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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 Debug.Trace
25import qualified Data.Map as Map
26import Data.Char
27import Data.List
28import Data.Vector.Unboxed (Vector)
29import qualified Data.Vector.Unboxed as V
30import qualified Data.Binary as B
31import Data.Binary hiding (get, put)
32import Foreign.Storable (sizeOf)
34import Util.Pretty hiding (Str)
36data Option = TTypeInTType
37 | CheckConv
38 deriving Eq
40-- | Source location. These are typically produced by the parser 'Idris.Parser.pfc'
41data FC = FC { fc_fname :: String, -- ^ Filename
42 fc_line :: Int -- ^ Line number
43 }
44 deriving Eq
45{-!
46deriving instance Binary FC
47!-}
49instance Sized FC where
50 size (FC f l) = 1 + length f
52instance Show FC where
53 show (FC f l) = f ++ ":" ++ show l
55data Err = Msg String
56 | InternalMsg String
57 | CantUnify Bool Term Term Err [(Name, Type)] Int
58 -- Int is 'score' - how much we did unify
59 -- Bool indicates recoverability, True indicates more info may make
60 -- unification succeed
61 | InfiniteUnify Name Term [(Name, Type)]
62 | CantConvert Term Term [(Name, Type)]
63 | UnifyScope Name Name Term [(Name, Type)]
64 | CantInferType String
65 | NonFunctionType Term Term
66 | CantIntroduce Term
67 | NoSuchVariable Name
68 | NoTypeDecl Name
69 | NotInjective Term Term Term
70 | CantResolve Term
71 | CantResolveAlts [String]
72 | IncompleteTerm Term
73 | UniverseError
74 | ProgramLineComment
75 | Inaccessible Name
76 | NonCollapsiblePostulate Name
77 | AlreadyDefined Name
78 | ProofSearchFail Err
79 | NoRewriting Term
80 | At FC Err
81 | Elaborating String Name Err
82 | ProviderError String
83 deriving Eq
85instance Sized Err where
86 size (Msg msg) = length msg
87 size (InternalMsg msg) = length msg
88 size (CantUnify _ left right err _ score) = size left + size right + size err
89 size (InfiniteUnify _ right _) = size right
90 size (CantConvert left right _) = size left + size right
91 size (UnifyScope _ _ right _) = size right
92 size (NoSuchVariable name) = size name
93 size (NoTypeDecl name) = size name
94 size (NotInjective l c r) = size l + size c + size r
95 size (CantResolve trm) = size trm
96 size (NoRewriting trm) = size trm
97 size (CantResolveAlts _) = 1
98 size (IncompleteTerm trm) = size trm
99 size UniverseError = 1
100 size ProgramLineComment = 1
101 size (At fc err) = size fc + size err
102 size (Elaborating _ n err) = size err
103 size (ProviderError msg) = length msg
104 size _ = 1
106score :: Err -> Int
107score (CantUnify _ _ _ m _ s) = s + score m
108score (CantResolve _) = 20
109score (NoSuchVariable _) = 1000
110score (ProofSearchFail _) = 10000
111score (InternalMsg _) = -1
112score _ = 0
114instance Show Err where
115 show (Msg s) = s
116 show (InternalMsg s) = "Internal error: " ++ show s
117 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
118 ++ show e ++ " in " ++ show sc ++ " " ++ show i
119 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
120 show (ProviderError msg) = "Type provider error: " ++ msg
121 show _ = "Error"
123instance Pretty Err where
124 pretty (Msg m) = text m
125 pretty (CantUnify _ l r e _ i) =
126 if size l + size r > breakingSize then
127 text "Cannot unify" <+> colon $$
128 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
129 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
130 else
131 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
132 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
133 pretty (ProviderError msg) = text msg
134 pretty _ = text "Error"
