' n i (Bind x b sc)
774-- We can assume the inner scope has been pToVed already, so continue to
775-- resolve names from the *outer* scope which may happen to have the same id.
776 | n == x = Bind x (fmap (pToV' n i) b) sc
777 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
778pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
779pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
780pToV' n i t = t
782-- increase de Bruijn indices, as if a binder has been added
783addBinder :: TT n -> TT n
784addBinder t = ab 0 t
785 where
786 ab top (V i) | i >= top = V (i + 1)
787 | otherwise = V i
788 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
789 ab top (App f a) = App (ab top f) (ab top a)
790 ab top (Proj t idx) = Proj (ab top t) idx
791 ab top t = t
793-- | Convert several names. First in the list comes out as V 0
794pToVs :: Eq n => [n] -> TT n -> TT n
795pToVs ns tm = pToVs' ns tm 0 where
796 pToVs' [] tm i = tm
797 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
799-- | Replace de Bruijn indices in the given term with explicit references to
800-- the names of the bindings they refer to. It is an error if the given term
801-- contains free de Bruijn indices.
802vToP :: TT n -> TT n
803vToP = vToP' [] where
804 vToP' env (V i) = let (n, b) = (env !! i) in
805 P Bound n (binderTy b)
806 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
807 Bind n b' (vToP' ((n, b'):env) sc)
808 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
809 vToP' env t = t
811-- | Replace every non-free reference to the name of a binding in
812-- the given term with a de Bruijn index.
813finalise :: Eq n => TT n -> TT n
814finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
815finalise (App f a) = App (finalise f) (finalise a)
816finalise t = t
818-- Once we've finished checking everything about a term we no longer need
819-- the type on the 'P' so erase it so save memory
821pEraseType :: TT n -> TT n
822pEraseType (P nt t _) = P nt t Erased
823pEraseType (App f a) = App (pEraseType f) (pEraseType a)
824pEraseType (Bind n b sc) = Bind n (fmap pEraseType b) (pEraseType sc)
825pEraseType t = t
827-- | As 'instantiate', but in addition to replacing @'V' 0@,
828-- replace references to the given 'Name'-like id.
829subst :: Eq n => n {-^ The id to replace -} ->
830 TT n {-^ The replacement term -} ->
831 TT n {-^ The term to replace in -} ->
832 TT n
833subst n v tm = instantiate v (pToV n tm)
835-- If there are no Vs in the term (i.e. in proof state)
836psubst :: Eq n => n -> TT n -> TT n -> TT n
837psubst n v tm = s' tm where
838 s' (P _ x _) | n == x = v
839 s' (Bind x b sc) | n == x = Bind x (fmap s' b) sc
840 | otherwise = Bind x (fmap s' b) (s' sc)
841 s' (App f a) = App (s' f) (s' a)
842 s' (Proj t idx) = Proj (s' t) idx
843 s' t = t
845-- | As 'subst', but takes a list of (name, substitution) pairs instead
846-- of a single name and substitution
847substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
848substNames [] t = t
849substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
851-- | Replaces all terms equal (in the sense of @(==)@) to
852-- the old term with the new term.
853substTerm :: Eq n => TT n {-^ Old term -} ->
854 TT n {-^ New term -} ->
855 TT n {-^ template term -}
856 -> TT n
857substTerm old new = st where
858 st t | t == old = new
859 st (App f a) = App (st f) (st a)
860 st (Bind x b sc) = Bind x (fmap st b) (st sc)
861 st t = t
863-- | Returns true if V 0 and bound name n do not occur in the term
864noOccurrence :: Eq n => n -> TT n -> Bool
865noOccurrence n t = no' 0 t
866 where
867 no' i (V x) = not (i == x)
868 no' i (P Bound x _) = not (n == x)
869 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
870 where noB' i (Let t v) = no' i t && no' i v
871 noB' i (Guess t v) = no' i t && no' i v
872 noB' i b = no' i (binderTy b)
873 no' i (App f a) = no' i f && no' i a
874 no' i (Proj x _) = no' i x
875 no' i _ = True
877-- | Returns all names used free in the term
878freeNames :: Eq n => TT n -> [n]
879freeNames (P _ n _) = [n]
880freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
881 ++ freeNames t
882freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
883freeNames (App f a) = nub $ freeNames f ++ freeNames a
884freeNames (Proj x i) = nub $ freeNames x
885freeNames _ = []
887-- | Return the arity of a (normalised) type
888arity :: TT n -> Int
889arity (Bind n (Pi t) sc) = 1 + arity sc
890arity _ = 0
892-- | Deconstruct an application; returns the function and a list of arguments
893unApply :: TT n -> (TT n, [TT n])
894unApply t = ua [] t where
895 ua args (App f a) = ua (a:args) f
896 ua args t = (t, args)
898-- | Returns a term representing the application of the first argument
899-- (a function) to every element of the second argument.
