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Idris-dev/src/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 Core.TT where
23import Control.Monad.State
24import Control.Monad.Trans.Error (Error(..))
25import Debug.Trace
26import qualified Data.Map as Map
27import Data.Char
28import Data.List
29import Data.Vector.Unboxed (Vector)
30import qualified Data.Vector.Unboxed as V
31import qualified Data.Binary as B
32import Data.Binary hiding (get, put)
33import Foreign.Storable (sizeOf)
35import Util.Pretty hiding (Str)
37data Option = TTypeInTType
38 | CheckConv
39 deriving Eq
41-- | Source location. These are typically produced by the parser 'Idris.Parser.getFC'
42data FC = FC { fc_fname :: String, -- ^ Filename
43 fc_line :: Int, -- ^ Line number
44 fc_column :: Int -- ^ Column number
45 }
47-- | Ignore source location equality (so deriving classes do not compare FCs)
48instance Eq FC where
49 _ == _ = True
51-- | FC with equality
52newtype FC' = FC' { unwrapFC :: FC }
54instance Eq FC' where
55 FC' fc == FC' fc' = fcEq fc fc'
56 where fcEq (FC n l c) (FC n' l' c') = n == n' && l == l' && c == c'
58-- | Empty source location
59emptyFC :: FC
60emptyFC = fileFC ""
62-- | Source location with file only
63fileFC :: String -> FC
64fileFC s = FC s 0 0
66{-!
67deriving instance Binary FC
68deriving instance NFData FC
69!-}
71instance Sized FC where
72 size (FC f l c) = 1 + length f
74instance Show FC where
75 show (FC f l c) = f ++ ":" ++ show l ++ ":" ++ show c
77data Err = Msg String
78 | InternalMsg String
79 | CantUnify Bool Term Term Err [(Name, Type)] Int
80 -- Int is 'score' - how much we did unify
81 -- Bool indicates recoverability, True indicates more info may make
82 -- unification succeed
83 | InfiniteUnify Name Term [(Name, Type)]
84 | CantConvert Term Term [(Name, Type)]
85 | UnifyScope Name Name Term [(Name, Type)]
86 | CantInferType String
87 | NonFunctionType Term Term
88 | TooManyArguments Name
89 | CantIntroduce Term
90 | NoSuchVariable Name
91 | NoTypeDecl Name
92 | NotInjective Term Term Term
93 | CantResolve Term
94 | CantResolveAlts [String]
95 | IncompleteTerm Term
96 | UniverseError
97 | ProgramLineComment
98 | Inaccessible Name
99 | NonCollapsiblePostulate Name
100 | AlreadyDefined Name
101 | ProofSearchFail Err
102 | NoRewriting Term
103 | At FC Err
104 | Elaborating String Name Err
105 | ProviderError String
106 | LoadingFailed String Err
107 deriving Eq
108{-!
109deriving instance NFData Err
110!-}
112instance Sized Err where
113 size (Msg msg) = length msg
114 size (InternalMsg msg) = length msg
115 size (CantUnify _ left right err _ score) = size left + size right + size err
116 size (InfiniteUnify _ right _) = size right
117 size (CantConvert left right _) = size left + size right
118 size (UnifyScope _ _ right _) = size right
119 size (NoSuchVariable name) = size name
120 size (NoTypeDecl name) = size name
121 size (NotInjective l c r) = size l + size c + size r
122 size (CantResolve trm) = size trm
123 size (NoRewriting trm) = size trm
124 size (CantResolveAlts _) = 1
125 size (IncompleteTerm trm) = size trm
126 size UniverseError = 1
127 size ProgramLineComment = 1
128 size (At fc err) = size fc + size err
129 size (Elaborating _ n err) = size err
130 size (ProviderError msg) = length msg
131 size (LoadingFailed fn e) = 1 + length fn + size e
132 size _ = 1
134score :: Err -> Int
135score (CantUnify _ _ _ m _ s) = s + score m
136score (CantResolve _) = 20
137score (NoSuchVariable _) = 1000
138score (ProofSearchFail _) = 10000
139score (InternalMsg _) = -1
140score _ = 0
142instance Show Err where
143 show (Msg s) = s
144 show (InternalMsg s) = "Internal error: " ++ show s
145 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
146 ++ show e ++ " in " ++ show sc ++ " " ++ show i
147 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
148 show (ProviderError msg) = "Type provider error: " ++ msg
149 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: " ++ show e
150 show _ = "Error"
152instance Pretty Err where
153 pretty (Msg m) = text m
154 pretty (CantUnify _ l r e _ i) =
155 if size l + size r > breakingSize then
