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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.pfc'
42data FC = FC { fc_fname :: String, -- ^ Filename
43 fc_line :: Int -- ^ Line number
44 }
45 deriving Eq
46{-!
47deriving instance Binary FC
48!-}
50instance Sized FC where
51 size (FC f l) = 1 + length f
53instance Show FC where
54 show (FC f l) = f ++ ":" ++ show l
56data Err = Msg String
57 | InternalMsg String
58 | CantUnify Bool Term Term Err [(Name, Type)] Int
59 -- Int is 'score' - how much we did unify
60 -- Bool indicates recoverability, True indicates more info may make
61 -- unification succeed
62 | InfiniteUnify Name Term [(Name, Type)]
63 | CantConvert Term Term [(Name, Type)]
64 | UnifyScope Name Name Term [(Name, Type)]
65 | CantInferType String
66 | NonFunctionType Term Term
67 | CantIntroduce Term
68 | NoSuchVariable Name
69 | NoTypeDecl Name
70 | NotInjective Term Term Term
71 | CantResolve Term
72 | CantResolveAlts [String]
73 | IncompleteTerm Term
74 | UniverseError
75 | ProgramLineComment
76 | Inaccessible Name
77 | NonCollapsiblePostulate Name
78 | AlreadyDefined Name
79 | ProofSearchFail Err
80 | NoRewriting Term
81 | At FC Err
82 | Elaborating String Name Err
83 | ProviderError String
84 deriving Eq
86instance Sized Err where
87 size (Msg msg) = length msg
88 size (InternalMsg msg) = length msg
89 size (CantUnify _ left right err _ score) = size left + size right + size err
90 size (InfiniteUnify _ right _) = size right
91 size (CantConvert left right _) = size left + size right
92 size (UnifyScope _ _ right _) = size right
93 size (NoSuchVariable name) = size name
94 size (NoTypeDecl name) = size name
95 size (NotInjective l c r) = size l + size c + size r
96 size (CantResolve trm) = size trm
97 size (NoRewriting trm) = size trm
98 size (CantResolveAlts _) = 1
99 size (IncompleteTerm trm) = size trm
100 size UniverseError = 1
101 size ProgramLineComment = 1
102 size (At fc err) = size fc + size err
103 size (Elaborating _ n err) = size err
104 size (ProviderError msg) = length msg
105 size _ = 1
107score :: Err -> Int
108score (CantUnify _ _ _ m _ s) = s + score m
109score (CantResolve _) = 20
110score (NoSuchVariable _) = 1000
111score (ProofSearchFail _) = 10000
112score (InternalMsg _) = -1
113score _ = 0
115instance Show Err where
116 show (Msg s) = s
117 show (InternalMsg s) = "Internal error: " ++ show s
118 show (CantUnify _ l r e sc i) = "CantUnify " ++ show l ++ " " ++ show r ++ " "
119 ++ show e ++ " in " ++ show sc ++ " " ++ show i
120 show (Inaccessible n) = show n ++ " is not an accessible pattern variable"
121 show (ProviderError msg) = "Type provider error: " ++ msg
122 show _ = "Error"
124instance Pretty Err where
125 pretty (Msg m) = text m
126 pretty (CantUnify _ l r e _ i) =
127 if size l + size r > breakingSize then
128 text "Cannot unify" <+> colon $$
129 nest nestingSize (pretty l <+> text "and" <+> pretty r) $$
130 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
131 else
132 text "Cannot unify" <+> colon <+> pretty l <+> text "and" <+> pretty r $$
133 nest nestingSize (text "where" <+> pretty e <+> text "with" <+> (text . show $ i))
134 pretty (ProviderError msg) = text msg
135 pretty _ = text "Error"
137instance Error Err where
138 strMsg = Msg
140data TC a = OK a
141 | Error Err
142 deriving (Eq, Functor)
144instance Pretty a => Pretty (TC a) where
145 pretty (OK ok) = pretty ok
146 pretty (Error err) =