136data TC a = OK a
137 | Error Err
138 deriving (Eq, Functor)
140instance Pretty a => Pretty (TC a) where
141 pretty (OK ok) = pretty ok
142 pretty (Error err) =
143 if size err > breakingSize then
144 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
145 else
146 text "Error" <+> colon <+> pretty err
148instance Show a => Show (TC a) where
149 show (OK x) = show x
150 show (Error str) = "Error: " ++ show str
152-- at some point, this instance should also carry type checking options
153-- (e.g. Type:Type)
155instance Monad TC where
156 return = OK
157 x >>= k = case x of
158 OK v -> k v
159 Error e -> Error e
160 fail e = Error (InternalMsg e)
162tfail :: Err -> TC a
163tfail e = Error e
165trun :: FC -> TC a -> TC a
166trun fc (OK a) = OK a
167trun fc (Error e) = Error (At fc e)
169instance MonadPlus TC where
170 mzero = fail "Unknown error"
171 (OK x) `mplus` _ = OK x
172 _ `mplus` (OK y) = OK y
173 err `mplus` _ = err
175discard :: Monad m => m a -> m ()
176discard f = f >> return ()
178showSep :: String -> [String] -> String
179showSep sep [] = ""
180showSep sep [x] = x
181showSep sep (x:xs) = x ++ sep ++ showSep sep xs
183pmap f (x, y) = (f x, f y)
185traceWhen True msg a = trace msg a
186traceWhen False _ a = a
188-- RAW TERMS ----------------------------------------------------------------
190-- | Names are hierarchies of strings, describing scope (so no danger of
191-- duplicate names, but need to be careful on lookup).
192data Name = UN String -- ^ User-provided name
193 | NS Name [String] -- ^ Root, namespaces
194 | MN Int String -- ^ Machine chosen names
195 | NErased -- ^ Name of somethng which is never used in scope
196 | SN SpecialName -- ^ Decorated function names
197 deriving (Eq, Ord)
198{-!
199deriving instance Binary Name
200!-}
202data SpecialName = WhereN Int Name Name
203 | InstanceN Name [String]
204 | ParentN Name String
205 | MethodN Name
206 | CaseN Name
207 deriving (Eq, Ord)
208{-!
209deriving instance Binary SpecialName
210!-}
212instance Sized Name where
213 size (UN n) = 1
214 size (NS n els) = 1 + length els
215 size (MN i n) = 1
216 size _ = 1
218instance Pretty Name where
219 pretty (UN n) = text n
220 pretty (NS n s) = pretty n
221 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
222 pretty (SN s) = text (show s)
224instance Show Name where
225 show (UN n) = n
226 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
227 show (MN _ "underscore") = "_"
228 show (MN i s) = "{" ++ s ++ show i ++ "}"
229 show (SN s) = show s
230 show NErased = "_"
232instance Show SpecialName where
233 show (WhereN i p c) = show p ++ ", " ++ show c
234 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
235 show (MethodN m) = "method " ++ show m
236 show (ParentN p c) = show p ++ "#" ++ c
237 show (CaseN n) = "case block in " ++ show n
239-- Show a name in a way decorated for code generation, not human reading
240showCG :: Name -> String
241showCG (UN n) = n
242showCG (NS n s) = showSep "." (reverse s) ++ "." ++ show n
243showCG (MN _ "underscore") = "_"
244showCG (MN i s) = "{" ++ s ++ show i ++ "}"
245showCG (SN s) = showCG' s
246 where showCG' (WhereN i p c) = show p ++ ":" ++ show c ++ ":" ++ show i
247 showCG' (InstanceN cl inst) = '@':show cl ++ '$':showSep ":" inst
248 showCG' (MethodN m) = '!':show m
249 showCG' (ParentN p c) = show p ++ "#" ++ show c
250 showCG' (CaseN c) = show c ++ "_case"
251showCG NErased = "_"
254-- |Contexts allow us to map names to things. A root name maps to a collection
255-- of things in different namespaces with that name.
