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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 | CantIntroduce Term
89 | NoSuchVariable Name
90 | NoTypeDecl Name
91 | NotInjective Term Term Term
92 | CantResolve Term
93 | CantResolveAlts [String]
94 | IncompleteTerm Term
95 | UniverseError
96 | ProgramLineComment
97 | Inaccessible Name
98 | NonCollapsiblePostulate Name
99 | AlreadyDefined Name
100 | ProofSearchFail Err
101 | NoRewriting Term
102 | At FC Err
103 | Elaborating String Name Err
104 | ProviderError String
105 | LoadingFailed String Err
106 deriving Eq
107{-!
108deriving instance NFData Err
109!-}
111instance Sized Err where
112 size (Msg msg) = length msg
113 size (InternalMsg msg) = length msg
114 size (CantUnify _ left right err _ score) = size left + size right + size err
115 size (InfiniteUnify _ right _) = size right
116 size (CantConvert left right _) = size left + size right
117 size (UnifyScope _ _ right _) = size right
118 size (NoSuchVariable name) = size name
119 size (NoTypeDecl name) = size name
120 size (NotInjective l c r) = size l + size c + size r
121 size (CantResolve trm) = size trm
122 size (NoRewriting trm) = size trm
123 size (CantResolveAlts _) = 1
124 size (IncompleteTerm trm) = size trm
125 size UniverseError = 1
126 size ProgramLineComment = 1
127 size (At fc err) = size fc + size err
128 size (Elaborating _ n err) = size err
129 size (ProviderError msg) = length msg
130 size (LoadingFailed fn e) = 1 + length fn + size e
131 size _ = 1
133score :: Err -> Int
134score (CantUnify _ _ _ m _ s) = s + score m
135score (CantResolve _) = 20
136score (NoSuchVariable _) = 1000
137score (ProofSearchFail _) = 10000
138score (InternalMsg _) = -1
139score _ = 0
141instance Show Err where
142 show (Msg s) = s
143 show (InternalMsg s) = "Internal error: " ++ show s
144 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
145 ++ show e ++ " in " ++ show sc ++ " " ++ show i
146 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
147 show (ProviderError msg) = "Type provider error: " ++ msg
148 show (LoadingFailed fn e) = "Loading " ++ fn ++ " failed: " ++ show e
149 show _ = "Error"
151instance Pretty Err where
152 pretty (Msg m) = text m
153 pretty (CantUnify _ l r e _ i) =
154 if size l + size r > breakingSize then
155 text "Cannot unify" <+> colon $$
156 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
157 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
158 else
159 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
160 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
161 pretty (ProviderError msg) = text msg
162 pretty err@(LoadingFailed _ _) = text (show err)
163 pretty _ = text "Error"
165instance Error Err where
166 strMsg = Msg
168data TC a = OK a
169 | Error Err
170 deriving (Eq, Functor)
172instance Pretty a => Pretty (TC a) where
173 pretty (OK ok) = pretty ok
174 pretty (Error err) =
175 if size err > breakingSize then
176 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
177 else
178 text "Error" <+> colon <+> pretty err
180instance Show a => Show (TC a) where
181 show (OK x) = show x
182 show (Error str) = "Error: " ++ show str
184-- at some point, this instance should also carry type checking options
185-- (e.g. Type:Type)
187instance Monad TC where
188 return = OK
189 x >>= k = case x of
190 OK v -> k v
191 Error e -> Error e
192 fail e = Error (InternalMsg e)
194tfail :: Err -> TC a
195tfail e = Error e
197trun :: FC -> TC a -> TC a
198trun fc (OK a) = OK a
199trun fc (Error e) = Error (At fc e)
201instance MonadPlus TC where
202 mzero = fail "Unknown error"
203 (OK x) `mplus` _ = OK x
204 _ `mplus` (OK y) = OK y
205 err `mplus` _ = err
207discard :: Monad m => m a -> m ()
208discard f = f >> return ()
210showSep :: String -> [String] -> String
211showSep sep [] = ""
212showSep sep [x] = x
213showSep sep (x:xs) = x ++ sep ++ showSep sep xs
215pmap f (x, y) = (f x, f y)
217traceWhen True msg a = trace msg a
218traceWhen False _ a = a
220-- RAW TERMS ----------------------------------------------------------------
222-- | Names are hierarchies of strings, describing scope (so no danger of
223-- duplicate names, but need to be careful on lookup).