147 if size err > breakingSize then
148 text "Error" <+> colon $$ (nest nestingSize $ pretty err)
149 else
150 text "Error" <+> colon <+> pretty err
152instance Show a => Show (TC a) where
153 show (OK x) = show x
154 show (Error str) = "Error: " ++ show str
156-- at some point, this instance should also carry type checking options
157-- (e.g. Type:Type)
159instance Monad TC where
160 return = OK
161 x >>= k = case x of
162 OK v -> k v
163 Error e -> Error e
164 fail e = Error (InternalMsg e)
166tfail :: Err -> TC a
167tfail e = Error e
169trun :: FC -> TC a -> TC a
170trun fc (OK a) = OK a
171trun fc (Error e) = Error (At fc e)
173instance MonadPlus TC where
174 mzero = fail "Unknown error"
175 (OK x) `mplus` _ = OK x
176 _ `mplus` (OK y) = OK y
177 err `mplus` _ = err
179discard :: Monad m => m a -> m ()
180discard f = f >> return ()
182showSep :: String -> [String] -> String
183showSep sep [] = ""
184showSep sep [x] = x
185showSep sep (x:xs) = x ++ sep ++ showSep sep xs
187pmap f (x, y) = (f x, f y)
189traceWhen True msg a = trace msg a
190traceWhen False _ a = a
192-- RAW TERMS ----------------------------------------------------------------
194-- | Names are hierarchies of strings, describing scope (so no danger of
195-- duplicate names, but need to be careful on lookup).
196data Name = UN String -- ^ User-provided name
197 | NS Name [String] -- ^ Root, namespaces
198 | MN Int String -- ^ Machine chosen names
199 | NErased -- ^ Name of somethng which is never used in scope
200 | SN SpecialName -- ^ Decorated function names
201 deriving (Eq, Ord)
202{-!
203deriving instance Binary Name
204!-}
206data SpecialName = WhereN Int Name Name
207 | InstanceN Name [String]
208 | ParentN Name String
209 | MethodN Name
210 | CaseN Name
211 deriving (Eq, Ord)
212{-!
213deriving instance Binary SpecialName
214!-}
216instance Sized Name where
217 size (UN n) = 1
218 size (NS n els) = 1 + length els
219 size (MN i n) = 1
220 size _ = 1
222instance Pretty Name where
223 pretty (UN n) = text n
224 pretty (NS n s) = pretty n
225 pretty (MN i s) = lbrace <+> text s <+> (text . show $ i) <+> rbrace
226 pretty (SN s) = text (show s)
228instance Show Name where
229 show (UN n) = n
230 show (NS n s) = showSep "." (reverse s) ++ "." ++ show n
231 show (MN _ "underscore") = "_"
232 show (MN i s) = "{" ++ s ++ show i ++ "}"
233 show (SN s) = show s
234 show NErased = "_"
236instance Show SpecialName where
237 show (WhereN i p c) = show p ++ ", " ++ show c
238 show (InstanceN cl inst) = showSep ", " inst ++ " instance of " ++ show cl
239 show (MethodN m) = "method " ++ show m
240 show (ParentN p c) = show p ++ "#" ++ c
241 show (CaseN n) = "case block in " ++ show n
243-- Show a name in a way decorated for code generation, not human reading
244showCG :: Name -> String
245showCG (UN n) = n
246showCG (NS n s) = showSep "." (reverse s) ++ "." ++ show n
247showCG (MN _ "underscore") = "_"
248showCG (MN i s) = "{" ++ s ++ show i ++ "}"
249showCG (SN s) = showCG' s
250 where showCG' (WhereN i p c) = show p ++ ":" ++ show c ++ ":" ++ show i
251 showCG' (InstanceN cl inst) = '@':show cl ++ '$':showSep ":" inst
252 showCG' (MethodN m) = '!':show m
253 showCG' (ParentN p c) = show p ++ "#" ++ show c
254 showCG' (CaseN c) = show c ++ "_case"
255showCG NErased = "_"
258-- |Contexts allow us to map names to things. A root name maps to a collection
259-- of things in different namespaces with that name.