156 text "Cannot unify" <+> colon $$
157 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
158 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
159 else
160 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
161 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
162 pretty (ProviderError msg) = text msg
163 pretty err@(LoadingFailed _ _) = text (show err)
164 pretty _ = text "Error"
166instance Error Err where
167 strMsg = Msg
169data TC a = OK a
170 | Error Err
171 deriving (Eq, Functor)
173instance Pretty a => Pretty (TC a) where
174 pretty (OK ok) = pretty ok
175 pretty (Error err) =
176 if size err > breakingSize then
177 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
178 else
179 text "Error" <+> colon <+> pretty err
181instance Show a => Show (TC a) where
182 show (OK x) = show x
183 show (Error str) = "Error: " ++ show str
185-- at some point, this instance should also carry type checking options
186-- (e.g. Type:Type)
188instance Monad TC where
189 return = OK
190 x >>= k = case x of
191 OK v -> k v
192 Error e -> Error e
193 fail e = Error (InternalMsg e)
195tfail :: Err -> TC a
196tfail e = Error e
198trun :: FC -> TC a -> TC a
199trun fc (OK a) = OK a
200trun fc (Error e) = Error (At fc e)
202instance MonadPlus TC where
203 mzero = fail "Unknown error"
204 (OK x) `mplus` _ = OK x
205 _ `mplus` (OK y) = OK y
206 err `mplus` _ = err
208discard :: Monad m => m a -> m ()
209discard f = f >> return ()
211showSep :: String -> [String] -> String
212showSep sep [] = ""
213showSep sep [x] = x
214showSep sep (x:xs) = x ++ sep ++ showSep sep xs
216pmap f (x, y) = (f x, f y)
218traceWhen True msg a = trace msg a
219traceWhen False _ a = a
221-- RAW TERMS ----------------------------------------------------------------
223-- | Names are hierarchies of strings, describing scope (so no danger of
224-- duplicate names, but need to be careful on lookup).
225data Name = UN String -- ^ User-provided name
226 | NS Name [String] -- ^ Root, namespaces
227 | MN Int String -- ^ Machine chosen names
228 | NErased -- ^ Name of somethng which is never used in scope
229 | SN SpecialName -- ^ Decorated function names
230 deriving (Eq, Ord)
231{-!
232deriving instance Binary Name
233deriving instance NFData Name
234!-}
236data SpecialName = WhereN Int Name Name
237 | InstanceN Name [String]
238 | ParentN Name String
239 | MethodN Name
240 | CaseN Name
241 | ElimN Name
242 deriving (Eq, Ord)
243{-!
244deriving instance Binary SpecialName
245deriving instance NFData SpecialName
246!-}
248instance Sized Name where
249 size (UN n) = 1
250 size (NS n els) = 1 + length els
251 size (MN i n) = 1
252 size _ = 1
254instance Pretty Name where
255 pretty (UN n) = text n
256 pretty (NS n s) = pretty n
257 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
258 pretty (SN s) = text (show s)
260instance Show Name where
261 show (UN n) = n
262 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
263 show (MN _ "underscore") = "_"
264 show (MN i s) = "{" ++ s ++ show i ++ "}"
265 show (SN s) = show s
266 show NErased = "_"
268instance Show SpecialName where
269 show (WhereN i p c) = show p ++ ", " ++ show c
270 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
271 show (MethodN m) = "method " ++ show m
272 show (ParentN p c) = show p ++ "#" ++ c
273 show (CaseN n) = "case block in " ++ show n
274 show (ElimN n) = "<<" ++ show n ++ " eliminator>>"
276-- Show a name in a way decorated for code generation, not human reading
277showCG :: Name -> String
278showCG (UN n) = n
279showCG (NS n s) = showSep "." (reverse s) ++ "." ++ showCG n
280showCG (MN _ "underscore") = "_"
281showCG (MN i s) = "{" ++ s ++ show i ++ "}"
282showCG (SN s) = showCG' s
283 where showCG' (WhereN i p c) = showCG p ++ ":" ++ showCG c ++ ":" ++ show i
284 showCG' (InstanceN cl inst) = '@':showCG cl ++ '$':showSep ":" inst
285 showCG' (MethodN m) = '!':showCG m
286 showCG' (ParentN p c) = showCG p ++ "#" ++ show c
287 showCG' (CaseN c) = showCG c ++ "_case"
288showCG NErased = "_"
291-- |Contexts allow us to map names to things. A root name maps to a collection
292-- of things in different namespaces with that name.