224data Name = UN String -- ^ User-provided name
225 | NS Name [String] -- ^ Root, namespaces
226 | MN Int String -- ^ Machine chosen names
227 | NErased -- ^ Name of somethng which is never used in scope
228 | SN SpecialName -- ^ Decorated function names
229 deriving (Eq, Ord)
230{-!
231deriving instance Binary Name
232deriving instance NFData Name
233!-}
235data SpecialName = WhereN Int Name Name
236 | InstanceN Name [String]
237 | ParentN Name String
238 | MethodN Name
239 | CaseN Name
240 deriving (Eq, Ord)
241{-!
242deriving instance Binary SpecialName
243deriving instance NFData SpecialName
244!-}
246instance Sized Name where
247 size (UN n) = 1
248 size (NS n els) = 1 + length els
249 size (MN i n) = 1
250 size _ = 1
252instance Pretty Name where
253 pretty (UN n) = text n
254 pretty (NS n s) = pretty n
255 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
256 pretty (SN s) = text (show s)
258instance Show Name where
259 show (UN n) = n
260 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
261 show (MN _ "underscore") = "_"
262 show (MN i s) = "{" ++ s ++ show i ++ "}"
263 show (SN s) = show s
264 show NErased = "_"
266instance Show SpecialName where
267 show (WhereN i p c) = show p ++ ", " ++ show c
268 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
269 show (MethodN m) = "method " ++ show m
270 show (ParentN p c) = show p ++ "#" ++ c
271 show (CaseN n) = "case block in " ++ show n
273-- Show a name in a way decorated for code generation, not human reading
274showCG :: Name -> String
275showCG (UN n) = n
276showCG (NS n s) = showSep "." (reverse s) ++ "." ++ show n
277showCG (MN _ "underscore") = "_"
278showCG (MN i s) = "{" ++ s ++ show i ++ "}"
279showCG (SN s) = showCG' s
280 where showCG' (WhereN i p c) = show p ++ ":" ++ show c ++ ":" ++ show i
281 showCG' (InstanceN cl inst) = '@':show cl ++ '$':showSep ":" inst
282 showCG' (MethodN m) = '!':show m
283 showCG' (ParentN p c) = show p ++ "#" ++ show c
284 showCG' (CaseN c) = show c ++ "_case"
285showCG NErased = "_"
288-- |Contexts allow us to map names to things. A root name maps to a collection
289-- of things in different namespaces with that name.
290type Ctxt a = Map.Map Name (Map.Map Name a)
291emptyContext = Map.empty
293tcname (UN ('@':_)) = True
294tcname (NS n _) = tcname n
295tcname (SN (InstanceN _ _)) = True
296tcname (SN (MethodN _)) = True
297tcname (SN (ParentN _ _)) = True
298tcname _ = False
300implicitable (NS n _) = implicitable n
301implicitable (UN (x:xs)) = isLower x
302implicitable (MN _ _) = True
303implicitable _ = False
305nsroot (NS n _) = n
306nsroot n = n
308addDef :: Name -> a -> Ctxt a -> Ctxt a
309addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
310 Nothing -> Map.insert (nsroot n)
311 (Map.insert n v Map.empty) ctxt
312 Just xs -> Map.insert (nsroot n)
313 (Map.insert n v xs) ctxt
315{-| Look up a name in the context, given an optional namespace.
316 The name (n) may itself have a (partial) namespace given.
318 Rules for resolution:
320 - if an explicit namespace is given, return the names which match it. If none
321 match, return all names.