260type Ctxt a = Map.Map Name (Map.Map Name a)
261emptyContext = Map.empty
263tcname (UN ('@':_)) = True
264tcname (NS n _) = tcname n
265tcname (SN (InstanceN _ _)) = True
266tcname (SN (MethodN _)) = True
267tcname (SN (ParentN _ _)) = True
268tcname _ = False
270implicitable (NS n _) = implicitable n
271implicitable (UN (x:xs)) = isLower x
272implicitable _ = False
274nsroot (NS n _) = n
275nsroot n = n
277addDef :: Name -> a -> Ctxt a -> Ctxt a
278addDef n v ctxt = case Map.lookup (nsroot n) ctxt of
279 Nothing -> Map.insert (nsroot n)
280 (Map.insert n v Map.empty) ctxt
281 Just xs -> Map.insert (nsroot n)
282 (Map.insert n v xs) ctxt
284{-| Look up a name in the context, given an optional namespace.
285 The name (n) may itself have a (partial) namespace given.
287 Rules for resolution:
289 - if an explicit namespace is given, return the names which match it. If none
290 match, return all names.
292 - if the name has has explicit namespace given, return the names which match it
293 and ignore the given namespace.
295 - otherwise, return all names.
297-}
299lookupCtxtName :: Name -> Ctxt a -> [(Name, a)]
300lookupCtxtName n ctxt = case Map.lookup (nsroot n) ctxt of
301 Just xs -> filterNS (Map.toList xs)
302 Nothing -> []
303 where
304 filterNS [] = []
305 filterNS ((found, v) : xs)
306 | nsmatch n found = (found, v) : filterNS xs
307 | otherwise = filterNS xs
309 nsmatch (NS n ns) (NS p ps) = ns `isPrefixOf` ps
310 nsmatch (NS _ _) _ = False
311 nsmatch looking found = True
313lookupCtxt :: Name -> Ctxt a -> [a]
314lookupCtxt n ctxt = map snd (lookupCtxtName n ctxt)
316lookupCtxtExact :: Name -> Ctxt a -> [a]
317lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
319updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
320updateDef n f ctxt
321 = let ds = lookupCtxtName n ctxt in
322 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
324toAlist :: Ctxt a -> [(Name, a)]
325toAlist ctxt = let allns = map snd (Map.toList ctxt) in
326 concat (map (Map.toList) allns)
328addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
329addAlist [] ctxt = ctxt
330addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
332data NativeTy = IT8 | IT16 | IT32 | IT64
333 deriving (Show, Eq, Ord, Enum)
335instance Pretty NativeTy where
336 pretty IT8 = text "Bits8"
337 pretty IT16 = text "Bits16"
338 pretty IT32 = text "Bits32"
339 pretty IT64 = text "Bits64"
341data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
342 | ITVec NativeTy Int
343 deriving (Show, Eq, Ord)
345data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
346 deriving (Show, Eq, Ord)
348instance Pretty ArithTy where
349 pretty (ATInt ITNative) = text "Int"
350 pretty (ATInt ITBig) = text "BigInt"
351 pretty (ATInt ITChar) = text "Char"
352 pretty (ATInt (ITFixed n)) = pretty n
353 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
354 pretty ATFloat = text "Float"
356nativeTyWidth :: NativeTy -> Int
357nativeTyWidth IT8 = 8
358nativeTyWidth IT16 = 16
359nativeTyWidth IT32 = 32
360nativeTyWidth IT64 = 64
362{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
363intTyWidth :: IntTy -> Int
364intTyWidth (ITFixed n) = nativeTyWidth n
365intTyWidth ITNative = 8 * sizeOf (0 :: Int)
366intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
367intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
369data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
370 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
371 | B8V (Vector Word8) | B16V (Vector Word16)
372 | B32V (Vector Word32) | B64V (Vector Word64)
373 | AType ArithTy | StrType
374 | PtrType | VoidType | Forgot
375 deriving (Eq, Ord)
376{-!