293type Ctxt a = Map.Map Name (Map.Map Name a)
294emptyContext = Map.empty
296tcname (UN ('@':_)) = True
297tcname (NS n _) = tcname n
298tcname (SN (InstanceN _ _)) = True
299tcname (SN (MethodN _)) = True
300tcname (SN (ParentN _ _)) = True
301tcname _ = False
303implicitable (NS n _) = implicitable n
304implicitable (UN (x:xs)) = isLower x
305implicitable (MN _ _) = True
306implicitable _ = False
308nsroot (NS n _) = n
309nsroot n = n
311addDef :: Name -> a -> Ctxt a -> Ctxt a
312addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
313 Nothing -> Map.insert (nsroot n)
314 (Map.insert n v Map.empty) ctxt
315 Just xs -> Map.insert (nsroot n)
316 (Map.insert n v xs) ctxt
318{-| Look up a name in the context, given an optional namespace.
319 The name (n) may itself have a (partial) namespace given.
321 Rules for resolution:
323 - if an explicit namespace is given, return the names which match it. If none
324 match, return all names.
326 - if the name has has explicit namespace given, return the names which match it
327 and ignore the given namespace.
329 - otherwise, return all names.
331-}
333lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
334lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
335 Just xs -> filterNS (Map.toList xs)
336 Nothing -> []
337 where
338 filterNS [] = []
339 filterNS ((found, v) : xs)
340 | nsmatch n found = (found, v) : filterNS xs
341 | otherwise = filterNS xs
343 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
344 nsmatch (NS _ _) _ = False
345 nsmatch looking found = True
347lookupCtxt :: Name -> Ctxt a -> [a]
348lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
350lookupCtxtExact :: Name -> Ctxt a -> [a]
351lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
353updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
354updateDef n f ctxt
355 = let ds = lookupCtxtName n ctxt in
356 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
358toAlist :: Ctxt a -> [(Name, a)]
359toAlist ctxt = let allns = map snd (Map.toList ctxt) in
360 concat (map (Map.toList) allns)
362addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
363addAlist [] ctxt = ctxt
364addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
366data NativeTy = IT8 | IT16 | IT32 | IT64
367 deriving (Show, Eq, Ord, Enum)
369instance Pretty NativeTy where
370 pretty IT8 = text "Bits8"
371 pretty IT16 = text "Bits16"
372 pretty IT32 = text "Bits32"
373 pretty IT64 = text "Bits64"
375data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
376 | ITVec NativeTy Int
377 deriving (Show, Eq, Ord)
379data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
380 deriving (Show, Eq, Ord)
381{-!
382deriving instance NFData IntTy
383deriving instance NFData NativeTy
384deriving instance NFData ArithTy
385!-}
387instance Pretty ArithTy where
388 pretty (ATInt ITNative) = text "Int"
389 pretty (ATInt ITBig) = text "BigInt"
390 pretty (ATInt ITChar) = text "Char"
391 pretty (ATInt (ITFixed n)) = pretty n
392 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
393 pretty ATFloat = text "Float"
395nativeTyWidth :: NativeTy -> Int
396nativeTyWidth IT8 = 8
397nativeTyWidth IT16 = 16
398nativeTyWidth IT32 = 32
399nativeTyWidth IT64 = 64
401{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
402intTyWidth :: IntTy -> Int
403intTyWidth (ITFixed n) = nativeTyWidth n
404intTyWidth ITNative = 8 * sizeOf (0 :: Int)
405intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
406intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
408data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
409 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
410 | B8V (Vector Word8) | B16V (Vector Word16)
411 | B32V (Vector Word32) | B64V (Vector Word64)
412 | AType ArithTy | StrType
413 | PtrType | VoidType | Forgot
414 deriving (Eq, Ord)
415{-!
