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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
68!-}
70instance Sized FC where
71 size (FC f l c) = 1 + length f
73instance Show FC where
74 show (FC f l c) = f ++ ":" ++ show l ++ ":" ++ show c
76data Err = Msg String
77 | InternalMsg String
78 | CantUnify Bool Term Term Err [(Name, Type)] Int
79 -- Int is 'score' - how much we did unify
80 -- Bool indicates recoverability, True indicates more info may make
81 -- unification succeed
82 | InfiniteUnify Name Term [(Name, Type)]
83 | CantConvert Term Term [(Name, Type)]
84 | UnifyScope Name Name Term [(Name, Type)]
85 | CantInferType String
86 | NonFunctionType Term Term
87 | CantIntroduce Term
88 | NoSuchVariable Name
89 | NoTypeDecl Name
90 | NotInjective Term Term Term
91 | CantResolve Term
92 | CantResolveAlts [String]
93 | IncompleteTerm Term
94 | UniverseError
95 | ProgramLineComment
96 | Inaccessible Name
97 | NonCollapsiblePostulate Name
98 | AlreadyDefined Name
99 | ProofSearchFail Err
100 | NoRewriting Term
101 | At FC Err
102 | Elaborating String Name Err
103 | ProviderError String
104 | LoadingFailed String Err
105 deriving Eq
107instance Sized Err where
108 size (Msg msg) = length msg
109 size (InternalMsg msg) = length msg
110 size (CantUnify _ left right err _ score) = size left + size right + size err
111 size (InfiniteUnify _ right _) = size right
112 size (CantConvert left right _) = size left + size right
113 size (UnifyScope _ _ right _) = size right
114 size (NoSuchVariable name) = size name
115 size (NoTypeDecl name) = size name
116 size (NotInjective l c r) = size l + size c + size r
117 size (CantResolve trm) = size trm
118 size (NoRewriting trm) = size trm
119 size (CantResolveAlts _) = 1
120 size (IncompleteTerm trm) = size trm
121 size UniverseError = 1
122 size ProgramLineComment = 1
123 size (At fc err) = size fc + size err
124 size (Elaborating _ n err) = size err
125 size (ProviderError msg) = length msg
126 size (LoadingFailed fn e) = 1 + length fn + size e
127 size _ = 1
129score :: Err -> Int
130score (CantUnify _ _ _ m _ s) = s + score m
131score (CantResolve _) = 20
132score (NoSuchVariable _) = 1000
133score (ProofSearchFail _) = 10000
134score (InternalMsg _) = -1
135score _ = 0
137instance Show Err where
138 show (Msg s) = s
139 show (InternalMsg s) = "Internal error: " ++ show s
140 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
141 ++ show e ++ " in " ++ show sc ++ " " ++ show i
142 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
143 show (ProviderError msg) = "Type provider error: " ++ msg
144 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: " ++ show e
145 show _ = "Error"
147instance Pretty Err where
148 pretty (Msg m) = text m
149 pretty (CantUnify _ l r e _ i) =
150 if size l + size r > breakingSize then
151 text "Cannot unify" <+> colon $$
152 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
153 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
154 else
155 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
156 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
157 pretty (ProviderError msg) = text msg
158 pretty err@(LoadingFailed _ _) = text (show err)
159 pretty _ = text "Error"
161instance Error Err where
162 strMsg = Msg
164data TC a = OK a
165 | Error Err
166 deriving (Eq, Functor)
168instance Pretty a => Pretty (TC a) where
169 pretty (OK ok) = pretty ok
170 pretty (Error err) =
171 if size err > breakingSize then
172 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
173 else
174 text "Error" <+> colon <+> pretty err
176instance Show a => Show (TC a) where
177 show (OK x) = show x
178 show (Error str) = "Error: " ++ show str
180-- at some point, this instance should also carry type checking options
181-- (e.g. Type:Type)
183instance Monad TC where
184 return = OK
185 x >>= k = case x of
186 OK v -> k v
187 Error e -> Error e
188 fail e = Error (InternalMsg e)
190tfail :: Err -> TC a
191tfail e = Error e
193trun :: FC -> TC a -> TC a
194trun fc (OK a) = OK a
195trun fc (Error e) = Error (At fc e)
197instance MonadPlus TC where
198 mzero = fail "Unknown error"
199 (OK x) `mplus` _ = OK x
200 _ `mplus` (OK y) = OK y
201 err `mplus` _ = err
203discard :: Monad m => m a -> m ()
204discard f = f >> return ()
206showSep :: String -> [String] -> String
207showSep sep [] = ""
208showSep sep [x] = x
209showSep sep (x:xs) = x ++ sep ++ showSep sep xs
211pmap f (x, y) = (f x, f y)
213traceWhen True msg a = trace msg a
214traceWhen False _ a = a
216-- RAW TERMS ----------------------------------------------------------------
218-- | Names are hierarchies of strings, describing scope (so no danger of
219-- duplicate names, but need to be careful on lookup).