256type Ctxt a = Map.Map Name (Map.Map Name a)
257emptyContext = Map.empty
259tcname (UN ('@':_)) = True
260tcname (NS n _) = tcname n
261tcname (SN (InstanceN _ _)) = True
262tcname (SN (MethodN _)) = True
263tcname (SN (ParentN _ _)) = True
264tcname _ = False
266implicitable (NS n _) = implicitable n
267implicitable (UN (x:xs)) = isLower x
268implicitable _ = False
270nsroot (NS n _) = n
271nsroot n = n
273addDef :: Name -> a -> Ctxt a -> Ctxt a
274addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
275 Nothing -> Map.insert (nsroot n)
276 (Map.insert n v Map.empty) ctxt
277 Just xs -> Map.insert (nsroot n)
278 (Map.insert n v xs) ctxt
280{-| Look up a name in the context, given an optional namespace.
281 The name (n) may itself have a (partial) namespace given.
283 Rules for resolution:
285 - if an explicit namespace is given, return the names which match it. If none
286 match, return all names.
288 - if the name has has explicit namespace given, return the names which match it
289 and ignore the given namespace.
291 - otherwise, return all names.
293-}
295lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
296lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
297 Just xs -> filterNS (Map.toList xs)
298 Nothing -> []
299 where
300 filterNS [] = []
301 filterNS ((found, v) : xs)
302 | nsmatch n found = (found, v) : filterNS xs
303 | otherwise = filterNS xs
305 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
306 nsmatch (NS _ _) _ = False
307 nsmatch looking found = True
309lookupCtxt :: Name -> Ctxt a -> [a]
310lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
312updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
313updateDef n f ctxt
314 = let ds = lookupCtxtName n ctxt in
315 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
317toAlist :: Ctxt a -> [(Name, a)]
318toAlist ctxt = let allns = map snd (Map.toList ctxt) in
319 concat (map (Map.toList) allns)
321addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
322addAlist [] ctxt = ctxt
323addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
325data NativeTy = IT8 | IT16 | IT32 | IT64
326 deriving (Show, Eq, Ord, Enum)
328instance Pretty NativeTy where
329 pretty IT8 = text "Bits8"
330 pretty IT16 = text "Bits16"
331 pretty IT32 = text "Bits32"
332 pretty IT64 = text "Bits64"
334data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
335 | ITVec NativeTy Int
336 deriving (Show, Eq, Ord)
338data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
339 deriving (Show, Eq, Ord)
341instance Pretty ArithTy where
342 pretty (ATInt ITNative) = text "Int"
343 pretty (ATInt ITBig) = text "BigInt"
344 pretty (ATInt ITChar) = text "Char"
345 pretty (ATInt (ITFixed n)) = pretty n
346 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
347 pretty ATFloat = text "Float"
349nativeTyWidth :: NativeTy -> Int
350nativeTyWidth IT8 = 8
351nativeTyWidth IT16 = 16
352nativeTyWidth IT32 = 32
353nativeTyWidth IT64 = 64
355{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
356intTyWidth :: IntTy -> Int
357intTyWidth (ITFixed n) = nativeTyWidth n
358intTyWidth ITNative = 8 * sizeOf (0 :: Int)
359intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
360intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
362data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
363 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
364 | B8V (Vector Word8) | B16V (Vector Word16)
365 | B32V (Vector Word32) | B64V (Vector Word64)
366 | AType ArithTy | StrType
367 | PtrType | VoidType | Forgot
368 deriving (Eq, Ord)
369{-!
370deriving instance Binary Const
371!-}
373instance Sized Const where
374 size _ = 1
376instance Pretty Const where
377 pretty (I i) = text . show $ i
378 pretty (BI i) = text . show $ i
379 pretty (Fl f) = text . show $ f
380 pretty (Ch c) = text . show $ c
381 pretty (Str s) = text s
382 pretty (AType a) = pretty a
383 pretty StrType = text "String"
384 pretty PtrType = text "Ptr"
385 pretty VoidType = text "Void"
386 pretty Forgot = text "Forgot"
387 pretty (B8 w) = text . show $ w
388 pretty (B16 w) = text . show $ w
389 pretty (B32 w) = text . show $ w
390 pretty (B64 w) = text . show $ w
392data Raw = Var Name
393 | RBind Name (Binder Raw) Raw
394 | RApp Raw Raw
395 | RType
396 | RForce Raw
397 | RConstant Const
398 deriving (Show, Eq)
400instance Sized Raw where
401 size (Var name) = 1
402 size (RBind name bind right) = 1 + size bind + size right
403 size (RApp left right) = 1 + size left + size right
404 size RType = 1
405 size (RForce raw) = 1 + size raw
406 size (RConstant const) = size const
408instance Pretty Raw where
409 pretty = text . show
411{-!