416deriving instance Binary Const
417deriving instance NFData Const
418!-}
420instance Sized Const where
421 size _ = 1
423instance Pretty Const where
424 pretty (I i) = text . show $ i
425 pretty (BI i) = text . show $ i
426 pretty (Fl f) = text . show $ f
427 pretty (Ch c) = text . show $ c
428 pretty (Str s) = text s
429 pretty (AType a) = pretty a
430 pretty StrType = text "String"
431 pretty PtrType = text "Ptr"
432 pretty VoidType = text "Void"
433 pretty Forgot = text "Forgot"
434 pretty (B8 w) = text . show $ w
435 pretty (B16 w) = text . show $ w
436 pretty (B32 w) = text . show $ w
437 pretty (B64 w) = text . show $ w
439data Raw = Var Name
440 | RBind Name (Binder Raw) Raw
441 | RApp Raw Raw
442 | RType
443 | RForce Raw
444 | RConstant Const
445 deriving (Show, Eq)
447instance Sized Raw where
448 size (Var name) = 1
449 size (RBind name bind right) = 1 + size bind + size right
450 size (RApp left right) = 1 + size left + size right
451 size RType = 1
452 size (RForce raw) = 1 + size raw
453 size (RConstant const) = size const
455instance Pretty Raw where
456 pretty = text . show
458{-!
459deriving instance Binary Raw
460deriving instance NFData Raw
461!-}
463-- | All binding forms are represented in a unform fashion.
464data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
465 | Pi { binderTy :: b }
466 | Let { binderTy :: b,
467 binderVal :: b {-^ value for bound variable-}}
468 | NLet { binderTy :: b,
469 binderVal :: b }
470 | Hole { binderTy :: b}
471 | GHole { envlen :: Int,
472 binderTy :: b}
473 | Guess { binderTy :: b,
474 binderVal :: b }
475 | PVar { binderTy :: b }
476 | PVTy { binderTy :: b }
477 deriving (Show, Eq, Ord, Functor)
478{-!
479deriving instance Binary Binder
480deriving instance NFData Binder
481!-}
483instance Sized a => Sized (Binder a) where
484 size (Lam ty) = 1 + size ty
485 size (Pi ty) = 1 + size ty
486 size (Let ty val) = 1 + size ty + size val
487 size (NLet ty val) = 1 + size ty + size val
488 size (Hole ty) = 1 + size ty
489 size (GHole _ ty) = 1 + size ty
490 size (Guess ty val) = 1 + size ty + size val
491 size (PVar ty) = 1 + size ty
492 size (PVTy ty) = 1 + size ty
494fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
495fmapMB f (Let t v) = liftM2 Let (f t) (f v)
496fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
497fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
498fmapMB f (Lam t) = liftM Lam (f t)
499fmapMB f (Pi t) = liftM Pi (f t)
500fmapMB f (Hole t) = liftM Hole (f t)
501fmapMB f (GHole i t) = liftM (GHole i) (f t)
502fmapMB f (PVar t) = liftM PVar (f t)
503fmapMB f (PVTy t) = liftM PVTy (f t)
505raw_apply :: Raw -> [Raw] -> Raw
506raw_apply f [] = f
507raw_apply f (a : as) = raw_apply (RApp f a) as
509raw_unapply :: Raw -> (Raw, [Raw])
510raw_unapply t = ua [] t where
511 ua args (RApp f a) = ua (a:args) f
512 ua args t = (t, args)
514data RawFun = RawFun { rtype :: Raw,
515 rval :: Raw
516 }
517 deriving Show
519data RawDatatype = RDatatype Name Raw [(Name, Raw)]
520 deriving Show
522data RDef = RFunction RawFun
523 | RConst Raw
524 | RData RawDatatype
525 deriving Show
527type RProgram = [(Name, RDef)]
529-- WELL TYPED TERMS ---------------------------------------------------------
531-- | Universe expressions for universe checking
532data UExp = UVar Int -- ^ universe variable
533 | UVal Int -- ^ explicit universe level
534 deriving (Eq, Ord)
535{-!