323 - if the name has has explicit namespace given, return the names which match it
324 and ignore the given namespace.
326 - otherwise, return all names.
328-}
330lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
331lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
332 Just xs -> filterNS (Map.toList xs)
333 Nothing -> []
334 where
335 filterNS [] = []
336 filterNS ((found, v) : xs)
337 | nsmatch n found = (found, v) : filterNS xs
338 | otherwise = filterNS xs
340 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
341 nsmatch (NS _ _) _ = False
342 nsmatch looking found = True
344lookupCtxt :: Name -> Ctxt a -> [a]
345lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
347lookupCtxtExact :: Name -> Ctxt a -> [a]
348lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
350updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
351updateDef n f ctxt
352 = let ds = lookupCtxtName n ctxt in
353 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
355toAlist :: Ctxt a -> [(Name, a)]
356toAlist ctxt = let allns = map snd (Map.toList ctxt) in
357 concat (map (Map.toList) allns)
359addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
360addAlist [] ctxt = ctxt
361addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
363data NativeTy = IT8 | IT16 | IT32 | IT64
364 deriving (Show, Eq, Ord, Enum)
366instance Pretty NativeTy where
367 pretty IT8 = text "Bits8"
368 pretty IT16 = text "Bits16"
369 pretty IT32 = text "Bits32"
370 pretty IT64 = text "Bits64"
372data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
373 | ITVec NativeTy Int
374 deriving (Show, Eq, Ord)
376data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
377 deriving (Show, Eq, Ord)
378{-!
379deriving instance NFData IntTy
380deriving instance NFData NativeTy
381deriving instance NFData ArithTy
382!-}
384instance Pretty ArithTy where
385 pretty (ATInt ITNative) = text "Int"
386 pretty (ATInt ITBig) = text "BigInt"
387 pretty (ATInt ITChar) = text "Char"
388 pretty (ATInt (ITFixed n)) = pretty n
389 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
390 pretty ATFloat = text "Float"
392nativeTyWidth :: NativeTy -> Int
393nativeTyWidth IT8 = 8
394nativeTyWidth IT16 = 16
395nativeTyWidth IT32 = 32
396nativeTyWidth IT64 = 64
398{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
399intTyWidth :: IntTy -> Int
400intTyWidth (ITFixed n) = nativeTyWidth n
401intTyWidth ITNative = 8 * sizeOf (0 :: Int)
402intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
403intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
405data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
406 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
407 | B8V (Vector Word8) | B16V (Vector Word16)
408 | B32V (Vector Word32) | B64V (Vector Word64)
409 | AType ArithTy | StrType
410 | PtrType | VoidType | Forgot
411 deriving (Eq, Ord)
412{-!
413deriving instance Binary Const
414deriving instance NFData Const
415!-}
417instance Sized Const where
418 size _ = 1
420instance Pretty Const where
421 pretty (I i) = text . show $ i
422 pretty (BI i) = text . show $ i
423 pretty (Fl f) = text . show $ f
424 pretty (Ch c) = text . show $ c
425 pretty (Str s) = text s
426 pretty (AType a) = pretty a
427 pretty StrType = text "String"
428 pretty PtrType = text "Ptr"
429 pretty VoidType = text "Void"
430 pretty Forgot = text "Forgot"
431 pretty (B8 w) = text . show $ w
432 pretty (B16 w) = text . show $ w
433 pretty (B32 w) = text . show $ w
434 pretty (B64 w) = text . show $ w
436data Raw = Var Name
437 | RBind Name (Binder Raw) Raw
438 | RApp Raw Raw
439 | RType
440 | RForce Raw
441 | RConstant Const
442 deriving (Show, Eq)
444instance Sized Raw where
445 size (Var name) = 1
446 size (RBind name bind right) = 1 + size bind + size right
447 size (RApp left right) = 1 + size left + size right
448 size RType = 1
449 size (RForce raw) = 1 + size raw
450 size (RConstant const) = size const
452instance Pretty Raw where
453 pretty = text . show
455{-!