377deriving instance Binary Const
378!-}
380instance Sized Const where
381 size _ = 1
383instance Pretty Const where
384 pretty (I i) = text . show $ i
385 pretty (BI i) = text . show $ i
386 pretty (Fl f) = text . show $ f
387 pretty (Ch c) = text . show $ c
388 pretty (Str s) = text s
389 pretty (AType a) = pretty a
390 pretty StrType = text "String"
391 pretty PtrType = text "Ptr"
392 pretty VoidType = text "Void"
393 pretty Forgot = text "Forgot"
394 pretty (B8 w) = text . show $ w
395 pretty (B16 w) = text . show $ w
396 pretty (B32 w) = text . show $ w
397 pretty (B64 w) = text . show $ w
399data Raw = Var Name
400 | RBind Name (Binder Raw) Raw
401 | RApp Raw Raw
402 | RType
403 | RForce Raw
404 | RConstant Const
405 deriving (Show, Eq)
407instance Sized Raw where
408 size (Var name) = 1
409 size (RBind name bind right) = 1 + size bind + size right
410 size (RApp left right) = 1 + size left + size right
411 size RType = 1
412 size (RForce raw) = 1 + size raw
413 size (RConstant const) = size const
415instance Pretty Raw where
416 pretty = text . show
418{-!
419deriving instance Binary Raw
420!-}
422-- | All binding forms are represented in a unform fashion.
423data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
424 | Pi { binderTy :: b }
425 | Let { binderTy :: b,
426 binderVal :: b {-^ value for bound variable-}}
427 | NLet { binderTy :: b,
428 binderVal :: b }
429 | Hole { binderTy :: b}
430 | GHole { binderTy :: b}
431 | Guess { binderTy :: b,
432 binderVal :: b }
433 | PVar { binderTy :: b }
434 | PVTy { binderTy :: b }
435 deriving (Show, Eq, Ord, Functor)
436{-!
437deriving instance Binary Binder
438!-}
440instance Sized a => Sized (Binder a) where
441 size (Lam ty) = 1 + size ty
442 size (Pi ty) = 1 + size ty
443 size (Let ty val) = 1 + size ty + size val
444 size (NLet ty val) = 1 + size ty + size val
445 size (Hole ty) = 1 + size ty
446 size (GHole ty) = 1 + size ty
447 size (Guess ty val) = 1 + size ty + size val
448 size (PVar ty) = 1 + size ty
449 size (PVTy ty) = 1 + size ty
451fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
452fmapMB f (Let t v) = liftM2 Let (f t) (f v)
453fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
454fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
455fmapMB f (Lam t) = liftM Lam (f t)
456fmapMB f (Pi t) = liftM Pi (f t)
457fmapMB f (Hole t) = liftM Hole (f t)
458fmapMB f (GHole t) = liftM GHole (f t)
459fmapMB f (PVar t) = liftM PVar (f t)
460fmapMB f (PVTy t) = liftM PVTy (f t)
462raw_apply :: Raw -> [Raw] -> Raw
463raw_apply f [] = f
464raw_apply f (a : as) = raw_apply (RApp f a) as
466raw_unapply :: Raw -> (Raw, [Raw])
467raw_unapply t = ua [] t where
468 ua args (RApp f a) = ua (a:args) f
469 ua args t = (t, args)
471data RawFun = RawFun { rtype :: Raw,
472 rval :: Raw
473 }
474 deriving Show
476data RawDatatype = RDatatype Name Raw [(Name, Raw)]
477 deriving Show
479data RDef = RFunction RawFun
480 | RConst Raw
481 | RData RawDatatype
482 deriving Show
484type RProgram = [(Name, RDef)]
486-- WELL TYPED TERMS ---------------------------------------------------------
488-- | Universe expressions for universe checking
489data UExp = UVar Int -- ^ universe variable
490 | UVal Int -- ^ explicit universe level
491 deriving (Eq, Ord)
493instance Sized UExp where
494 size _ = 1
496-- We assume that universe levels have been checked, so anything external
497-- can just have the same universe variable and we won't get any new
498-- cycles.
500instance Binary UExp where
501 put x = return ()
502 get = return (UVar (-1))
504instance Show UExp where
505 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
506 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
507 show (UVal x) = show x
508-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
510-- | Universe constraints
511data UConstraint = ULT UExp UExp -- ^ Strictly less than
512 | ULE UExp UExp -- ^ Less than or equal to
513 deriving Eq
515instance Show UConstraint where
516 show (ULT x y) = show x ++ " < " ++ show y
517 show (ULE x y) = show x ++ " <= " ++ show y
519type UCs = (Int, [UConstraint])
521data NameType = Bound
522 | Ref
523 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
524 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
525 deriving (Show, Ord)
526{-!