220data Name = UN String -- ^ User-provided name
221 | NS Name [String] -- ^ Root, namespaces
222 | MN Int String -- ^ Machine chosen names
223 | NErased -- ^ Name of somethng which is never used in scope
224 | SN SpecialName -- ^ Decorated function names
225 deriving (Eq, Ord)
226{-!
227deriving instance Binary Name
228!-}
230data SpecialName = WhereN Int Name Name
231 | InstanceN Name [String]
232 | ParentN Name String
233 | MethodN Name
234 | CaseN Name
235 deriving (Eq, Ord)
236{-!
237deriving instance Binary SpecialName
238!-}
240instance Sized Name where
241 size (UN n) = 1
242 size (NS n els) = 1 + length els
243 size (MN i n) = 1
244 size _ = 1
246instance Pretty Name where
247 pretty (UN n) = text n
248 pretty (NS n s) = pretty n
249 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
250 pretty (SN s) = text (show s)
252instance Show Name where
253 show (UN n) = n
254 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
255 show (MN _ "underscore") = "_"
256 show (MN i s) = "{" ++ s ++ show i ++ "}"
257 show (SN s) = show s
258 show NErased = "_"
260instance Show SpecialName where
261 show (WhereN i p c) = show p ++ ", " ++ show c
262 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
263 show (MethodN m) = "method " ++ show m
264 show (ParentN p c) = show p ++ "#" ++ c
265 show (CaseN n) = "case block in " ++ show n
267-- Show a name in a way decorated for code generation, not human reading
268showCG :: Name -> String
269showCG (UN n) = n
270showCG (NS n s) = showSep "." (reverse s) ++ "." ++ show n
271showCG (MN _ "underscore") = "_"
272showCG (MN i s) = "{" ++ s ++ show i ++ "}"
273showCG (SN s) = showCG' s
274 where showCG' (WhereN i p c) = show p ++ ":" ++ show c ++ ":" ++ show i
275 showCG' (InstanceN cl inst) = '@':show cl ++ '$':showSep ":" inst
276 showCG' (MethodN m) = '!':show m
277 showCG' (ParentN p c) = show p ++ "#" ++ show c
278 showCG' (CaseN c) = show c ++ "_case"
279showCG NErased = "_"
282-- |Contexts allow us to map names to things. A root name maps to a collection
283-- of things in different namespaces with that name.
284type Ctxt a = Map.Map Name (Map.Map Name a)
285emptyContext = Map.empty
287tcname (UN ('@':_)) = True
288tcname (NS n _) = tcname n
289tcname (SN (InstanceN _ _)) = True
290tcname (SN (MethodN _)) = True
291tcname (SN (ParentN _ _)) = True
292tcname _ = False
294implicitable (NS n _) = implicitable n
295implicitable (UN (x:xs)) = isLower x
296implicitable _ = False
298nsroot (NS n _) = n
299nsroot n = n
301addDef :: Name -> a -> Ctxt a -> Ctxt a
302addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
303 Nothing -> Map.insert (nsroot n)
304 (Map.insert n v Map.empty) ctxt
305 Just xs -> Map.insert (nsroot n)
306 (Map.insert n v xs) ctxt
308{-| Look up a name in the context, given an optional namespace.