536deriving instance NFData UExp
537!-}
539instance Sized UExp where
540 size _ = 1
542-- We assume that universe levels have been checked, so anything external
543-- can just have the same universe variable and we won't get any new
544-- cycles.
546instance Binary UExp where
547 put x = return ()
548 get = return (UVar (-1))
550instance Show UExp where
551 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
552 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
553 show (UVal x) = show x
554-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
556-- | Universe constraints
557data UConstraint = ULT UExp UExp -- ^ Strictly less than
558 | ULE UExp UExp -- ^ Less than or equal to
559 deriving Eq
561instance Show UConstraint where
562 show (ULT x y) = show x ++ " < " ++ show y
563 show (ULE x y) = show x ++ " <= " ++ show y
565type UCs = (Int, [UConstraint])
567data NameType = Bound
568 | Ref
569 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
570 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
571 deriving (Show, Ord)
572{-!
573deriving instance Binary NameType
574deriving instance NFData NameType
575!-}
577instance Sized NameType where
578 size _ = 1
580instance Pretty NameType where
581 pretty = text . show
583instance Eq NameType where
584 Bound == Bound = True
585 Ref == Ref = True
586 DCon _ a == DCon _ b = (a == b) -- ignore tag
587 TCon _ a == TCon _ b = (a == b) -- ignore tag
588 _ == _ = False
590-- | Terms in the core language
591data TT n = P NameType n (TT n) -- ^ named references
592 | V Int -- ^ a resolved de Bruijn-indexed variable
593 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
594 | App (TT n) (TT n) -- ^ function, function type, arg
595 | Constant Const -- ^ constant
596 | Proj (TT n) Int -- ^ argument projection; runtime only
597 -- (-1) is a special case for 'subtract one from BI'
598 | Erased -- ^ an erased term
599 | Impossible -- ^ special case for totality checking
600 | TType UExp -- ^ the type of types at some level
601 deriving (Ord, Functor)
602{-!
603deriving instance Binary TT
604deriving instance NFData TT
605!-}
607class TermSize a where
608 termsize :: Name -> a -> Int
610instance TermSize a => TermSize [a] where
611 termsize n [] = 0
612 termsize n (x : xs) = termsize n x + termsize n xs
614instance TermSize (TT Name) where
615 termsize n (P _ x _)
616 | x == n = 1000000 -- recursive => really big
617 | otherwise = 1
618 termsize n (V _) = 1
619 termsize n (Bind n' (Let t v) sc)
620 = let rn = if n == n' then MN 0 "noname" else n in
621 termsize rn v + termsize rn sc
622 termsize n (Bind n' b sc)
623 = let rn = if n == n' then MN 0 "noname" else n in
624 termsize rn sc
625 termsize n (App f a) = termsize n f + termsize n a
626 termsize n (Proj t i) = termsize n t
627 termsize n _ = 1
629instance Sized a => Sized (TT a) where
630 size (P name n trm) = 1 + size name + size n + size trm
631 size (V v) = 1
632 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
633 size (App l r) = 1 + size l + size r
634 size (Constant c) = size c
635 size Erased = 1
636 size (TType u) = 1 + size u
638instance Pretty a => Pretty (TT a) where
639 pretty _ = text "test"
641type EnvTT n = [(n, Binder (TT n))]
643data Datatype n = Data { d_typename :: n,
644 d_typetag :: Int,
645 d_type :: (TT n),
646 d_cons :: [(n, TT n)] }
647 deriving (Show, Functor, Eq)
649instance Eq n => Eq (TT n) where
650 (==) (P xt x _) (P yt y _) = x == y
651 (==) (V x) (V y) = x == y
652 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
653 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
654 (==) (TType _) (TType _) = True -- deal with constraints later
655 (==) (Constant x) (Constant y) = x == y
656 (==) (Proj x i) (Proj y j) = x == y && i == j
657 (==) Erased _ = True
658 (==) _ Erased = True
659 (==) _ _ = False
661-- * A few handy operations on well typed terms:
663-- | A term is injective iff it is a data constructor, type constructor,
664-- constant, the type Type, pi-binding, or an application of an injective
665-- term.