456deriving instance Binary Raw
457deriving instance NFData Raw
458!-}
460-- | All binding forms are represented in a unform fashion.
461data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
462 | Pi { binderTy :: b }
463 | Let { binderTy :: b,
464 binderVal :: b {-^ value for bound variable-}}
465 | NLet { binderTy :: b,
466 binderVal :: b }
467 | Hole { binderTy :: b}
468 | GHole { envlen :: Int,
469 binderTy :: b}
470 | Guess { binderTy :: b,
471 binderVal :: b }
472 | PVar { binderTy :: b }
473 | PVTy { binderTy :: b }
474 deriving (Show, Eq, Ord, Functor)
475{-!
476deriving instance Binary Binder
477deriving instance NFData Binder
478!-}
480instance Sized a => Sized (Binder a) where
481 size (Lam ty) = 1 + size ty
482 size (Pi ty) = 1 + size ty
483 size (Let ty val) = 1 + size ty + size val
484 size (NLet ty val) = 1 + size ty + size val
485 size (Hole ty) = 1 + size ty
486 size (GHole _ ty) = 1 + size ty
487 size (Guess ty val) = 1 + size ty + size val
488 size (PVar ty) = 1 + size ty
489 size (PVTy ty) = 1 + size ty
491fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
492fmapMB f (Let t v) = liftM2 Let (f t) (f v)
493fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
494fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
495fmapMB f (Lam t) = liftM Lam (f t)
496fmapMB f (Pi t) = liftM Pi (f t)
497fmapMB f (Hole t) = liftM Hole (f t)
498fmapMB f (GHole i t) = liftM (GHole i) (f t)
499fmapMB f (PVar t) = liftM PVar (f t)
500fmapMB f (PVTy t) = liftM PVTy (f t)
502raw_apply :: Raw -> [Raw] -> Raw
503raw_apply f [] = f
504raw_apply f (a : as) = raw_apply (RApp f a) as
506raw_unapply :: Raw -> (Raw, [Raw])
507raw_unapply t = ua [] t where
508 ua args (RApp f a) = ua (a:args) f
509 ua args t = (t, args)
511data RawFun = RawFun { rtype :: Raw,
512 rval :: Raw
513 }
514 deriving Show
516data RawDatatype = RDatatype Name Raw [(Name, Raw)]
517 deriving Show
519data RDef = RFunction RawFun
520 | RConst Raw
521 | RData RawDatatype
522 deriving Show
524type RProgram = [(Name, RDef)]
526-- WELL TYPED TERMS ---------------------------------------------------------
528-- | Universe expressions for universe checking
529data UExp = UVar Int -- ^ universe variable
530 | UVal Int -- ^ explicit universe level
531 deriving (Eq, Ord)
532{-!
533deriving instance NFData UExp
534!-}
536instance Sized UExp where
537 size _ = 1
539-- We assume that universe levels have been checked, so anything external
540-- can just have the same universe variable and we won't get any new
541-- cycles.
543instance Binary UExp where
544 put x = return ()
545 get = return (UVar (-1))
547instance Show UExp where
548 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
549 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
550 show (UVal x) = show x
551-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
553-- | Universe constraints
554data UConstraint = ULT UExp UExp -- ^ Strictly less than
555 | ULE UExp UExp -- ^ Less than or equal to
556 deriving Eq
558instance Show UConstraint where
559 show (ULT x y) = show x ++ " < " ++ show y
560 show (ULE x y) = show x ++ " <= " ++ show y
562type UCs = (Int, [UConstraint])
564data NameType = Bound
565 | Ref
566 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
567 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
568 deriving (Show, Ord)
569{-!
