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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)
312lookupCtxtExact :: Name -> Ctxt a -> [a]
313lookupCtxtExact n ctxt = [ v | (nm, v) <- lookupCtxtName n ctxt, nm == n]
315updateDef :: Name -> (a -> a) -> Ctxt a -> Ctxt a
316updateDef n f ctxt
317 = let ds = lookupCtxtName n ctxt in
318 foldr (\ (n, t) c -> addDef n (f t) c) ctxt ds
320toAlist :: Ctxt a -> [(Name, a)]
321toAlist ctxt = let allns = map snd (Map.toList ctxt) in
322 concat (map (Map.toList) allns)
324addAlist :: Show a => [(Name, a)] -> Ctxt a -> Ctxt a
325addAlist [] ctxt = ctxt
326addAlist ((n, tm) : ds) ctxt = addDef n tm (addAlist ds ctxt)
328data NativeTy = IT8 | IT16 | IT32 | IT64
329 deriving (Show, Eq, Ord, Enum)
331instance Pretty NativeTy where
332 pretty IT8 = text "Bits8"
333 pretty IT16 = text "Bits16"
334 pretty IT32 = text "Bits32"
335 pretty IT64 = text "Bits64"
337data IntTy = ITFixed NativeTy | ITNative | ITBig | ITChar
338 | ITVec NativeTy Int
339 deriving (Show, Eq, Ord)
341data ArithTy = ATInt IntTy | ATFloat -- TODO: Float vectors
342 deriving (Show, Eq, Ord)
344instance Pretty ArithTy where
345 pretty (ATInt ITNative) = text "Int"
346 pretty (ATInt ITBig) = text "BigInt"
347 pretty (ATInt ITChar) = text "Char"
348 pretty (ATInt (ITFixed n)) = pretty n
349 pretty (ATInt (ITVec e c)) = pretty e <> text "x" <> (text . show $ c)
350 pretty ATFloat = text "Float"
352nativeTyWidth :: NativeTy -> Int
353nativeTyWidth IT8 = 8
354nativeTyWidth IT16 = 16
355nativeTyWidth IT32 = 32
356nativeTyWidth IT64 = 64
358{-# DEPRECATED intTyWidth "Non-total function, use nativeTyWidth and appropriate casing" #-}
359intTyWidth :: IntTy -> Int
360intTyWidth (ITFixed n) = nativeTyWidth n
361intTyWidth ITNative = 8 * sizeOf (0 :: Int)
362intTyWidth ITChar = error "IRTS.Lang.intTyWidth: Characters have platform and backend dependent width"
363intTyWidth ITBig = error "IRTS.Lang.intTyWidth: Big integers have variable width"
365data Const = I Int | BI Integer | Fl Double | Ch Char | Str String
366 | B8 Word8 | B16 Word16 | B32 Word32 | B64 Word64
367 | B8V (Vector Word8) | B16V (Vector Word16)
368 | B32V (Vector Word32) | B64V (Vector Word64)
369 | AType ArithTy | StrType
370 | PtrType | VoidType | Forgot
371 deriving (Eq, Ord)
372{-!
373deriving instance Binary Const
374!-}
376instance Sized Const where
377 size _ = 1
379instance Pretty Const where
380 pretty (I i) = text . show $ i
381 pretty (BI i) = text . show $ i
382 pretty (Fl f) = text . show $ f
383 pretty (Ch c) = text . show $ c
384 pretty (Str s) = text s
385 pretty (AType a) = pretty a
386 pretty StrType = text "String"
387 pretty PtrType = text "Ptr"
388 pretty VoidType = text "Void"
389 pretty Forgot = text "Forgot"
390 pretty (B8 w) = text . show $ w
391 pretty (B16 w) = text . show $ w
392 pretty (B32 w) = text . show $ w
393 pretty (B64 w) = text . show $ w
395data Raw = Var Name
396 | RBind Name (Binder Raw) Raw
397 | RApp Raw Raw
398 | RType
399 | RForce Raw
400 | RConstant Const
401 deriving (Show, Eq)
403instance Sized Raw where
404 size (Var name) = 1
405 size (RBind name bind right) = 1 + size bind + size right
406 size (RApp left right) = 1 + size left + size right
407 size RType = 1
408 size (RForce raw) = 1 + size raw
409 size (RConstant const) = size const
411instance Pretty Raw where
412 pretty = text . show
414{-!