900mkApp :: TT n -> [TT n] -> TT n
901mkApp f [] = f
902mkApp f (a:as) = mkApp (App f a) as
904unList :: Term -> Maybe [Term]
905unList tm = case unApply tm of
906 (nil, [_]) -> Just []
907 (cons, ([_, x, xs])) ->
908 do rest <- unList xs
909 return $ x:rest
910 (f, args) -> Nothing
912-- | Cast a 'TT' term to a 'Raw' value, discarding universe information and
913-- the types of named references and replacing all de Bruijn indices
914-- with the corresponding name. It is an error if there are free de
915-- Bruijn indices.
916forget :: TT Name -> Raw
917forget tm = fe [] tm
918 where
919 fe env (P _ n _) = Var n
920 fe env (V i) = Var (env !! i)
921 fe env (Bind n b sc) = let n' = uniqueName n env in
922 RBind n' (fmap (fe env) b)
923 (fe (n':env) sc)
924 fe env (App f a) = RApp (fe env f) (fe env a)
925 fe env (Constant c)
926 = RConstant c
927 fe env (TType i) = RType
928 fe env Erased = RConstant Forgot
930-- | Introduce a 'Bind' into the given term for each element of the
931-- given list of (name, binder) pairs.
932bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
933bindAll [] t = t
934bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
936-- | Like 'bindAll', but the 'Binder's are 'TT' terms instead.
937-- The first argument is a function to map @TT@ terms to @Binder@s.
938-- This function might often be something like 'Lam', which directly
939-- constructs a @Binder@ from a @TT@ term.
940bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
941bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
943-- | Return a list of pairs of the names of the outermost 'Pi'-bound
944-- variables in the given term, together with their types.
945getArgTys :: TT n -> [(n, TT n)]
946getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
947getArgTys _ = []
949getRetTy :: TT n -> TT n
950getRetTy (Bind n (PVar _) sc) = getRetTy sc
951getRetTy (Bind n (PVTy _) sc) = getRetTy sc
952getRetTy (Bind n (Pi _) sc) = getRetTy sc
953getRetTy sc = sc
955uniqueNameFrom :: [Name] -> [Name] -> Name
956uniqueNameFrom (s : supply) hs
957 | s `elem` hs = uniqueNameFrom supply hs
958 | otherwise = s
960uniqueName :: Name -> [Name] -> Name
961uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
962 | otherwise = n
964uniqueBinders :: [Name] -> TT Name -> TT Name
965uniqueBinders ns (Bind n b sc)
966 = let n' = uniqueName n ns in
967 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
968uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
969uniqueBinders ns t = t
972nextName (NS x s) = NS (nextName x) s
973nextName (MN i n) = MN (i+1) n
974nextName (UN x) = let (num', nm') = T.span isDigit (T.reverse x)
975 nm = T.reverse nm'
976 num = readN (T.reverse num') in
977 UN (nm `T.append` txt (show (num+1)))
978 where
979 readN x | not (T.null x) = read (T.unpack x)
980 readN x = 0
981nextName (SN x) = SN (nextName' x)
982 where
983 nextName' (WhereN i f x) = WhereN i f (nextName x)
984 nextName' (CaseN n) = CaseN (nextName n)
985 nextName' (MethodN n) = MethodN (nextName n)
987type Term = TT Name
988type Type = Term
990type Env = EnvTT Name
992-- | an environment with de Bruijn indices 'normalised' so that they all refer to
993-- this environment
995newtype WkEnvTT n = Wk (EnvTT n)
996type WkEnv = WkEnvTT Name
998instance (Eq n, Show n) => Show (TT n) where
999 show t = showEnv [] t
1001itBitsName IT8 = "Bits8"
1002itBitsName IT16 = "Bits16"
1003itBitsName IT32 = "Bits32"
1004itBitsName IT64 = "Bits64"
1006instance Show Const where
1007 show (I i) = show i
1008 show (BI i) = show i
1009 show (Fl f) = show f
1010 show (Ch c) = show c
1011 show (Str s) = show s
1012 show (B8 x) = show x
1013 show (B16 x) = show x
1014 show (B32 x) = show x
1015 show (B64 x) = show x
1016 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1017 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1018 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1019 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
1020 show (AType ATFloat) = "Float"
1021 show (AType (ATInt ITBig)) = "Integer"
1022 show (AType (ATInt ITNative)) = "Int"
1023 show (AType (ATInt ITChar)) = "Char"
1024 show (AType (ATInt (ITFixed it))) = itBitsName it
1025 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
1026 show StrType = "String"
1027 show PtrType = "Ptr"
1028 show VoidType = "Void"
1030showEnv :: (Eq n, Show n) => EnvTT n -> TT n -> String
1031showEnv env t = showEnv' env t False
1032showEnvDbg env t = showEnv' env t True
1034prettyEnv env t = prettyEnv' env t False
1035 where
1036 prettyEnv' env t dbg = prettySe 10 env t dbg
1038 bracket outer inner p
1039 | inner > outer = lparen <> p <> rparen
1040 | otherwise = p
1042 prettySe p env (P nt n t) debug =
1043 pretty n <+>
1044 if debug then
1045 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
1046 else
1047 empty
1048 prettySe p env (V i) debug
1049 | i < length env =
1050 if debug then
1051 text . show . fst $ env!!i
1052 else
1053 lbrack <+> text (show i) <+> rbrack
1054 | otherwise = text "unbound" <+> text (show i) <+> text "!"