570deriving instance Binary NameType
571deriving instance NFData NameType
572!-}
574instance Sized NameType where
575 size _ = 1
577instance Pretty NameType where
578 pretty = text . show
580instance Eq NameType where
581 Bound == Bound = True
582 Ref == Ref = True
583 DCon _ a == DCon _ b = (a == b) -- ignore tag
584 TCon _ a == TCon _ b = (a == b) -- ignore tag
585 _ == _ = False
587-- | Terms in the core language
588data TT n = P NameType n (TT n) -- ^ named references
589 | V Int -- ^ a resolved de Bruijn-indexed variable
590 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
591 | App (TT n) (TT n) -- ^ function, function type, arg
592 | Constant Const -- ^ constant
593 | Proj (TT n) Int -- ^ argument projection; runtime only
594 -- (-1) is a special case for 'subtract one from BI'
595 | Erased -- ^ an erased term
596 | Impossible -- ^ special case for totality checking
597 | TType UExp -- ^ the type of types at some level
598 deriving (Ord, Functor)
599{-!
600deriving instance Binary TT
601deriving instance NFData TT
602!-}
604class TermSize a where
605 termsize :: Name -> a -> Int
607instance TermSize a => TermSize [a] where
608 termsize n [] = 0
609 termsize n (x : xs) = termsize n x + termsize n xs
611instance TermSize (TT Name) where
612 termsize n (P _ x _)
613 | x == n = 1000000 -- recursive => really big
614 | otherwise = 1
615 termsize n (V _) = 1
616 termsize n (Bind n' (Let t v) sc)
617 = let rn = if n == n' then MN 0 "noname" else n in
618 termsize rn v + termsize rn sc
619 termsize n (Bind n' b sc)
620 = let rn = if n == n' then MN 0 "noname" else n in
621 termsize rn sc
622 termsize n (App f a) = termsize n f + termsize n a
623 termsize n (Proj t i) = termsize n t
624 termsize n _ = 1
626instance Sized a => Sized (TT a) where
627 size (P name n trm) = 1 + size name + size n + size trm
628 size (V v) = 1
629 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
630 size (App l r) = 1 + size l + size r
631 size (Constant c) = size c
632 size Erased = 1
633 size (TType u) = 1 + size u
635instance Pretty a => Pretty (TT a) where
636 pretty _ = text "test"
638type EnvTT n = [(n, Binder (TT n))]
640data Datatype n = Data { d_typename :: n,
641 d_typetag :: Int,
642 d_type :: (TT n),
643 d_cons :: [(n, TT n)] }
644 deriving (Show, Functor, Eq)
646instance Eq n => Eq (TT n) where
647 (==) (P xt x _) (P yt y _) = x == y
648 (==) (V x) (V y) = x == y
649 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
650 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
651 (==) (TType _) (TType _) = True -- deal with constraints later
652 (==) (Constant x) (Constant y) = x == y
653 (==) (Proj x i) (Proj y j) = x == y && i == j
654 (==) Erased _ = True
655 (==) _ Erased = True
656 (==) _ _ = False
658-- * A few handy operations on well typed terms:
660-- | A term is injective iff it is a data constructor, type constructor,
661-- constant, the type Type, pi-binding, or an application of an injective
662-- term.
663isInjective :: TT n -> Bool
664isInjective (P (DCon _ _) _ _) = True
665isInjective (P (TCon _ _) _ _) = True
666isInjective (Constant _) = True
667isInjective (TType x) = True
668isInjective (Bind _ (Pi _) sc) = True
669isInjective (App f a) = isInjective f
670isInjective _ = False
672-- | Count the number of instances of a de Bruijn index in a term
673vinstances :: Int -> TT n -> Int
674vinstances i (V x) | i == x = 1
675vinstances i (App f a) = vinstances i f + vinstances i a
676vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
677 where instancesB (Let t v) = vinstances i v
678 instancesB _ = 0
679vinstances i t = 0
681instantiate :: TT n -> TT n -> TT n
682instantiate e = subst 0 where
683 subst i (V x) | i == x = e
684 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
685 subst i (App f a) = App (subst i f) (subst i a)
686 subst i (Proj x idx) = Proj (subst i x) idx
687 subst i t = t
689substV :: TT n -> TT n -> TT n
690substV x tm = dropV 0 (instantiate x tm) where
691 dropV i (V x) | x > i = V (x - 1)
692 | otherwise = V x
693 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
694 dropV i (App f a) = App (dropV i f) (dropV i a)
695 dropV i (Proj x idx) = Proj (dropV i x) idx
696 dropV i t = t
698explicitNames :: TT n -> TT n
699explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
700 Bind x b'
701 (explicitNames (instantiate
702 (P Bound x (binderTy b')) sc))
703explicitNames (App f a) = App (explicitNames f) (explicitNames a)
704explicitNames (Proj x idx) = Proj (explicitNames x) idx
705explicitNames t = t
707pToV :: Eq n => n -> TT n -> TT n
708pToV n = pToV' n 0
709pToV' n i (P _ x _) | n == x = V i
710pToV' n i (Bind x b sc)
711-- We can assume the inner scope has been pToVed already, so continue to
712-- resolve names from the *outer* scope which may happen to have the same id.