527deriving instance Binary NameType
528!-}
530instance Sized NameType where
531 size _ = 1
533instance Pretty NameType where
534 pretty = text . show
536instance Eq NameType where
537 Bound == Bound = True
538 Ref == Ref = True
539 DCon _ a == DCon _ b = (a == b) -- ignore tag
540 TCon _ a == TCon _ b = (a == b) -- ignore tag
541 _ == _ = False
543-- | Terms in the core language
544data TT n = P NameType n (TT n) -- ^ named references
545 | V Int -- ^ a resolved de Bruijn-indexed variable
546 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
547 | App (TT n) (TT n) -- ^ function, function type, arg
548 | Constant Const -- ^ constant
549 | Proj (TT n) Int -- ^ argument projection; runtime only
550 | Erased -- ^ an erased term
551 | Impossible -- ^ special case for totality checking
552 | TType UExp -- ^ the type of types at some level
553 deriving (Ord, Functor)
554{-!
555deriving instance Binary TT
556!-}
558class TermSize a where
559 termsize :: Name -> a -> Int
561instance TermSize a => TermSize [a] where
562 termsize n [] = 0
563 termsize n (x : xs) = termsize n x + termsize n xs
565instance TermSize (TT Name) where
566 termsize n (P _ x _)
567 | x == n = 1000000 -- recursive => really big
568 | otherwise = 1
569 termsize n (V _) = 1
570 termsize n (Bind n' (Let t v) sc)
571 = let rn = if n == n' then MN 0 "noname" else n in
572 termsize rn v + termsize rn sc
573 termsize n (Bind n' b sc)
574 = let rn = if n == n' then MN 0 "noname" else n in
575 termsize rn sc
576 termsize n (App f a) = termsize n f + termsize n a
577 termsize n (Proj t i) = termsize n t
578 termsize n _ = 1
580instance Sized a => Sized (TT a) where
581 size (P name n trm) = 1 + size name + size n + size trm
582 size (V v) = 1
583 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
584 size (App l r) = 1 + size l + size r
585 size (Constant c) = size c
586 size Erased = 1
587 size (TType u) = 1 + size u
589instance Pretty a => Pretty (TT a) where
590 pretty _ = text "test"
592type EnvTT n = [(n, Binder (TT n))]
594data Datatype n = Data { d_typename :: n,
595 d_typetag :: Int,
596 d_type :: (TT n),
597 d_cons :: [(n, TT n)] }
598 deriving (Show, Functor, Eq)
600instance Eq n => Eq (TT n) where
601 (==) (P xt x _) (P yt y _) = x == y
602 (==) (V x) (V y) = x == y
603 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
604 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
605 (==) (TType _) (TType _) = True -- deal with constraints later
606 (==) (Constant x) (Constant y) = x == y
607 (==) (Proj x i) (Proj y j) = x == y && i == j
608 (==) Erased _ = True
609 (==) _ Erased = True
610 (==) _ _ = False
612-- * A few handy operations on well typed terms:
614-- | A term is injective iff it is a data constructor, type constructor,
615-- constant, the type Type, pi-binding, or an application of an injective
616-- term.