415deriving instance Binary Raw
416!-}
418-- | All binding forms are represented in a unform fashion.
419data Binder b = Lam { binderTy :: b {-^ type annotation for bound variable-}}
420 | Pi { binderTy :: b }
421 | Let { binderTy :: b,
422 binderVal :: b {-^ value for bound variable-}}
423 | NLet { binderTy :: b,
424 binderVal :: b }
425 | Hole { binderTy :: b}
426 | GHole { binderTy :: b}
427 | Guess { binderTy :: b,
428 binderVal :: b }
429 | PVar { binderTy :: b }
430 | PVTy { binderTy :: b }
431 deriving (Show, Eq, Ord, Functor)
432{-!
433deriving instance Binary Binder
434!-}
436instance Sized a => Sized (Binder a) where
437 size (Lam ty) = 1 + size ty
438 size (Pi ty) = 1 + size ty
439 size (Let ty val) = 1 + size ty + size val
440 size (NLet ty val) = 1 + size ty + size val
441 size (Hole ty) = 1 + size ty
442 size (GHole ty) = 1 + size ty
443 size (Guess ty val) = 1 + size ty + size val
444 size (PVar ty) = 1 + size ty
445 size (PVTy ty) = 1 + size ty
447fmapMB :: Monad m => (a -> m b) -> Binder a -> m (Binder b)
448fmapMB f (Let t v) = liftM2 Let (f t) (f v)
449fmapMB f (NLet t v) = liftM2 NLet (f t) (f v)
450fmapMB f (Guess t v) = liftM2 Guess (f t) (f v)
451fmapMB f (Lam t) = liftM Lam (f t)
452fmapMB f (Pi t) = liftM Pi (f t)
453fmapMB f (Hole t) = liftM Hole (f t)
454fmapMB f (GHole t) = liftM GHole (f t)
455fmapMB f (PVar t) = liftM PVar (f t)
456fmapMB f (PVTy t) = liftM PVTy (f t)
458raw_apply :: Raw -> [Raw] -> Raw
459raw_apply f [] = f
460raw_apply f (a : as) = raw_apply (RApp f a) as
462raw_unapply :: Raw -> (Raw, [Raw])
463raw_unapply t = ua [] t where
464 ua args (RApp f a) = ua (a:args) f
465 ua args t = (t, args)
467data RawFun = RawFun { rtype :: Raw,
468 rval :: Raw
469 }
470 deriving Show
472data RawDatatype = RDatatype Name Raw [(Name, Raw)]
473 deriving Show
475data RDef = RFunction RawFun
476 | RConst Raw
477 | RData RawDatatype
478 deriving Show
480type RProgram = [(Name, RDef)]
482-- WELL TYPED TERMS ---------------------------------------------------------
484-- | Universe expressions for universe checking
485data UExp = UVar Int -- ^ universe variable
486 | UVal Int -- ^ explicit universe level
487 deriving (Eq, Ord)
489instance Sized UExp where
490 size _ = 1
492-- We assume that universe levels have been checked, so anything external
493-- can just have the same universe variable and we won't get any new
494-- cycles.
496instance Binary UExp where
497 put x = return ()
498 get = return (UVar (-1))
500instance Show UExp where
501 show (UVar x) | x < 26 = [toEnum (x + fromEnum 'a')]
502 | otherwise = toEnum ((x `mod` 26) + fromEnum 'a') : show (x `div` 26)
503 show (UVal x) = show x
504-- show (UMax l r) = "max(" ++ show l ++ ", " ++ show r ++")"
506-- | Universe constraints
507data UConstraint = ULT UExp UExp -- ^ Strictly less than
508 | ULE UExp UExp -- ^ Less than or equal to
509 deriving Eq
511instance Show UConstraint where
512 show (ULT x y) = show x ++ " < " ++ show y
513 show (ULE x y) = show x ++ " <= " ++ show y
515type UCs = (Int, [UConstraint])
517data NameType = Bound
518 | Ref
519 | DCon Int Int -- ^ Data constructor; Ints are tag and arity
520 | TCon Int Int -- ^ Type constructor; Ints are tag and arity
521 deriving (Show, Ord)
522{-!