713 | n == x = Bind x (fmap (pToV' n i) b) sc
714 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
715pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
716pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
717pToV' n i t = t
719-- increase de Bruijn indices, as if a binder has been added
720addBinder :: TT n -> TT n
721addBinder t = ab 0 t
722 where
723 ab top (V i) | i >= top = V (i + 1)
724 | otherwise = V i
725 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
726 ab top (App f a) = App (ab top f) (ab top a)
727 ab top (Proj t idx) = Proj (ab top t) idx
728 ab top t = t
730-- | Convert several names. First in the list comes out as V 0
731pToVs :: Eq n => [n] -> TT n -> TT n
732pToVs ns tm = pToVs' ns tm 0 where
733 pToVs' [] tm i = tm
734 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
736vToP :: TT n -> TT n
737vToP = vToP' [] where
738 vToP' env (V i) = let (n, b) = (env !! i) in
739 P Bound n (binderTy b)
740 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
741 Bind n b' (vToP' ((n, b'):env) sc)
742 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
743 vToP' env t = t
745finalise :: Eq n => TT n -> TT n
746finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
747finalise (App f a) = App (finalise f) (finalise a)
748finalise t = t
750subst :: Eq n => n -> TT n -> TT n -> TT n
751subst n v tm = instantiate v (pToV n tm)
753substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
754substNames [] t = t
755substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
757substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
758substTerm old new = st where
759 st t | t == old = new
760 st (App f a) = App (st f) (st a)
761 st (Bind x b sc) = Bind x (fmap st b) (st sc)
762 st t = t
764-- Returns true if V 0 and bound name n do not occur in the term
766noOccurrence :: Eq n => n -> TT n -> Bool
767noOccurrence n t = no' 0 t
768 where
769 no' i (V x) = not (i == x)
770 no' i (P Bound x _) = not (n == x)
771 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
772 where noB' i (Let t v) = no' i t && no' i v
773 noB' i (Guess t v) = no' i t && no' i v
774 noB' i b = no' i (binderTy b)
775 no' i (App f a) = no' i f && no' i a
776 no' i (Proj x _) = no' i x
777 no' i _ = True
779-- | Returns all names used free in the term
780freeNames :: Eq n => TT n -> [n]
781freeNames (P _ n _) = [n]
782freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
783 ++ freeNames t
784freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
785freeNames (App f a) = nub $ freeNames f ++ freeNames a
786freeNames (Proj x i) = nub $ freeNames x
787freeNames _ = []
789-- | Return the arity of a (normalised) type
790arity :: TT n -> Int
791arity (Bind n (Pi t) sc) = 1 + arity sc
792arity _ = 0
794-- | Deconstruct an application; returns the function and a list of arguments
795unApply :: TT n -> (TT n, [TT n])
796unApply t = ua [] t where
797 ua args (App f a) = ua (a:args) f
798 ua args t = (t, args)
800mkApp :: TT n -> [TT n] -> TT n
801mkApp f [] = f
802mkApp f (a:as) = mkApp (App f a) as
804forget :: TT Name -> Raw
805forget tm = fe [] tm
806 where
807 fe env (P _ n _) = Var n
808 fe env (V i) = Var (env !! i)
809 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
810 (fe (n:env) sc)
811 fe env (App f a) = RApp (fe env f) (fe env a)
812 fe env (Constant c)
813 = RConstant c