666isInjective :: TT n -> Bool
667isInjective (P (DCon _ _) _ _) = True
668isInjective (P (TCon _ _) _ _) = True
669isInjective (Constant _) = True
670isInjective (TType x) = True
671isInjective (Bind _ (Pi _) sc) = True
672isInjective (App f a) = isInjective f
673isInjective _ = False
675-- | Count the number of instances of a de Bruijn index in a term
676vinstances :: Int -> TT n -> Int
677vinstances i (V x) | i == x = 1
678vinstances i (App f a) = vinstances i f + vinstances i a
679vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
680 where instancesB (Let t v) = vinstances i v
681 instancesB _ = 0
682vinstances i t = 0
684instantiate :: TT n -> TT n -> TT n
685instantiate e = subst 0 where
686 subst i (V x) | i == x = e
687 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
688 subst i (App f a) = App (subst i f) (subst i a)
689 subst i (Proj x idx) = Proj (subst i x) idx
690 subst i t = t
692substV :: TT n -> TT n -> TT n
693substV x tm = dropV 0 (instantiate x tm) where
694 dropV i (V x) | x > i = V (x - 1)
695 | otherwise = V x
696 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
697 dropV i (App f a) = App (dropV i f) (dropV i a)
698 dropV i (Proj x idx) = Proj (dropV i x) idx
699 dropV i t = t
701explicitNames :: TT n -> TT n
702explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
703 Bind x b'
704 (explicitNames (instantiate
705 (P Bound x (binderTy b')) sc))
706explicitNames (App f a) = App (explicitNames f) (explicitNames a)
707explicitNames (Proj x idx) = Proj (explicitNames x) idx
708explicitNames t = t
710pToV :: Eq n => n -> TT n -> TT n
711pToV n = pToV' n 0
712pToV' n i (P _ x _) | n == x = V i
713pToV' n i (Bind x b sc)
714-- We can assume the inner scope has been pToVed already, so continue to
715-- resolve names from the *outer* scope which may happen to have the same id.
716 | n == x = Bind x (fmap (pToV' n i) b) sc
717 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
718pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
719pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
720pToV' n i t = t
722-- increase de Bruijn indices, as if a binder has been added
723addBinder :: TT n -> TT n
724addBinder t = ab 0 t
725 where
726 ab top (V i) | i >= top = V (i + 1)
727 | otherwise = V i
728 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
729 ab top (App f a) = App (ab top f) (ab top a)
730 ab top (Proj t idx) = Proj (ab top t) idx
731 ab top t = t
733-- | Convert several names. First in the list comes out as V 0
734pToVs :: Eq n => [n] -> TT n -> TT n
735pToVs ns tm = pToVs' ns tm 0 where
736 pToVs' [] tm i = tm
737 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
739vToP :: TT n -> TT n
740vToP = vToP' [] where
741 vToP' env (V i) = let (n, b) = (env !! i) in
742 P Bound n (binderTy b)
743 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
744 Bind n b' (vToP' ((n, b'):env) sc)
745 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
746 vToP' env t = t
748finalise :: Eq n => TT n -> TT n
749finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
750finalise (App f a) = App (finalise f) (finalise a)
751finalise t = t
753subst :: Eq n => n -> TT n -> TT n -> TT n
754subst n v tm = instantiate v (pToV n tm)
756substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
757substNames [] t = t
758substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
760substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
761substTerm old new = st where
762 st t | t == old = new
763 st (App f a) = App (st f) (st a)
764 st (Bind x b sc) = Bind x (fmap st b) (st sc)
765 st t = t
767-- Returns true if V 0 and bound name n do not occur in the term
769noOccurrence :: Eq n => n -> TT n -> Bool
770noOccurrence n t = no' 0 t
771 where
772 no' i (V x) = not (i == x)
773 no' i (P Bound x _) = not (n == x)
774 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
775 where noB' i (Let t v) = no' i t && no' i v
776 noB' i (Guess t v) = no' i t && no' i v
777 noB' i b = no' i (binderTy b)
778 no' i (App f a) = no' i f && no' i a
779 no' i (Proj x _) = no' i x
780 no' i _ = True
782-- | Returns all names used free in the term
783freeNames :: Eq n => TT n -> [n]
784freeNames (P _ n _) = [n]
785freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
786 ++ freeNames t
787freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
788freeNames (App f a) = nub $ freeNames f ++ freeNames a
789freeNames (Proj x i) = nub $ freeNames x
790freeNames _ = []
792-- | Return the arity of a (normalised) type
793arity :: TT n -> Int
794arity (Bind n (Pi t) sc) = 1 + arity sc
795arity _ = 0
797-- | Deconstruct an application; returns the function and a list of arguments
798unApply :: TT n -> (TT n, [TT n])
799unApply t = ua [] t where
800 ua args (App f a) = ua (a:args) f
801 ua args t = (t, args)
803mkApp :: TT n -> [TT n] -> TT n
804mkApp f [] = f
805mkApp f (a:as) = mkApp (App f a) as
807forget :: TT Name -> Raw
808forget tm = fe [] tm
809 where
810 fe env (P _ n _) = Var n
811 fe env (V i) = Var (env !! i)
812 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
813 (fe (n:env) sc)
814 fe env (App f a) = RApp (fe env f) (fe env a)
815 fe env (Constant c)
816 = RConstant c
817 fe env (TType i) = RType
818 fe env Erased = RConstant Forgot
820bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
821bindAll [] t =t
822bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
824bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
825bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
827getArgTys :: TT n -> [(n, TT n)]
828getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
829getArgTys _ = []
831getRetTy :: TT n -> TT n
832getRetTy (Bind n (PVar _) sc) = getRetTy sc
833getRetTy (Bind n (PVTy _) sc) = getRetTy sc
834getRetTy (Bind n (Pi _) sc) = getRetTy sc
835getRetTy sc = sc
837uniqueName :: Name -> [Name] -> Name
838uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
839 | otherwise = n
841uniqueBinders :: [Name] -> TT Name -> TT Name
842uniqueBinders ns (Bind n b sc)
843 = let n' = uniqueName n ns in
844 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
845uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
846uniqueBinders ns t = t
849nextName (NS x s) = NS (nextName x) s
850nextName (MN i n) = MN (i+1) n
851nextName (UN x) = let (num', nm') = span isDigit (reverse x)
852 nm = reverse nm'
853 num = readN (reverse num') in
854 UN (nm ++ show (num+1))
855 where
856 readN "" = 0
857 readN x = read x
858nextName (SN x) = SN (nextName' x)
859 where
860 nextName' (WhereN i f x) = WhereN i f (nextName x)
861 nextName' (CaseN n) = CaseN (nextName n)
862 nextName' (MethodN n) = MethodN (nextName n)
864type Term = TT Name
865type Type = Term
867type Env = EnvTT Name
869-- an environment with de Bruijn indices 'normalised' so that they all refer to
870-- this environment
872newtype WkEnvTT n = Wk (EnvTT n)
873type WkEnv = WkEnvTT Name
875instance (Eq n, Show n) => Show (TT n) where
876 show t = showEnv [] t
878itBitsName IT8 = "Bits8"
879itBitsName IT16 = "Bits16"
880itBitsName IT32 = "Bits32"
881itBitsName IT64 = "Bits64"
883instance Show Const where
884 show (I i) = show i
885 show (BI i) = show i
886 show (Fl f) = show f
887 show (Ch c) = show c
888 show (Str s) = show s
889 show (B8 x) = show x
890 show (B16 x) = show x
891 show (B32 x) = show x
892 show (B64 x) = show x
893 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
894 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
895 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
896 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
897 show (AType ATFloat) = "Float"
898 show (AType (ATInt ITBig)) = "Integer"
899 show (AType (ATInt ITNative)) = "Int"
900 show (AType (ATInt ITChar)) = "Char"
901 show (AType (ATInt (ITFixed it))) = itBitsName it
902 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
903 show StrType = "String"
904 show PtrType = "Ptr"
905 show VoidType = "Void"
907showEnv env t = showEnv' env t False
908showEnvDbg env t = showEnv' env t True
910prettyEnv env t = prettyEnv' env t False
911 where
912 prettyEnv' env t dbg = prettySe 10 env t dbg
914 bracket outer inner p
915 | inner > outer = lparen <> p <> rparen
916 | otherwise = p
918 prettySe p env (P nt n t) debug =
919 pretty n <+>
920 if debug then
921 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
922 else
923 empty
924 prettySe p env (V i) debug
925 | i < length env =
926 if debug then
927 text . show . fst $ env!!i
928 else
929 lbrack <+> text (show i) <+> rbrack
930 | otherwise = text "unbound" <+> text (show i) <+> text "!"