523deriving instance Binary NameType
524!-}
526instance Sized NameType where
527 size _ = 1
529instance Pretty NameType where
530 pretty = text . show
532instance Eq NameType where
533 Bound == Bound = True
534 Ref == Ref = True
535 DCon _ a == DCon _ b = (a == b) -- ignore tag
536 TCon _ a == TCon _ b = (a == b) -- ignore tag
537 _ == _ = False
539-- | Terms in the core language
540data TT n = P NameType n (TT n) -- ^ named references
541 | V Int -- ^ a resolved de Bruijn-indexed variable
542 | Bind n (Binder (TT n)) (TT n) -- ^ a binding
543 | App (TT n) (TT n) -- ^ function, function type, arg
544 | Constant Const -- ^ constant
545 | Proj (TT n) Int -- ^ argument projection; runtime only
546 | Erased -- ^ an erased term
547 | Impossible -- ^ special case for totality checking
548 | TType UExp -- ^ the type of types at some level
549 deriving (Ord, Functor)
550{-!
551deriving instance Binary TT
552!-}
554class TermSize a where
555 termsize :: Name -> a -> Int
557instance TermSize a => TermSize [a] where
558 termsize n [] = 0
559 termsize n (x : xs) = termsize n x + termsize n xs
561instance TermSize (TT Name) where
562 termsize n (P _ x _)
563 | x == n = 1000000 -- recursive => really big
564 | otherwise = 1
565 termsize n (V _) = 1
566 termsize n (Bind n' (Let t v) sc)
567 = let rn = if n == n' then MN 0 "noname" else n in
568 termsize rn v + termsize rn sc
569 termsize n (Bind n' b sc)
570 = let rn = if n == n' then MN 0 "noname" else n in
571 termsize rn sc
572 termsize n (App f a) = termsize n f + termsize n a
573 termsize n (Proj t i) = termsize n t
574 termsize n _ = 1
576instance Sized a => Sized (TT a) where
577 size (P name n trm) = 1 + size name + size n + size trm
578 size (V v) = 1
579 size (Bind nm binder bdy) = 1 + size nm + size binder + size bdy
580 size (App l r) = 1 + size l + size r
581 size (Constant c) = size c
582 size Erased = 1
583 size (TType u) = 1 + size u
585instance Pretty a => Pretty (TT a) where
586 pretty _ = text "test"
588type EnvTT n = [(n, Binder (TT n))]
590data Datatype n = Data { d_typename :: n,
591 d_typetag :: Int,
592 d_type :: (TT n),
593 d_cons :: [(n, TT n)] }
594 deriving (Show, Functor, Eq)
596instance Eq n => Eq (TT n) where
597 (==) (P xt x _) (P yt y _) = x == y
598 (==) (V x) (V y) = x == y
599 (==) (Bind _ xb xs) (Bind _ yb ys) = xb == yb && xs == ys
600 (==) (App fx ax) (App fy ay) = fx == fy && ax == ay
601 (==) (TType _) (TType _) = True -- deal with constraints later
602 (==) (Constant x) (Constant y) = x == y
603 (==) (Proj x i) (Proj y j) = x == y && i == j
604 (==) Erased _ = True
605 (==) _ Erased = True
606 (==) _ _ = False
608-- * A few handy operations on well typed terms:
610-- | A term is injective iff it is a data constructor, type constructor,
611-- constant, the type Type, pi-binding, or an application of an injective
612-- term.