814 fe env (TType i) = RType
815 fe env Erased = RConstant Forgot
817bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
818bindAll [] t =t
819bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
821bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
822bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
824getArgTys :: TT n -> [(n, TT n)]
825getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
826getArgTys _ = []
828getRetTy :: TT n -> TT n
829getRetTy (Bind n (PVar _) sc) = getRetTy sc
830getRetTy (Bind n (PVTy _) sc) = getRetTy sc
831getRetTy (Bind n (Pi _) sc) = getRetTy sc
832getRetTy sc = sc
834uniqueName :: Name -> [Name] -> Name
835uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
836 | otherwise = n
838uniqueBinders :: [Name] -> TT Name -> TT Name
839uniqueBinders ns (Bind n b sc)
840 = let n' = uniqueName n ns in
841 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
842uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
843uniqueBinders ns t = t
846nextName (NS x s) = NS (nextName x) s
847nextName (MN i n) = MN (i+1) n
848nextName (UN x) = let (num', nm') = span isDigit (reverse x)
849 nm = reverse nm'
850 num = readN (reverse num') in
851 UN (nm ++ show (num+1))
852 where
853 readN "" = 0
854 readN x = read x
855nextName (SN x) = SN (nextName' x)
856 where
857 nextName' (WhereN i f x) = WhereN i f (nextName x)
858 nextName' (CaseN n) = CaseN (nextName n)
859 nextName' (MethodN n) = MethodN (nextName n)
861type Term = TT Name
862type Type = Term
864type Env = EnvTT Name
866-- an environment with de Bruijn indices 'normalised' so that they all refer to
867-- this environment
869newtype WkEnvTT n = Wk (EnvTT n)
870type WkEnv = WkEnvTT Name
872instance (Eq n, Show n) => Show (TT n) where
873 show t = showEnv [] t
875itBitsName IT8 = "Bits8"
876itBitsName IT16 = "Bits16"
877itBitsName IT32 = "Bits32"
878itBitsName IT64 = "Bits64"
880instance Show Const where
881 show (I i) = show i
882 show (BI i) = show i
883 show (Fl f) = show f
884 show (Ch c) = show c
885 show (Str s) = show s
886 show (B8 x) = show x
887 show (B16 x) = show x
888 show (B32 x) = show x
889 show (B64 x) = show x
890 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
891 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
892 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
893 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
894 show (AType ATFloat) = "Float"
895 show (AType (ATInt ITBig)) = "Integer"
896 show (AType (ATInt ITNative)) = "Int"
897 show (AType (ATInt ITChar)) = "Char"
898 show (AType (ATInt (ITFixed it))) = itBitsName it
899 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
900 show StrType = "String"
901 show PtrType = "Ptr"
902 show VoidType = "Void"
904showEnv env t = showEnv' env t False
905showEnvDbg env t = showEnv' env t True
907prettyEnv env t = prettyEnv' env t False
908 where
909 prettyEnv' env t dbg = prettySe 10 env t dbg
911 bracket outer inner p
912 | inner > outer = lparen <> p <> rparen
913 | otherwise = p
915 prettySe p env (P nt n t) debug =
916 pretty n <+>
917 if debug then
918 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
919 else
920 empty
921 prettySe p env (V i) debug
922 | i < length env =
923 if debug then
924 text . show . fst $ env!!i
925 else
926 lbrack <+> text (show i) <+> rbrack
927 | otherwise = text "unbound" <+> text (show i) <+> text "!"