309 The name (n) may itself have a (partial) namespace given.
311 Rules for resolution:
313 - if an explicit namespace is given, return the names which match it. If none
314 match, return all names.
316 - if the name has has explicit namespace given, return the names which match it
317 and ignore the given namespace.
319 - otherwise, return all names.
321-}
323lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
324lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
325 Just xs -> filterNS (Map.toList xs)
326 Nothing -> []
327 where
328 filterNS [] = []
329 filterNS ((found, v) : xs)
330 | nsmatch n found = (found, v) : filterNS xs
331 | otherwise = filterNS xs
333 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
334 nsmatch (NS _ _) _ = False
335 nsmatch looking found = True
337lookupCtxt :: Name -> Ctxt a -> [a]
338lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
340lookupCtxtExact :: Name -> Ctxt a -> [a]
341lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
343updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
344updateDef n f ctxt
345 = let ds = lookupCtxtName n ctxt in
346 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
348toAlist :: Ctxt a -> [(Name, a)]
349toAlist ctxt = let allns = map snd (Map.toList ctxt) in
350 concat (map (Map.toList) allns)
352addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
353addAlist [] ctxt = ctxt
354addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
356data NativeTy = IT8 | IT16 | IT32 | IT64
357 deriving (Show, Eq, Ord, Enum)
359instance Pretty NativeTy where
360 pretty IT8 = text "Bits8"
361 pretty IT16 = text "Bits16"
362 pretty IT32 = text "Bits32"
363 pretty IT64 = text "Bits64"
365data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
366 | ITVec NativeTy Int
367 deriving (Show, Eq, Ord)
369data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
370 deriving (Show, Eq, Ord)
372instance Pretty ArithTy where
373 pretty (ATInt ITNative) = text "Int"
374 pretty (ATInt ITBig) = text "BigInt"
375 pretty (ATInt ITChar) = text "Char"
376 pretty (ATInt (ITFixed n)) = pretty n
377 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
378 pretty ATFloat = text "Float"
380nativeTyWidth :: NativeTy -> Int
381nativeTyWidth IT8 = 8
382nativeTyWidth IT16 = 16
383nativeTyWidth IT32 = 32
384nativeTyWidth IT64 = 64
386{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
387intTyWidth :: IntTy -> Int
388intTyWidth (ITFixed n) = nativeTyWidth n
389intTyWidth ITNative = 8 * sizeOf (0 :: Int)
390intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
391intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
393data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
394 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
395 | B8V (Vector Word8) | B16V (Vector Word16)
396 | B32V (Vector Word32) | B64V (Vector Word64)
397 | AType ArithTy | StrType
398 | PtrType | VoidType | Forgot
399 deriving (Eq, Ord)
400{-!
401deriving instance Binary Const
402!-}
404instance Sized Const where
405 size _ = 1
407instance Pretty Const where
408 pretty (I i) = text . show $ i
409 pretty (BI i) = text . show $ i
410 pretty (Fl f) = text . show $ f
411 pretty (Ch c) = text . show $ c
412 pretty (Str s) = text s
413 pretty (AType a) = pretty a
414 pretty StrType = text "String"
415 pretty PtrType = text "Ptr"
416 pretty VoidType = text "Void"
417 pretty Forgot = text "Forgot"
418 pretty (B8 w) = text . show $ w
419 pretty (B16 w) = text . show $ w
420 pretty (B32 w) = text . show $ w
421 pretty (B64 w) = text . show $ w
423data Raw = Var Name
424 | RBind Name (Binder Raw) Raw
425 | RApp Raw Raw
426 | RType
427 | RForce Raw
428 | RConstant Const
429 deriving (Show, Eq)
431instance Sized Raw where
432 size (Var name) = 1
433 size (RBind name bind right) = 1 + size bind + size right
434 size (RApp left right) = 1 + size left + size right
435 size RType = 1
436 size (RForce raw) = 1 + size raw
437 size (RConstant const) = size const
439instance Pretty Raw where
440 pretty = text . show
442{-!