613isInjective :: TT n -> Bool
614isInjective (P (DCon _ _) _ _) = True
615isInjective (P (TCon _ _) _ _) = True
616isInjective (Constant _) = True
617isInjective (TType x) = True
618isInjective (Bind _ (Pi _) sc) = True
619isInjective (App f a) = isInjective f
620isInjective _ = False
622-- | Count the number of instances of a de Bruijn index in a term
623vinstances :: Int -> TT n -> Int
624vinstances i (V x) | i == x = 1
625vinstances i (App f a) = vinstances i f + vinstances i a
626vinstances i (Bind x b sc) = instancesB b + vinstances (i + 1) sc
627 where instancesB (Let t v) = vinstances i v
628 instancesB _ = 0
629vinstances i t = 0
631instantiate :: TT n -> TT n -> TT n
632instantiate e = subst 0 where
633 subst i (V x) | i == x = e
634 subst i (Bind x b sc) = Bind x (fmap (subst i) b) (subst (i+1) sc)
635 subst i (App f a) = App (subst i f) (subst i a)
636 subst i (Proj x idx) = Proj (subst i x) idx
637 subst i t = t
639substV :: TT n -> TT n -> TT n
640substV x tm = dropV 0 (instantiate x tm) where
641 dropV i (V x) | x > i = V (x - 1)
642 | otherwise = V x
643 dropV i (Bind x b sc) = Bind x (fmap (dropV i) b) (dropV (i+1) sc)
644 dropV i (App f a) = App (dropV i f) (dropV i a)
645 dropV i (Proj x idx) = Proj (dropV i x) idx
646 dropV i t = t
648explicitNames :: TT n -> TT n
649explicitNames (Bind x b sc) = let b' = fmap explicitNames b in
650 Bind x b'
651 (explicitNames (instantiate
652 (P Bound x (binderTy b')) sc))
653explicitNames (App f a) = App (explicitNames f) (explicitNames a)
654explicitNames (Proj x idx) = Proj (explicitNames x) idx
655explicitNames t = t
657pToV :: Eq n => n -> TT n -> TT n
658pToV n = pToV' n 0
659pToV' n i (P _ x _) | n == x = V i
660pToV' n i (Bind x b sc)
661-- We can assume the inner scope has been pToVed already, so continue to
662-- resolve names from the *outer* scope which may happen to have the same id.
663 | n == x = Bind x (fmap (pToV' n i) b) sc
664 | otherwise = Bind x (fmap (pToV' n i) b) (pToV' n (i+1) sc)
665pToV' n i (App f a) = App (pToV' n i f) (pToV' n i a)
666pToV' n i (Proj t idx) = Proj (pToV' n i t) idx
667pToV' n i t = t
669-- increase de Bruijn indices, as if a binder has been added
670addBinder :: TT n -> TT n
671addBinder t = ab 0 t
672 where
673 ab top (V i) | i >= top = V (i + 1)
674 | otherwise = V i
675 ab top (Bind x b sc) = Bind x (fmap (ab top) b) (ab (top + 1) sc)
676 ab top (App f a) = App (ab top f) (ab top a)
677 ab top (Proj t idx) = Proj (ab top t) idx
678 ab top t = t
680-- | Convert several names. First in the list comes out as V 0
681pToVs :: Eq n => [n] -> TT n -> TT n
682pToVs ns tm = pToVs' ns tm 0 where
683 pToVs' [] tm i = tm
684 pToVs' (n:ns) tm i = pToV' n i (pToVs' ns tm (i+1))
686vToP :: TT n -> TT n
687vToP = vToP' [] where
688 vToP' env (V i) = let (n, b) = (env !! i) in
689 P Bound n (binderTy b)
690 vToP' env (Bind n b sc) = let b' = fmap (vToP' env) b in
691 Bind n b' (vToP' ((n, b'):env) sc)
692 vToP' env (App f a) = App (vToP' env f) (vToP' env a)
693 vToP' env t = t
695finalise :: Eq n => TT n -> TT n
696finalise (Bind x b sc) = Bind x (fmap finalise b) (pToV x (finalise sc))
697finalise (App f a) = App (finalise f) (finalise a)
698finalise t = t
700subst :: Eq n => n -> TT n -> TT n -> TT n
701subst n v tm = instantiate v (pToV n tm)
703substNames :: Eq n => [(n, TT n)] -> TT n -> TT n
704substNames [] t = t