928 prettySe p env (Bind n b@(Pi t) sc) debug
929 | noOccurrence n sc && not debug =
930 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
931 prettySe p env (Bind n b sc) debug =
932 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
933 prettySe p env (App f a) debug =
934 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
935 prettySe p env (Proj x i) debug =
936 prettySe 1 env x debug <+> text ("!" ++ show i)
937 prettySe p env (Constant c) debug = pretty c
938 prettySe p env Erased debug = text "[_]"
939 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
941 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
942 prettySb env n (Hole t) = prettyB env "?defer" "." n t
943 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
944 prettySb env n (PVar t) = prettyB env "pat" "." n t
945 prettySb env n (PVTy t) = prettyB env "pty" "." n t
946 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
947 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
949 prettyB env op sc n t debug =
950 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
952 prettyBv env op sc n t v debug =
953 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
954 prettySe 10 env v debug <> text sc
957showEnv' env t dbg = se 10 env t where
958 se p env (P nt n t) = show n
959 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
960 se p env (V i) | i < length env && i >= 0
961 = (show $ fst $ env!!i) ++
962 if dbg then "{" ++ show i ++ "}" else ""
963 | otherwise = "!!V " ++ show i ++ "!!"
964 se p env (Bind n b@(Pi t) sc)
965 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
966 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
967 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
968 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
969 se p env (Constant c) = show c
970 se p env Erased = "[__]"
971 se p env Impossible = "[impossible]"
972 se p env (TType i) = "Type " ++ show i
974 sb env n (Lam t) = showb env "\\ " " => " n t
975 sb env n (Hole t) = showb env "? " ". " n t
976 sb env n (GHole i t) = showb env "?defer " ". " n t
977 sb env n (Pi t) = showb env "(" ") -> " n t
978 sb env n (PVar t) = showb env "pat " ". " n t
979 sb env n (PVTy t) = showb env "pty " ". " n t
980 sb env n (Let t v) = showbv env "let " " in " n t v
981 sb env n (Guess t v) = showbv env "?? " " in " n t v
983 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
984 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
985 se 10 env v ++ sc
987 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
988 | otherwise = str
990-- | Check whether a term has any holes in it - impure if so
991pureTerm :: TT Name -> Bool
992pureTerm (App f a) = pureTerm f && pureTerm a
993pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
994 pureBinder (Hole _) = False
995 pureBinder (Guess _ _) = False
996 pureBinder (Let t v) = pureTerm t && pureTerm v
997 pureBinder t = pureTerm (binderTy t)
999 notClassName (MN _ "class") = False
1000 notClassName _ = True
1002pureTerm _ = True
1004-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
1005weakenTm :: Int -> TT n -> TT n
1006weakenTm i t = wk i 0 t
1007 where wk i min (V x) | x >= min = V (i + x)
1008 wk i m (App f a) = App (wk i m f) (wk i m a)
1009 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
1010 wk i m t = t
1011 wkb i m t = fmap (wk i m) t
1013-- | Weaken an environment so that all the de Bruijn indices are correct according
1014-- to the latest bound variable
1016weakenEnv :: EnvTT n -> EnvTT n
1017weakenEnv env = wk (length env - 1) env
1018 where wk i [] = []
1019 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
1020 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
1021 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
1022 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
1024weakenTmEnv :: Int -> EnvTT n -> EnvTT n
1025weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
1027orderPats :: Term -> Term
1028orderPats tm = op [] tm
1029 where
1030 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
1031 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
1032 op ps sc = bindAll (sortP ps) sc
1034 sortP ps = pick [] (reverse ps)
1036 namesIn (P _ n _) = [n]
1037 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
1038 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
1039 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
1040 nb t = namesIn (binderTy t)
1041 namesIn (App f a) = nub (namesIn f ++ namesIn a)
1042 namesIn _ = []
1044 pick acc [] = reverse acc
1045 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1047 insert n t [] = [(n, t)]
1048 insert n t ((n',t') : ps)
1049 | n `elem` (namesIn (binderTy t') ++
1050 concatMap namesIn (map (binderTy . snd) ps))
1051 = (n', t') : insert n t ps
1052 | otherwise = (n,t):(n',t'):ps