931 prettySe p env (Bind n b@(Pi t) sc) debug
932 | noOccurrence n sc && not debug =
933 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
934 prettySe p env (Bind n b sc) debug =
935 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
936 prettySe p env (App f a) debug =
937 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
938 prettySe p env (Proj x i) debug =
939 prettySe 1 env x debug <+> text ("!" ++ show i)
940 prettySe p env (Constant c) debug = pretty c
941 prettySe p env Erased debug = text "[_]"
942 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
944 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
945 prettySb env n (Hole t) = prettyB env "?defer" "." n t
946 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
947 prettySb env n (PVar t) = prettyB env "pat" "." n t
948 prettySb env n (PVTy t) = prettyB env "pty" "." n t
949 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
950 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
952 prettyB env op sc n t debug =
953 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
955 prettyBv env op sc n t v debug =
956 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
957 prettySe 10 env v debug <> text sc
960showEnv' env t dbg = se 10 env t where
961 se p env (P nt n t) = show n
962 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
963 se p env (V i) | i < length env && i >= 0
964 = (show $ fst $ env!!i) ++
965 if dbg then "{" ++ show i ++ "}" else ""
966 | otherwise = "!!V " ++ show i ++ "!!"
967 se p env (Bind n b@(Pi t) sc)
968 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
969 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
970 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
971 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
972 se p env (Constant c) = show c
973 se p env Erased = "[__]"
974 se p env Impossible = "[impossible]"
975 se p env (TType i) = "Type " ++ show i
977 sb env n (Lam t) = showb env "\\ " " => " n t
978 sb env n (Hole t) = showb env "? " ". " n t
979 sb env n (GHole i t) = showb env "?defer " ". " n t
980 sb env n (Pi t) = showb env "(" ") -> " n t
981 sb env n (PVar t) = showb env "pat " ". " n t
982 sb env n (PVTy t) = showb env "pty " ". " n t
983 sb env n (Let t v) = showbv env "let " " in " n t v
984 sb env n (Guess t v) = showbv env "?? " " in " n t v
986 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
987 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
988 se 10 env v ++ sc
990 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
991 | otherwise = str
993-- | Check whether a term has any holes in it - impure if so
994pureTerm :: TT Name -> Bool
995pureTerm (App f a) = pureTerm f && pureTerm a
996pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
997 pureBinder (Hole _) = False
998 pureBinder (Guess _ _) = False
999 pureBinder (Let t v) = pureTerm t && pureTerm v
1000 pureBinder t = pureTerm (binderTy t)
1002 notClassName (MN _ "class") = False
1003 notClassName _ = True
1005pureTerm _ = True
1007-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1008weakenTm :: Int -> TT n -> TT n
1009weakenTm i t = wk i 0 t
1010 where wk i min (V x) | x >= min = V (i + x)
1011 wk i m (App f a) = App (wk i m f) (wk i m a)
1012 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1013 wk i m t = t
1014 wkb i m t = fmap (wk i m) t
1016-- | Weaken an environment so that all the de Bruijn indices are correct according
1017-- to the latest bound variable
1019weakenEnv :: EnvTT n -> EnvTT n
1020weakenEnv env = wk (length env - 1) env
1021 where wk i [] = []
1022 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1023 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1024 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1025 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1027weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1028weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1030orderPats :: Term -> Term
1031orderPats tm = op [] tm
1032 where
1033 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1034 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1035 op ps sc = bindAll (sortP ps) sc
1037 sortP ps = pick [] (reverse ps)
1039 namesIn (P _ n _) = [n]
1040 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
1041 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
1042 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
1043 nb t = namesIn (binderTy t)
1044 namesIn (App f a) = nub (namesIn f ++ namesIn a)
1045 namesIn _ = []
1047 pick acc [] = reverse acc
1048 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1050 insert n t [] = [(n, t)]
1051 insert n t ((n',t') : ps)
1052 | n `elem` (namesIn (binderTy t') ++
1053 concatMap namesIn (map (binderTy . snd) ps))
1054 = (n', t') : insert n t ps
1055 | otherwise = (n,t):(n',t'):ps