443deriving instance Binary Raw
444!-}
446-- | All binding forms are represented in a unform fashion.
447data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
448 | Pi { binderTy :: b }
449 | Let { binderTy :: b,
450 binderVal :: b {-^ value for bound variable-}}
451 | NLet { binderTy :: b,
452 binderVal :: b }
453 | Hole { binderTy :: b}
454 | GHole { binderTy :: b}
455 | Guess { binderTy :: b,
456 binderVal :: b }
457 | PVar { binderTy :: b }
458 | PVTy { binderTy :: b }
459 deriving (Show, Eq, Ord, Functor)
460{-!
461deriving instance Binary Binder
462!-}
464instance Sized a => Sized (Binder a) where
465 size (Lam ty) = 1 + size ty
466 size (Pi ty) = 1 + size ty
467 size (Let ty val) = 1 + size ty + size val
468 size (NLet ty val) = 1 + size ty + size val
469 size (Hole ty) = 1 + size ty
470 size (GHole ty) = 1 + size ty
471 size (Guess ty val) = 1 + size ty + size val
472 size (PVar ty) = 1 + size ty
473 size (PVTy ty) = 1 + size ty
475fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
476fmapMB f (Let t v) = liftM2 Let (f t) (f v)
477fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
478fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
479fmapMB f (Lam t) = liftM Lam (f t)
480fmapMB f (Pi t) = liftM Pi (f t)
481fmapMB f (Hole t) = liftM Hole (f t)
482fmapMB f (GHole t) = liftM GHole (f t)
483fmapMB f (PVar t) = liftM PVar (f t)
484fmapMB f (PVTy t) = liftM PVTy (f t)
486raw_apply :: Raw -> [Raw] -> Raw
487raw_apply f [] = f
488raw_apply f (a : as) = raw_apply (RApp f a) as
490raw_unapply :: Raw -> (Raw, [Raw])
491raw_unapply t = ua [] t where
492 ua args (RApp f a) = ua (a:args) f
493 ua args t = (t, args)
495data RawFun = RawFun { rtype :: Raw,
496 rval :: Raw
497 }
498 deriving Show
500data RawDatatype = RDatatype Name Raw [(Name, Raw)]
501 deriving Show
503data RDef = RFunction RawFun
504 | RConst Raw
505 | RData RawDatatype
506 deriving Show
508type RProgram = [(Name, RDef)]
510-- WELL TYPED TERMS ---------------------------------------------------------
512-- | Universe expressions for universe checking
513data UExp = UVar Int -- ^ universe variable
514 | UVal Int -- ^ explicit universe level
515 deriving (Eq, Ord)
517instance Sized UExp where
518 size _ = 1
520-- We assume that universe levels have been checked, so anything external
521-- can just have the same universe variable and we won't get any new
522-- cycles.
524instance Binary UExp where
525 put x = return ()
526 get = return (UVar (-1))
528instance Show UExp where
529 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
530 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
531 show (UVal x) = show x
532-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
534-- | Universe constraints
535data UConstraint = ULT UExp UExp -- ^ Strictly less than
536 | ULE UExp UExp -- ^ Less than or equal to
537 deriving Eq
539instance Show UConstraint where
540 show (ULT x y) = show x ++ " < " ++ show y
541 show (ULE x y) = show x ++ " <= " ++ show y
543type UCs = (Int, [UConstraint])
545data NameType = Bound
546 | Ref
547 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
548 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
549 deriving (Show, Ord)
550{-!