617isInjective :: TT n -> Bool
618isInjective (P (DCon _ _) _ _) = True
619isInjective (P (TCon _ _) _ _) = True
620isInjective (Constant _) = True
621isInjective (TType x) = True
622isInjective (Bind _ (Pi _) sc) = True
623isInjective (App f a) = isInjective f
624isInjective _ = False
626-- | Count the number of instances of a de Bruijn index in a term
627vinstances :: Int -> TT n -> Int
628vinstances i (V x) | i == x = 1
629vinstances i (App f a) = vinstances i f + vinstances i a
630vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
631 where instancesB (Let t v) = vinstances i v
632 instancesB _ = 0
633vinstances i t = 0
635instantiate :: TT n -> TT n -> TT n
636instantiate e = subst 0 where
637 subst i (V x) | i == x = e
638 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
639 subst i (App f a) = App (subst i f) (subst i a)
640 subst i (Proj x idx) = Proj (subst i x) idx
641 subst i t = t
643substV :: TT n -> TT n -> TT n
644substV x tm = dropV 0 (instantiate x tm) where
645 dropV i (V x) | x > i = V (x - 1)
646 | otherwise = V x
647 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
648 dropV i (App f a) = App (dropV i f) (dropV i a)
649 dropV i (Proj x idx) = Proj (dropV i x) idx
650 dropV i t = t
652explicitNames :: TT n -> TT n
653explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
654 Bind x b'
655 (explicitNames (instantiate
656 (P Bound x (binderTy b')) sc))
657explicitNames (App f a) = App (explicitNames f) (explicitNames a)
658explicitNames (Proj x idx) = Proj (explicitNames x) idx
659explicitNames t = t
661pToV :: Eq n => n -> TT n -> TT n
662pToV n = pToV' n 0
663pToV' n i (P _ x _) | n == x = V i
664pToV' n i (Bind x b sc)
665-- We can assume the inner scope has been pToVed already, so continue to
666-- resolve names from the *outer* scope which may happen to have the same id.
667 | n == x = Bind x (fmap (pToV' n i) b) sc
668 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
669pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
670pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
671pToV' n i t = t
673-- increase de Bruijn indices, as if a binder has been added
674addBinder :: TT n -> TT n
675addBinder t = ab 0 t
676 where
677 ab top (V i) | i >= top = V (i + 1)
678 | otherwise = V i
679 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
680 ab top (App f a) = App (ab top f) (ab top a)
681 ab top (Proj t idx) = Proj (ab top t) idx
682 ab top t = t
684-- | Convert several names. First in the list comes out as V 0
685pToVs :: Eq n => [n] -> TT n -> TT n
686pToVs ns tm = pToVs' ns tm 0 where
687 pToVs' [] tm i = tm
688 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
690vToP :: TT n -> TT n
691vToP = vToP' [] where
692 vToP' env (V i) = let (n, b) = (env !! i) in
693 P Bound n (binderTy b)
694 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
695 Bind n b' (vToP' ((n, b'):env) sc)
696 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
697 vToP' env t = t
699finalise :: Eq n => TT n -> TT n
700finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
701finalise (App f a) = App (finalise f) (finalise a)
702finalise t = t
704subst :: Eq n => n -> TT n -> TT n -> TT n
705subst n v tm = instantiate v (pToV n tm)
707substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
708substNames [] t = t
709substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
711substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
712substTerm old new = st where
713 st t | t == old = new
714 st (App f a) = App (st f) (st a)
715 st (Bind x b sc) = Bind x (fmap st b) (st sc)
716 st t = t
718-- Returns true if V 0 and bound name n do not occur in the term
720noOccurrence :: Eq n => n -> TT n -> Bool
721noOccurrence n t = no' 0 t
722 where
723 no' i (V x) = not (i == x)
724 no' i (P Bound x _) = not (n == x)
725 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
726 where noB' i (Let t v) = no' i t && no' i v
727 noB' i (Guess t v) = no' i t && no' i v
728 noB' i b = no' i (binderTy b)
729 no' i (App f a) = no' i f && no' i a
730 no' i (Proj x _) = no' i x
731 no' i _ = True
733-- | Returns all names used free in the term
734freeNames :: Eq n => TT n -> [n]
735freeNames (P _ n _) = [n]
736freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
737 ++ freeNames t
738freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
739freeNames (App f a) = nub $ freeNames f ++ freeNames a
740freeNames (Proj x i) = nub $ freeNames x
741freeNames _ = []
743-- | Return the arity of a (normalised) type
744arity :: TT n -> Int
745arity (Bind n (Pi t) sc) = 1 + arity sc
746arity _ = 0
748-- | Deconstruct an application; returns the function and a list of arguments
749unApply :: TT n -> (TT n, [TT n])
750unApply t = ua [] t where
751 ua args (App f a) = ua (a:args) f
752 ua args t = (t, args)
754mkApp :: TT n -> [TT n] -> TT n
755mkApp f [] = f
756mkApp f (a:as) = mkApp (App f a) as
758forget :: TT Name -> Raw
759forget tm = fe [] tm
760 where
761 fe env (P _ n _) = Var n
762 fe env (V i) = Var (env !! i)
763 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
764 (fe (n:env) sc)
765 fe env (App f a) = RApp (fe env f) (fe env a)
766 fe env (Constant c)
767 = RConstant c
768 fe env (TType i) = RType
769 fe env Erased = RConstant Forgot
771bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
772bindAll [] t =t
773bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
775bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
776bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
778getArgTys :: TT n -> [(n, TT n)]
779getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
780getArgTys _ = []
782getRetTy :: TT n -> TT n
783getRetTy (Bind n (PVar _) sc) = getRetTy sc
784getRetTy (Bind n (PVTy _) sc) = getRetTy sc
785getRetTy (Bind n (Pi _) sc) = getRetTy sc
786getRetTy sc = sc
788uniqueName :: Name -> [Name] -> Name
789uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
790 | otherwise = n
792uniqueBinders :: [Name] -> TT Name -> TT Name
793uniqueBinders ns (Bind n b sc)
794 = let n' = uniqueName n ns in
795 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
796uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
797uniqueBinders ns t = t
800nextName (NS x s) = NS (nextName x) s
801nextName (MN i n) = MN (i+1) n
802nextName (UN x) = let (num', nm') = span isDigit (reverse x)
803 nm = reverse nm'
804 num = readN (reverse num') in
805 UN (nm ++ show (num+1))
806 where
807 readN "" = 0
808 readN x = read x
809nextName (SN x) = SN (nextName' x)
810 where
811 nextName' (WhereN i f x) = WhereN i f (nextName x)
812 nextName' (CaseN n) = CaseN (nextName n)
813 nextName' (MethodN n) = MethodN (nextName n)
815type Term = TT Name
816type Type = Term
818type Env = EnvTT Name
820-- an environment with de Bruijn indices 'normalised' so that they all refer to
821-- this environment
823newtype WkEnvTT n = Wk (EnvTT n)
824type WkEnv = WkEnvTT Name
826instance (Eq n, Show n) => Show (TT n) where
827 show t = showEnv [] t
829itBitsName IT8 = "Bits8"
830itBitsName IT16 = "Bits16"
831itBitsName IT32 = "Bits32"
832itBitsName IT64 = "Bits64"
834instance Show Const where
835 show (I i) = show i
836 show (BI i) = show i
837 show (Fl f) = show f
838 show (Ch c) = show c
839 show (Str s) = show s
840 show (B8 x) = show x
841 show (B16 x) = show x
842 show (B32 x) = show x
843 show (B64 x) = show x
844 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
845 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
846 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
847 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
848 show (AType ATFloat) = "Float"
849 show (AType (ATInt ITBig)) = "Integer"
850 show (AType (ATInt ITNative)) = "Int"
851 show (AType (ATInt ITChar)) = "Char"
852 show (AType (ATInt (ITFixed it))) = itBitsName it
853 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
854 show StrType = "String"
855 show PtrType = "Ptr"
856 show VoidType = "Void"
858showEnv env t = showEnv' env t False
859showEnvDbg env t = showEnv' env t True
861prettyEnv env t = prettyEnv' env t False
862 where
863 prettyEnv' env t dbg = prettySe 10 env t dbg
865 bracket outer inner p
866 | inner > outer = lparen <> p <> rparen
867 | otherwise = p
869 prettySe p env (P nt n t) debug =
870 pretty n <+>
871 if debug then
872 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
873 else
874 empty
875 prettySe p env (V i) debug
876 | i < length env =
877 if debug then
878 text . show . fst $ env!!i
879 else
880 lbrack <+> text (show i) <+> rbrack
881 | otherwise = text "unbound" <+> text (show i) <+> text "!"