412deriving instance Binary Raw
413!-}
415-- | All binding forms are represented in a unform fashion.
416data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
417 | Pi { binderTy :: b }
418 | Let { binderTy :: b,
419 binderVal :: b {-^ value for bound variable-}}
420 | NLet { binderTy :: b,
421 binderVal :: b }
422 | Hole { binderTy :: b}
423 | GHole { binderTy :: b}
424 | Guess { binderTy :: b,
425 binderVal :: b }
426 | PVar { binderTy :: b }
427 | PVTy { binderTy :: b }
428 deriving (Show, Eq, Ord, Functor)
429{-!
430deriving instance Binary Binder
431!-}
433instance Sized a => Sized (Binder a) where
434 size (Lam ty) = 1 + size ty
435 size (Pi ty) = 1 + size ty
436 size (Let ty val) = 1 + size ty + size val
437 size (NLet ty val) = 1 + size ty + size val
438 size (Hole ty) = 1 + size ty
439 size (GHole ty) = 1 + size ty
440 size (Guess ty val) = 1 + size ty + size val
441 size (PVar ty) = 1 + size ty
442 size (PVTy ty) = 1 + size ty
444fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
445fmapMB f (Let t v) = liftM2 Let (f t) (f v)
446fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
447fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
448fmapMB f (Lam t) = liftM Lam (f t)
449fmapMB f (Pi t) = liftM Pi (f t)
450fmapMB f (Hole t) = liftM Hole (f t)
451fmapMB f (GHole t) = liftM GHole (f t)
452fmapMB f (PVar t) = liftM PVar (f t)
453fmapMB f (PVTy t) = liftM PVTy (f t)
455raw_apply :: Raw -> [Raw] -> Raw
456raw_apply f [] = f
457raw_apply f (a : as) = raw_apply (RApp f a) as
459raw_unapply :: Raw -> (Raw, [Raw])
460raw_unapply t = ua [] t where
461 ua args (RApp f a) = ua (a:args) f
462 ua args t = (t, args)
464data RawFun = RawFun { rtype :: Raw,
465 rval :: Raw
466 }
467 deriving Show
469data RawDatatype = RDatatype Name Raw [(Name, Raw)]
470 deriving Show
472data RDef = RFunction RawFun
473 | RConst Raw
474 | RData RawDatatype
475 deriving Show
477type RProgram = [(Name, RDef)]
479-- WELL TYPED TERMS ---------------------------------------------------------
481-- | Universe expressions for universe checking
482data UExp = UVar Int -- ^ universe variable
483 | UVal Int -- ^ explicit universe level
484 deriving (Eq, Ord)
486instance Sized UExp where
487 size _ = 1
489-- We assume that universe levels have been checked, so anything external
490-- can just have the same universe variable and we won't get any new
491-- cycles.
493instance Binary UExp where
494 put x = return ()
495 get = return (UVar (-1))
497instance Show UExp where
498 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
499 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
500 show (UVal x) = show x
501-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
503-- | Universe constraints
504data UConstraint = ULT UExp UExp -- ^ Strictly less than
505 | ULE UExp UExp -- ^ Less than or equal to
506 deriving Eq
508instance Show UConstraint where
509 show (ULT x y) = show x ++ " < " ++ show y
510 show (ULE x y) = show x ++ " <= " ++ show y
512type UCs = (Int, [UConstraint])
514data NameType = Bound
515 | Ref
516 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
517 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
518 deriving (Show, Ord)
519{-!