551deriving instance Binary NameType
552!-}
554instance Sized NameType where
555 size _ = 1
557instance Pretty NameType where
558 pretty = text . show
560instance Eq NameType where
561 Bound == Bound = True
562 Ref == Ref = True
563 DCon _ a == DCon _ b = (a == b) -- ignore tag
564 TCon _ a == TCon _ b = (a == b) -- ignore tag
565 _ == _ = False
567-- | Terms in the core language
568data TT n = P NameType n (TT n) -- ^ named references
569 | V Int -- ^ a resolved de Bruijn-indexed variable
570 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
571 | App (TT n) (TT n) -- ^ function, function type, arg
572 | Constant Const -- ^ constant
573 | Proj (TT n) Int -- ^ argument projection; runtime only
574 | Erased -- ^ an erased term
575 | Impossible -- ^ special case for totality checking
576 | TType UExp -- ^ the type of types at some level
577 deriving (Ord, Functor)
578{-!
579deriving instance Binary TT
580!-}
582class TermSize a where
583 termsize :: Name -> a -> Int
585instance TermSize a => TermSize [a] where
586 termsize n [] = 0
587 termsize n (x : xs) = termsize n x + termsize n xs
589instance TermSize (TT Name) where
590 termsize n (P _ x _)
591 | x == n = 1000000 -- recursive => really big
592 | otherwise = 1
593 termsize n (V _) = 1
594 termsize n (Bind n' (Let t v) sc)
595 = let rn = if n == n' then MN 0 "noname" else n in
596 termsize rn v + termsize rn sc
597 termsize n (Bind n' b sc)
598 = let rn = if n == n' then MN 0 "noname" else n in
599 termsize rn sc
600 termsize n (App f a) = termsize n f + termsize n a
601 termsize n (Proj t i) = termsize n t
602 termsize n _ = 1
604instance Sized a => Sized (TT a) where
605 size (P name n trm) = 1 + size name + size n + size trm
606 size (V v) = 1
607 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
608 size (App l r) = 1 + size l + size r
609 size (Constant c) = size c
610 size Erased = 1
611 size (TType u) = 1 + size u
613instance Pretty a => Pretty (TT a) where
614 pretty _ = text "test"
616type EnvTT n = [(n, Binder (TT n))]
618data Datatype n = Data { d_typename :: n,
619 d_typetag :: Int,
620 d_type :: (TT n),
621 d_cons :: [(n, TT n)] }
622 deriving (Show, Functor, Eq)
624instance Eq n => Eq (TT n) where
625 (==) (P xt x _) (P yt y _) = x == y
626 (==) (V x) (V y) = x == y
627 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
628 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
629 (==) (TType _) (TType _) = True -- deal with constraints later
630 (==) (Constant x) (Constant y) = x == y
631 (==) (Proj x i) (Proj y j) = x == y && i == j
632 (==) Erased _ = True
633 (==) _ Erased = True
634 (==) _ _ = False
636-- * A few handy operations on well typed terms:
638-- | A term is injective iff it is a data constructor, type constructor,
639-- constant, the type Type, pi-binding, or an application of an injective
640-- term.
641isInjective :: TT n -> Bool
642isInjective (P (DCon _ _) _ _) = True
643isInjective (P (TCon _ _) _ _) = True
644isInjective (Constant _) = True
645isInjective (TType x) = True
646isInjective (Bind _ (Pi _) sc) = True
647isInjective (App f a) = isInjective f
648isInjective _ = False
650-- | Count the number of instances of a de Bruijn index in a term
651vinstances :: Int -> TT n -> Int
652vinstances i (V x) | i == x = 1
653vinstances i (App f a) = vinstances i f + vinstances i a
654vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
655 where instancesB (Let t v) = vinstances i v
656 instancesB _ = 0
657vinstances i t = 0
659instantiate :: TT n -> TT n -> TT n
660instantiate e = subst 0 where
661 subst i (V x) | i == x = e
662 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
663 subst i (App f a) = App (subst i f) (subst i a)
664 subst i (Proj x idx) = Proj (subst i x) idx
665 subst i t = t
667substV :: TT n -> TT n -> TT n
668substV x tm = dropV 0 (instantiate x tm) where
669 dropV i (V x) | x > i = V (x - 1)
670 | otherwise = V x
671 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
672 dropV i (App f a) = App (dropV i f) (dropV i a)
673 dropV i (Proj x idx) = Proj (dropV i x) idx
674 dropV i t = t
676explicitNames :: TT n -> TT n
677explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
678 Bind x b'
679 (explicitNames (instantiate
680 (P Bound x (binderTy b')) sc))
681explicitNames (App f a) = App (explicitNames f) (explicitNames a)
682explicitNames (Proj x idx) = Proj (explicitNames x) idx
683explicitNames t = t
685pToV :: Eq n => n -> TT n -> TT n
686pToV n = pToV' n 0
687pToV' n i (P _ x _) | n == x = V i
688pToV' n i (Bind x b sc)
689-- We can assume the inner scope has been pToVed already, so continue to
690-- resolve names from the *outer* scope which may happen to have the same id.