882 prettySe p env (Bind n b@(Pi t) sc) debug
883 | noOccurrence n sc && not debug =
884 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
885 prettySe p env (Bind n b sc) debug =
886 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
887 prettySe p env (App f a) debug =
888 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
889 prettySe p env (Proj x i) debug =
890 prettySe 1 env x debug <+> text ("!" ++ show i)
891 prettySe p env (Constant c) debug = pretty c
892 prettySe p env Erased debug = text "[_]"
893 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
895 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
896 prettySb env n (Hole t) = prettyB env "?defer" "." n t
897 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
898 prettySb env n (PVar t) = prettyB env "pat" "." n t
899 prettySb env n (PVTy t) = prettyB env "pty" "." n t
900 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
901 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
903 prettyB env op sc n t debug =
904 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
906 prettyBv env op sc n t v debug =
907 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
908 prettySe 10 env v debug <> text sc
911showEnv' env t dbg = se 10 env t where
912 se p env (P nt n t) = show n
913 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
914 se p env (V i) | i < length env && i >= 0
915 = (show $ fst $ env!!i) ++
916 if dbg then "{" ++ show i ++ "}" else ""
917 | otherwise = "!!V " ++ show i ++ "!!"
918 se p env (Bind n b@(Pi t) sc)
919 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
920 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
921 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
922 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
923 se p env (Constant c) = show c
924 se p env Erased = "[__]"
925 se p env Impossible = "[impossible]"
926 se p env (TType i) = "Type " ++ show i
928 sb env n (Lam t) = showb env "\\ " " => " n t
929 sb env n (Hole t) = showb env "? " ". " n t
930 sb env n (GHole t) = showb env "?defer " ". " n t
931 sb env n (Pi t) = showb env "(" ") -> " n t
932 sb env n (PVar t) = showb env "pat " ". " n t
933 sb env n (PVTy t) = showb env "pty " ". " n t
934 sb env n (Let t v) = showbv env "let " " in " n t v
935 sb env n (Guess t v) = showbv env "?? " " in " n t v
937 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
938 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
939 se 10 env v ++ sc
941 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
942 | otherwise = str
944-- | Check whether a term has any holes in it - impure if so
945pureTerm :: TT Name -> Bool
946pureTerm (App f a) = pureTerm f && pureTerm a
947pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
948 pureBinder (Hole _) = False
949 pureBinder (Guess _ _) = False
950 pureBinder (Let t v) = pureTerm t && pureTerm v
951 pureBinder t = pureTerm (binderTy t)
953 notClassName (MN _ "class") = False
954 notClassName _ = True
956pureTerm _ = True
958-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
959weakenTm :: Int -> TT n -> TT n
960weakenTm i t = wk i 0 t
961 where wk i min (V x) | x >= min = V (i + x)
962 wk i m (App f a) = App (wk i m f) (wk i m a)
963 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
964 wk i m t = t
965 wkb i m t = fmap (wk i m) t
967-- | Weaken an environment so that all the de Bruijn indices are correct according
968-- to the latest bound variable
970weakenEnv :: EnvTT n -> EnvTT n
971weakenEnv env = wk (length env - 1) env
972 where wk i [] = []
973 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
974 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
975 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
976 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
978weakenTmEnv :: Int -> EnvTT n -> EnvTT n
979weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
981orderPats :: Term -> Term
982orderPats tm = op [] tm
983 where
984 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
985 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
986 op ps sc = bindAll (map (\ (n, t) -> (n, t)) (sortP ps)) sc
988 sortP ps = pick [] (reverse ps)
990 namesIn (P _ n _) = [n]
991 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
992 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
993 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
994 nb t = namesIn (binderTy t)
995 namesIn (App f a) = nub (namesIn f ++ namesIn a)
996 namesIn _ = []
998 pick acc [] = reverse acc
999 pick acc ((n, t) : ps) = pick (insert n t acc) ps
1001 insert n t [] = [(n, t)]
1002 insert n t ((n',t') : ps)
1003 | n `elem` (namesIn (binderTy t') ++
1004 concatMap namesIn (map (binderTy . snd) ps))
1005 = (n', t') : insert n t ps
1006 | otherwise = (n,t):(n',t'):ps