520deriving instance Binary NameType
521!-}
523instance Sized NameType where
524 size _ = 1
526instance Pretty NameType where
527 pretty = text . show
529instance Eq NameType where
530 Bound == Bound = True
531 Ref == Ref = True
532 DCon _ a == DCon _ b = (a == b) -- ignore tag
533 TCon _ a == TCon _ b = (a == b) -- ignore tag
534 _ == _ = False
536-- | Terms in the core language
537data TT n = P NameType n (TT n) -- ^ named references
538 | V Int -- ^ a resolved de Bruijn-indexed variable
539 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
540 | App (TT n) (TT n) -- ^ function, function type, arg
541 | Constant Const -- ^ constant
542 | Proj (TT n) Int -- ^ argument projection; runtime only
543 | Erased -- ^ an erased term
544 | Impossible -- ^ special case for totality checking
545 | TType UExp -- ^ the type of types at some level
546 deriving (Ord, Functor)
547{-!
548deriving instance Binary TT
549!-}
551class TermSize a where
552 termsize :: Name -> a -> Int
554instance TermSize a => TermSize [a] where
555 termsize n [] = 0
556 termsize n (x : xs) = termsize n x + termsize n xs
558instance TermSize (TT Name) where
559 termsize n (P _ x _)
560 | x == n = 1000000 -- recursive => really big
561 | otherwise = 1
562 termsize n (V _) = 1
563 termsize n (Bind n' (Let t v) sc)
564 = let rn = if n == n' then MN 0 "noname" else n in
565 termsize rn v + termsize rn sc
566 termsize n (Bind n' b sc)
567 = let rn = if n == n' then MN 0 "noname" else n in
568 termsize rn sc
569 termsize n (App f a) = termsize n f + termsize n a
570 termsize n (Proj t i) = termsize n t
571 termsize n _ = 1
573instance Sized a => Sized (TT a) where
574 size (P name n trm) = 1 + size name + size n + size trm
575 size (V v) = 1
576 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
577 size (App l r) = 1 + size l + size r
578 size (Constant c) = size c
579 size Erased = 1
580 size (TType u) = 1 + size u
582instance Pretty a => Pretty (TT a) where
583 pretty _ = text "test"
585type EnvTT n = [(n, Binder (TT n))]
587data Datatype n = Data { d_typename :: n,
588 d_typetag :: Int,
589 d_type :: (TT n),
590 d_cons :: [(n, TT n)] }
591 deriving (Show, Functor, Eq)
593instance Eq n => Eq (TT n) where
594 (==) (P xt x _) (P yt y _) = x == y
595 (==) (V x) (V y) = x == y
596 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
597 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
598 (==) (TType _) (TType _) = True -- deal with constraints later
599 (==) (Constant x) (Constant y) = x == y
600 (==) (Proj x i) (Proj y j) = x == y && i == j
601 (==) Erased _ = True
602 (==) _ Erased = True
603 (==) _ _ = False
605-- * A few handy operations on well typed terms:
607-- | A term is injective iff it is a data constructor, type constructor,
608-- constant, the type Type, pi-binding, or an application of an injective
609-- term.