691 | n == x = Bind x (fmap (pToV' n i) b) sc
692 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
693pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
694pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
695pToV' n i t = t
697-- increase de Bruijn indices, as if a binder has been added
698addBinder :: TT n -> TT n
699addBinder t = ab 0 t
700 where
701 ab top (V i) | i >= top = V (i + 1)
702 | otherwise = V i
703 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
704 ab top (App f a) = App (ab top f) (ab top a)
705 ab top (Proj t idx) = Proj (ab top t) idx
706 ab top t = t
708-- | Convert several names. First in the list comes out as V 0
709pToVs :: Eq n => [n] -> TT n -> TT n
710pToVs ns tm = pToVs' ns tm 0 where
711 pToVs' [] tm i = tm
712 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
714vToP :: TT n -> TT n
715vToP = vToP' [] where
716 vToP' env (V i) = let (n, b) = (env !! i) in
717 P Bound n (binderTy b)
718 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
719 Bind n b' (vToP' ((n, b'):env) sc)
720 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
721 vToP' env t = t
723finalise :: Eq n => TT n -> TT n
724finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
725finalise (App f a) = App (finalise f) (finalise a)
726finalise t = t
728subst :: Eq n => n -> TT n -> TT n -> TT n
729subst n v tm = instantiate v (pToV n tm)
731substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
732substNames [] t = t
733substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
735substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
736substTerm old new = st where
737 st t | t == old = new
738 st (App f a) = App (st f) (st a)
739 st (Bind x b sc) = Bind x (fmap st b) (st sc)
740 st t = t
742-- Returns true if V 0 and bound name n do not occur in the term
744noOccurrence :: Eq n => n -> TT n -> Bool
745noOccurrence n t = no' 0 t
746 where
747 no' i (V x) = not (i == x)
748 no' i (P Bound x _) = not (n == x)
749 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
750 where noB' i (Let t v) = no' i t && no' i v
751 noB' i (Guess t v) = no' i t && no' i v
752 noB' i b = no' i (binderTy b)
753 no' i (App f a) = no' i f && no' i a
754 no' i (Proj x _) = no' i x
755 no' i _ = True
757-- | Returns all names used free in the term
758freeNames :: Eq n => TT n -> [n]
759freeNames (P _ n _) = [n]
760freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
761 ++ freeNames t
762freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
763freeNames (App f a) = nub $ freeNames f ++ freeNames a
764freeNames (Proj x i) = nub $ freeNames x
765freeNames _ = []
767-- | Return the arity of a (normalised) type
768arity :: TT n -> Int
769arity (Bind n (Pi t) sc) = 1 + arity sc
770arity _ = 0
772-- | Deconstruct an application; returns the function and a list of arguments
773unApply :: TT n -> (TT n, [TT n])
774unApply t = ua [] t where
775 ua args (App f a) = ua (a:args) f
776 ua args t = (t, args)
778mkApp :: TT n -> [TT n] -> TT n
779mkApp f [] = f
780mkApp f (a:as) = mkApp (App f a) as
782forget :: TT Name -> Raw
783forget tm = fe [] tm
784 where
785 fe env (P _ n _) = Var n
786 fe env (V i) = Var (env !! i)
787 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
788 (fe (n:env) sc)
789 fe env (App f a) = RApp (fe env f) (fe env a)
790 fe env (Constant c)
791 = RConstant c