1055 prettySe p env (Bind n b@(Pi t) sc) debug
1056 | noOccurrence n sc && not debug =
1057 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1058 prettySe p env (Bind n b sc) debug =
1059 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
1060 prettySe p env (App f a) debug =
1061 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
1062 prettySe p env (Proj x i) debug =
1063 prettySe 1 env x debug <+> text ("!" ++ show i)
1064 prettySe p env (Constant c) debug = pretty c
1065 prettySe p env Erased debug = text "[_]"
1066 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
1068 -- Render a `Binder` and its name
1069 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
1070 prettySb env n (Hole t) = prettyB env "?defer" "." n t
1071 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
1072 prettySb env n (PVar t) = prettyB env "pat" "." n t
1073 prettySb env n (PVTy t) = prettyB env "pty" "." n t
1074 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
1075 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
1077 -- Use `op` and `sc` to delimit `n` (a binding name) and its type
1078 -- declaration
1079 -- e.g. "λx : Int =>" for the Lam case
1080 prettyB env op sc n t debug =
1081 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
1083 -- Like `prettyB`, but handle the bindings that have values in addition
1084 -- to names and types
1085 prettyBv env op sc n t v debug =
1086 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
1087 prettySe 10 env v debug <> text sc
1090showEnv' env t dbg = se 10 env t where
1091 se p env (P nt n t) = show n
1092 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
1093 se p env (V i) | i < length env && i >= 0
1094 = (show $ fst $ env!!i) ++
1095 if dbg then "{" ++ show i ++ "}" else ""
1096 | otherwise = "!!V " ++ show i ++ "!!"
1097 se p env (Bind n b@(Pi t) sc)
1098 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
1099 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
1100 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
1101 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
1102 se p env (Constant c) = show c
1103 se p env Erased = "[__]"
1104 se p env Impossible = "[impossible]"
1105 se p env (TType i) = "Type " ++ show i
1107 sb env n (Lam t) = showb env "\\ " " => " n t
1108 sb env n (Hole t) = showb env "? " ". " n t
1109 sb env n (GHole i t) = showb env "?defer " ". " n t
1110 sb env n (Pi t) = showb env "(" ") -> " n t
1111 sb env n (PVar t) = showb env "pat " ". " n t
1112 sb env n (PVTy t) = showb env "pty " ". " n t
1113 sb env n (Let t v) = showbv env "let " " in " n t v
1114 sb env n (Guess t v) = showbv env "?? " " in " n t v
1116 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
1117 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
1118 se 10 env v ++ sc
1120 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
1121 | otherwise = str
1123-- | Check whether a term has any holes in it - impure if so
1124pureTerm :: TT Name -> Bool
1125pureTerm (App f a) = pureTerm f && pureTerm a
1126pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
1127 pureBinder (Hole _) = False
1128 pureBinder (Guess _ _) = False
1129 pureBinder (Let t v) = pureTerm t && pureTerm v
1130 pureBinder t = pureTerm (binderTy t)
1132 notClassName (MN _ c) | c == txt "class" = False
1133 notClassName _ = True
1135pureTerm _ = True
1137-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1138weakenTm :: Int -> TT n -> TT n
1139weakenTm i t = wk i 0 t
1140 where wk i min (V x) | x >= min = V (i + x)
1141 wk i m (App f a) = App (wk i m f) (wk i m a)
1142 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1143 wk i m t = t
1144 wkb i m t = fmap (wk i m) t
1146-- | Weaken an environment so that all the de Bruijn indices are correct according
1147-- to the latest bound variable
1149weakenEnv :: EnvTT n -> EnvTT n
1150weakenEnv env = wk (length env - 1) env
1151 where wk i [] = []
1152 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1153 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1154 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1155 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1157-- | Weaken every term in the environment by the given amount
1158weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1159weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1161-- | Gather up all the outer 'PVar's and 'Hole's in an expression and reintroduce
1162-- them in a canonical order
1163orderPats :: Term -> Term
1164orderPats tm = op [] tm
1165 where
1166 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1167 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1168 op ps sc = bindAll (sortP ps) sc
1170 sortP ps = pick [] (reverse ps)
1172 namesIn (P _ n _) = [n]
1173 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
1174 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
1175 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
1176 nb t = namesIn (binderTy t)
1177 namesIn (App f a) = nub (namesIn f ++ namesIn a)
1178 namesIn _ = []
1180 pick acc [] = reverse acc
1181 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1183 insert n t [] = [(n, t)]
1184 insert n t ((n',t') : ps)
1185 | n `elem` (namesIn (binderTy t') ++
1186 concatMap namesIn (map (binderTy . snd) ps))
1187 = (n', t') : insert n t ps
1188 | otherwise = (n,t):(n',t'):ps