610isInjective :: TT n -> Bool
611isInjective (P (DCon _ _) _ _) = True
612isInjective (P (TCon _ _) _ _) = True
613isInjective (Constant _) = True
614isInjective (TType x) = True
615isInjective (Bind _ (Pi _) sc) = True
616isInjective (App f a) = isInjective f
617isInjective _ = False
619-- | Count the number of instances of a de Bruijn index in a term
620vinstances :: Int -> TT n -> Int
621vinstances i (V x) | i == x = 1
622vinstances i (App f a) = vinstances i f + vinstances i a
623vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
624 where instancesB (Let t v) = vinstances i v
625 instancesB _ = 0
626vinstances i t = 0
628instantiate :: TT n -> TT n -> TT n
629instantiate e = subst 0 where
630 subst i (V x) | i == x = e
631 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
632 subst i (App f a) = App (subst i f) (subst i a)
633 subst i (Proj x idx) = Proj (subst i x) idx
634 subst i t = t
636substV :: TT n -> TT n -> TT n
637substV x tm = dropV 0 (instantiate x tm) where
638 dropV i (V x) | x > i = V (x - 1)
639 | otherwise = V x
640 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
641 dropV i (App f a) = App (dropV i f) (dropV i a)
642 dropV i (Proj x idx) = Proj (dropV i x) idx
643 dropV i t = t
645explicitNames :: TT n -> TT n
646explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
647 Bind x b'
648 (explicitNames (instantiate
649 (P Bound x (binderTy b')) sc))
650explicitNames (App f a) = App (explicitNames f) (explicitNames a)
651explicitNames (Proj x idx) = Proj (explicitNames x) idx
652explicitNames t = t
654pToV :: Eq n => n -> TT n -> TT n
655pToV n = pToV' n 0
656pToV' n i (P _ x _) | n == x = V i
657pToV' n i (Bind x b sc)
658-- We can assume the inner scope has been pToVed already, so continue to
659-- resolve names from the *outer* scope which may happen to have the same id.
660 | n == x = Bind x (fmap (pToV' n i) b) sc
661 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
662pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
663pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
664pToV' n i t = t
666-- increase de Bruijn indices, as if a binder has been added
667addBinder :: TT n -> TT n
668addBinder t = ab 0 t
669 where
670 ab top (V i) | i >= top = V (i + 1)
671 | otherwise = V i
672 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
673 ab top (App f a) = App (ab top f) (ab top a)
674 ab top (Proj t idx) = Proj (ab top t) idx
675 ab top t = t
677-- | Convert several names. First in the list comes out as V 0
678pToVs :: Eq n => [n] -> TT n -> TT n
679pToVs ns tm = pToVs' ns tm 0 where
680 pToVs' [] tm i = tm
681 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
683vToP :: TT n -> TT n
684vToP = vToP' [] where
685 vToP' env (V i) = let (n, b) = (env !! i) in
686 P Bound n (binderTy b)
687 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
688 Bind n b' (vToP' ((n, b'):env) sc)
689 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
690 vToP' env t = t
692finalise :: Eq n => TT n -> TT n
693finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
694finalise (App f a) = App (finalise f) (finalise a)
695finalise t = t
697subst :: Eq n => n -> TT n -> TT n -> TT n
698subst n v tm = instantiate v (pToV n tm)
700substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
701substNames [] t = t
702substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
704substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
705substTerm old new = st where
706 st t | t == old = new
707 st (App f a) = App (st f) (st a)
708 st (Bind x b sc) = Bind x (fmap st b) (st sc)
709 st t = t
711-- Returns true if V 0 and bound name n do not occur in the term
713noOccurrence :: Eq n => n -> TT n -> Bool
714noOccurrence n t = no' 0 t
715 where
716 no' i (V x) = not (i == x)
717 no' i (P Bound x _) = not (n == x)
718 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
719 where noB' i (Let t v) = no' i t && no' i v
720 noB' i (Guess t v) = no' i t && no' i v
721 noB' i b = no' i (binderTy b)
722 no' i (App f a) = no' i f && no' i a
723 no' i (Proj x _) = no' i x
724 no' i _ = True
726-- | Returns all names used free in the term
727freeNames :: Eq n => TT n -> [n]
728freeNames (P _ n _) = [n]
729freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
730 ++ freeNames t
731freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
732freeNames (App f a) = nub $ freeNames f ++ freeNames a
733freeNames (Proj x i) = nub $ freeNames x
734freeNames _ = []
736-- | Return the arity of a (normalised) type
737arity :: TT n -> Int
738arity (Bind n (Pi t) sc) = 1 + arity sc
739arity _ = 0
741-- | Deconstruct an application; returns the function and a list of arguments
742unApply :: TT n -> (TT n, [TT n])
743unApply t = ua [] t where
744 ua args (App f a) = ua (a:args) f
745 ua args t = (t, args)
747mkApp :: TT n -> [TT n] -> TT n
748mkApp f [] = f
749mkApp f (a:as) = mkApp (App f a) as
751forget :: TT Name -> Raw
752forget tm = fe [] tm
753 where
754 fe env (P _ n _) = Var n
755 fe env (V i) = Var (env !! i)
756 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
757 (fe (n:env) sc)
758 fe env (App f a) = RApp (fe env f) (fe env a)
759 fe env (Constant c)
760 = RConstant c
761 fe env (TType i) = RType
762 fe env Erased = RConstant Forgot
764bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
765bindAll [] t =t
766bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
768bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
769bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
771getArgTys :: TT n -> [(n, TT n)]
772getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
773getArgTys _ = []
775getRetTy :: TT n -> TT n
776getRetTy (Bind n (PVar _) sc) = getRetTy sc
777getRetTy (Bind n (PVTy _) sc) = getRetTy sc
778getRetTy (Bind n (Pi _) sc) = getRetTy sc
779getRetTy sc = sc
781uniqueName :: Name -> [Name] -> Name
782uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
783 | otherwise = n
785uniqueBinders :: [Name] -> TT Name -> TT Name
786uniqueBinders ns (Bind n b sc)
787 = let n' = uniqueName n ns in
788 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
789uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
790uniqueBinders ns t = t
793nextName (NS x s) = NS (nextName x) s
794nextName (MN i n) = MN (i+1) n
795nextName (UN x) = let (num', nm') = span isDigit (reverse x)
796 nm = reverse nm'
797 num = readN (reverse num') in
798 UN (nm ++ show (num+1))
799 where
800 readN "" = 0
801 readN x = read x
802nextName (SN x) = SN (nextName' x)
803 where
804 nextName' (WhereN i f x) = WhereN i f (nextName x)
805 nextName' (CaseN n) = CaseN (nextName n)
806 nextName' (MethodN n) = MethodN (nextName n)
808type Term = TT Name
809type Type = Term
811type Env = EnvTT Name
813-- an environment with de Bruijn indices 'normalised' so that they all refer to
814-- this environment
816newtype WkEnvTT n = Wk (EnvTT n)
817type WkEnv = WkEnvTT Name
819instance (Eq n, Show n) => Show (TT n) where
820 show t = showEnv [] t
822itBitsName IT8 = "Bits8"
823itBitsName IT16 = "Bits16"
824itBitsName IT32 = "Bits32"
825itBitsName IT64 = "Bits64"
827instance Show Const where
828 show (I i) = show i
829 show (BI i) = show i
830 show (Fl f) = show f
831 show (Ch c) = show c
832 show (Str s) = show s
833 show (B8 x) = show x
834 show (B16 x) = show x
835 show (B32 x) = show x
836 show (B64 x) = show x
837 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
838 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
839 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
840 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
841 show (AType ATFloat) = "Float"
842 show (AType (ATInt ITBig)) = "Integer"
843 show (AType (ATInt ITNative)) = "Int"
844 show (AType (ATInt ITChar)) = "Char"
845 show (AType (ATInt (ITFixed it))) = itBitsName it
846 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
847 show StrType = "String"
848 show PtrType = "Ptr"
849 show VoidType = "Void"
851showEnv env t = showEnv' env t False
852showEnvDbg env t = showEnv' env t True
854prettyEnv env t = prettyEnv' env t False
855 where
856 prettyEnv' env t dbg = prettySe 10 env t dbg
858 bracket outer inner p
859 | inner > outer = lparen <> p <> rparen
860 | otherwise = p
862 prettySe p env (P nt n t) debug =
863 pretty n <+>
864 if debug then
865 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
866 else
867 empty
868 prettySe p env (V i) debug
869 | i < length env =
870 if debug then
871 text . show . fst $ env!!i
872 else
873 lbrack <+> text (show i) <+> rbrack
874 | otherwise = text "unbound" <+> text (show i) <+> text "!"