792 fe env (TType i) = RType
793 fe env Erased = RConstant Forgot
795bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
796bindAll [] t =t
797bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
799bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
800bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
802getArgTys :: TT n -> [(n, TT n)]
803getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
804getArgTys _ = []
806getRetTy :: TT n -> TT n
807getRetTy (Bind n (PVar _) sc) = getRetTy sc
808getRetTy (Bind n (PVTy _) sc) = getRetTy sc
809getRetTy (Bind n (Pi _) sc) = getRetTy sc
810getRetTy sc = sc
812uniqueName :: Name -> [Name] -> Name
813uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
814 | otherwise = n
816uniqueBinders :: [Name] -> TT Name -> TT Name
817uniqueBinders ns (Bind n b sc)
818 = let n' = uniqueName n ns in
819 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
820uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
821uniqueBinders ns t = t
824nextName (NS x s) = NS (nextName x) s
825nextName (MN i n) = MN (i+1) n
826nextName (UN x) = let (num', nm') = span isDigit (reverse x)
827 nm = reverse nm'
828 num = readN (reverse num') in
829 UN (nm ++ show (num+1))
830 where
831 readN "" = 0
832 readN x = read x
833nextName (SN x) = SN (nextName' x)
834 where
835 nextName' (WhereN i f x) = WhereN i f (nextName x)
836 nextName' (CaseN n) = CaseN (nextName n)
837 nextName' (MethodN n) = MethodN (nextName n)
839type Term = TT Name
840type Type = Term
842type Env = EnvTT Name
844-- an environment with de Bruijn indices 'normalised' so that they all refer to
845-- this environment
847newtype WkEnvTT n = Wk (EnvTT n)
848type WkEnv = WkEnvTT Name
850instance (Eq n, Show n) => Show (TT n) where
851 show t = showEnv [] t
853itBitsName IT8 = "Bits8"
854itBitsName IT16 = "Bits16"
855itBitsName IT32 = "Bits32"
856itBitsName IT64 = "Bits64"
858instance Show Const where
859 show (I i) = show i
860 show (BI i) = show i
861 show (Fl f) = show f
862 show (Ch c) = show c
863 show (Str s) = show s
864 show (B8 x) = show x
865 show (B16 x) = show x
866 show (B32 x) = show x
867 show (B64 x) = show x
868 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
869 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
870 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
871 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
872 show (AType ATFloat) = "Float"
873 show (AType (ATInt ITBig)) = "Integer"
874 show (AType (ATInt ITNative)) = "Int"
875 show (AType (ATInt ITChar)) = "Char"
876 show (AType (ATInt (ITFixed it))) = itBitsName it
877 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
878 show StrType = "String"
879 show PtrType = "Ptr"
880 show VoidType = "Void"
882showEnv env t = showEnv' env t False
883showEnvDbg env t = showEnv' env t True
885prettyEnv env t = prettyEnv' env t False
886 where
887 prettyEnv' env t dbg = prettySe 10 env t dbg
889 bracket outer inner p
890 | inner > outer = lparen <> p <> rparen
891 | otherwise = p
893 prettySe p env (P nt n t) debug =
894 pretty n <+>
895 if debug then
896 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
897 else
898 empty
899 prettySe p env (V i) debug
900 | i < length env =
901 if debug then
902 text . show . fst $ env!!i
903 else
904 lbrack <+> text (show i) <+> rbrack
905 | otherwise = text "unbound" <+> text (show i) <+> text "!"