875 prettySe p env (Bind n b@(Pi t) sc) debug
876 | noOccurrence n sc && not debug =
877 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
878 prettySe p env (Bind n b sc) debug =
879 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
880 prettySe p env (App f a) debug =
881 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
882 prettySe p env (Proj x i) debug =
883 prettySe 1 env x debug <+> text ("!" ++ show i)
884 prettySe p env (Constant c) debug = pretty c
885 prettySe p env Erased debug = text "[_]"
886 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
888 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
889 prettySb env n (Hole t) = prettyB env "?defer" "." n t
890 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
891 prettySb env n (PVar t) = prettyB env "pat" "." n t
892 prettySb env n (PVTy t) = prettyB env "pty" "." n t
893 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
894 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
896 prettyB env op sc n t debug =
897 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
899 prettyBv env op sc n t v debug =
900 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
901 prettySe 10 env v debug <> text sc
904showEnv' env t dbg = se 10 env t where
905 se p env (P nt n t) = show n
906 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
907 se p env (V i) | i < length env && i >= 0
908 = (show $ fst $ env!!i) ++
909 if dbg then "{" ++ show i ++ "}" else ""
910 | otherwise = "!!V " ++ show i ++ "!!"
911 se p env (Bind n b@(Pi t) sc)
912 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
913 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
914 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
915 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
916 se p env (Constant c) = show c
917 se p env Erased = "[__]"
918 se p env Impossible = "[impossible]"
919 se p env (TType i) = "Type " ++ show i
921 sb env n (Lam t) = showb env "\\ " " => " n t
922 sb env n (Hole t) = showb env "? " ". " n t
923 sb env n (GHole t) = showb env "?defer " ". " n t
924 sb env n (Pi t) = showb env "(" ") -> " n t
925 sb env n (PVar t) = showb env "pat " ". " n t
926 sb env n (PVTy t) = showb env "pty " ". " n t
927 sb env n (Let t v) = showbv env "let " " in " n t v
928 sb env n (Guess t v) = showbv env "?? " " in " n t v
930 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
931 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
932 se 10 env v ++ sc
934 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
935 | otherwise = str
937-- | Check whether a term has any holes in it - impure if so
938pureTerm :: TT Name -> Bool
939pureTerm (App f a) = pureTerm f && pureTerm a
940pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
941 pureBinder (Hole _) = False
942 pureBinder (Guess _ _) = False
943 pureBinder (Let t v) = pureTerm t && pureTerm v
944 pureBinder t = pureTerm (binderTy t)
946 notClassName (MN _ "class") = False
947 notClassName _ = True
949pureTerm _ = True
951-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
952weakenTm :: Int -> TT n -> TT n
953weakenTm i t = wk i 0 t
954 where wk i min (V x) | x >= min = V (i + x)
955 wk i m (App f a) = App (wk i m f) (wk i m a)
956 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
957 wk i m t = t
958 wkb i m t = fmap (wk i m) t
960-- | Weaken an environment so that all the de Bruijn indices are correct according
961-- to the latest bound variable
963weakenEnv :: EnvTT n -> EnvTT n
964weakenEnv env = wk (length env - 1) env
965 where wk i [] = []
966 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
967 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
968 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
969 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
971weakenTmEnv :: Int -> EnvTT n -> EnvTT n
972weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
974orderPats :: Term -> Term
975orderPats tm = op [] tm
976 where
977 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
978 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
979 op ps sc = bindAll (map (\ (n, t) -> (n, t)) (sortP ps)) sc
981 sortP ps = pick [] (reverse ps)
983 namesIn (P _ n _) = [n]
984 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
985 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
986 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
987 nb t = namesIn (binderTy t)
988 namesIn (App f a) = nub (namesIn f ++ namesIn a)
989 namesIn _ = []
991 pick acc [] = reverse acc
992 pick acc ((n, t) : ps) = pick (insert n t acc) ps
994 insert n t [] = [(n, t)]
995 insert n t ((n',t') : ps)
996 | n `elem` (namesIn (binderTy t') ++
997 concatMap namesIn (map (binderTy . snd) ps))
998 = (n', t') : insert n t ps
999 | otherwise = (n,t):(n',t'):ps