906 prettySe p env (Bind n b@(Pi t) sc) debug
907 | noOccurrence n sc && not debug =
908 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
909 prettySe p env (Bind n b sc) debug =
910 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
911 prettySe p env (App f a) debug =
912 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
913 prettySe p env (Proj x i) debug =
914 prettySe 1 env x debug <+> text ("!" ++ show i)
915 prettySe p env (Constant c) debug = pretty c
916 prettySe p env Erased debug = text "[_]"
917 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
919 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
920 prettySb env n (Hole t) = prettyB env "?defer" "." n t
921 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
922 prettySb env n (PVar t) = prettyB env "pat" "." n t
923 prettySb env n (PVTy t) = prettyB env "pty" "." n t
924 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
925 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
927 prettyB env op sc n t debug =
928 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
930 prettyBv env op sc n t v debug =
931 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
932 prettySe 10 env v debug <> text sc
935showEnv' env t dbg = se 10 env t where
936 se p env (P nt n t) = show n
937 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
938 se p env (V i) | i < length env && i >= 0
939 = (show $ fst $ env!!i) ++
940 if dbg then "{" ++ show i ++ "}" else ""
941 | otherwise = "!!V " ++ show i ++ "!!"
942 se p env (Bind n b@(Pi t) sc)
943 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
944 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
945 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
946 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
947 se p env (Constant c) = show c
948 se p env Erased = "[__]"
949 se p env Impossible = "[impossible]"
950 se p env (TType i) = "Type " ++ show i
952 sb env n (Lam t) = showb env "\\ " " => " n t
953 sb env n (Hole t) = showb env "? " ". " n t
954 sb env n (GHole t) = showb env "?defer " ". " n t
955 sb env n (Pi t) = showb env "(" ") -> " n t
956 sb env n (PVar t) = showb env "pat " ". " n t
957 sb env n (PVTy t) = showb env "pty " ". " n t
958 sb env n (Let t v) = showbv env "let " " in " n t v
959 sb env n (Guess t v) = showbv env "?? " " in " n t v
961 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
962 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
963 se 10 env v ++ sc
965 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
966 | otherwise = str
968-- | Check whether a term has any holes in it - impure if so
969pureTerm :: TT Name -> Bool
970pureTerm (App f a) = pureTerm f && pureTerm a
971pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
972 pureBinder (Hole _) = False
973 pureBinder (Guess _ _) = False
974 pureBinder (Let t v) = pureTerm t && pureTerm v
975 pureBinder t = pureTerm (binderTy t)
977 notClassName (MN _ "class") = False
978 notClassName _ = True
980pureTerm _ = True
982-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
983weakenTm :: Int -> TT n -> TT n
984weakenTm i t = wk i 0 t
985 where wk i min (V x) | x >= min = V (i + x)
986 wk i m (App f a) = App (wk i m f) (wk i m a)
987 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
988 wk i m t = t
989 wkb i m t = fmap (wk i m) t
991-- | Weaken an environment so that all the de Bruijn indices are correct according
992-- to the latest bound variable
994weakenEnv :: EnvTT n -> EnvTT n
995weakenEnv env = wk (length env - 1) env
996 where wk i [] = []
997 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
998 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
999 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1000 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1002weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1003weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1005orderPats :: Term -> Term
1006orderPats tm = op [] tm
1007 where
1008 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1009 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1010 op ps sc = bindAll (map (\ (n, t) -> (n, t)) (sortP ps)) sc
1012 sortP ps = pick [] (reverse ps)
1014 namesIn (P _ n _) = [n]
1015 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
1016 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
1017 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
1018 nb t = namesIn (binderTy t)
1019 namesIn (App f a) = nub (namesIn f ++ namesIn a)
1020 namesIn _ = []
1022 pick acc [] = reverse acc
1023 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1025 insert n t [] = [(n, t)]
1026 insert n t ((n',t') : ps)
1027 | n `elem` (namesIn (binderTy t') ++
1028 concatMap namesIn (map (binderTy . snd) ps))
1029 = (n', t') : insert n t ps
1030 | otherwise = (n,t):(n',t'):ps