705substNames ((n, tm) : xs) t = subst n tm (substNames xs t)
707substTerm :: Eq n => TT n -> TT n -> TT n -> TT n
708substTerm old new = st where
709 st t | t == old = new
710 st (App f a) = App (st f) (st a)
711 st (Bind x b sc) = Bind x (fmap st b) (st sc)
712 st t = t
714-- Returns true if V 0 and bound name n do not occur in the term
716noOccurrence :: Eq n => n -> TT n -> Bool
717noOccurrence n t = no' 0 t
718 where
719 no' i (V x) = not (i == x)
720 no' i (P Bound x _) = not (n == x)
721 no' i (Bind n b sc) = noB' i b && no' (i+1) sc
722 where noB' i (Let t v) = no' i t && no' i v
723 noB' i (Guess t v) = no' i t && no' i v
724 noB' i b = no' i (binderTy b)
725 no' i (App f a) = no' i f && no' i a
726 no' i (Proj x _) = no' i x
727 no' i _ = True
729-- | Returns all names used free in the term
730freeNames :: Eq n => TT n -> [n]
731freeNames (P _ n _) = [n]
732freeNames (Bind n (Let t v) sc) = nub $ freeNames v ++ (freeNames sc \\ [n])
733 ++ freeNames t
734freeNames (Bind n b sc) = nub $ freeNames (binderTy b) ++ (freeNames sc \\ [n])
735freeNames (App f a) = nub $ freeNames f ++ freeNames a
736freeNames (Proj x i) = nub $ freeNames x
737freeNames _ = []
739-- | Return the arity of a (normalised) type
740arity :: TT n -> Int
741arity (Bind n (Pi t) sc) = 1 + arity sc
742arity _ = 0
744-- | Deconstruct an application; returns the function and a list of arguments
745unApply :: TT n -> (TT n, [TT n])
746unApply t = ua [] t where
747 ua args (App f a) = ua (a:args) f
748 ua args t = (t, args)
750mkApp :: TT n -> [TT n] -> TT n
751mkApp f [] = f
752mkApp f (a:as) = mkApp (App f a) as
754forget :: TT Name -> Raw
755forget tm = fe [] tm
756 where
757 fe env (P _ n _) = Var n
758 fe env (V i) = Var (env !! i)
759 fe env (Bind n b sc) = RBind n (fmap (fe env) b)
760 (fe (n:env) sc)
761 fe env (App f a) = RApp (fe env f) (fe env a)
762 fe env (Constant c)
763 = RConstant c
764 fe env (TType i) = RType
765 fe env Erased = RConstant Forgot
767bindAll :: [(n, Binder (TT n))] -> TT n -> TT n
768bindAll [] t =t
769bindAll ((n, b) : bs) t = Bind n b (bindAll bs t)
771bindTyArgs :: (TT n -> Binder (TT n)) -> [(n, TT n)] -> TT n -> TT n
772bindTyArgs b xs = bindAll (map (\ (n, ty) -> (n, b ty)) xs)
774getArgTys :: TT n -> [(n, TT n)]
775getArgTys (Bind n (Pi t) sc) = (n, t) : getArgTys sc
776getArgTys _ = []
778getRetTy :: TT n -> TT n
779getRetTy (Bind n (PVar _) sc) = getRetTy sc
780getRetTy (Bind n (PVTy _) sc) = getRetTy sc
781getRetTy (Bind n (Pi _) sc) = getRetTy sc
782getRetTy sc = sc
784uniqueName :: Name -> [Name] -> Name
785uniqueName n hs | n `elem` hs = uniqueName (nextName n) hs
786 | otherwise = n
788uniqueBinders :: [Name] -> TT Name -> TT Name
789uniqueBinders ns (Bind n b sc)
790 = let n' = uniqueName n ns in
791 Bind n' (fmap (uniqueBinders (n':ns)) b) (uniqueBinders ns sc)
792uniqueBinders ns (App f a) = App (uniqueBinders ns f) (uniqueBinders ns a)
793uniqueBinders ns t = t
796nextName (NS x s) = NS (nextName x) s
797nextName (MN i n) = MN (i+1) n
798nextName (UN x) = let (num', nm') = span isDigit (reverse x)
799 nm = reverse nm'
800 num = readN (reverse num') in
801 UN (nm ++ show (num+1))
802 where
803 readN "" = 0
804 readN x = read x
805nextName (SN x) = SN (nextName' x)
806 where
807 nextName' (WhereN i f x) = WhereN i f (nextName x)
808 nextName' (CaseN n) = CaseN (nextName n)
809 nextName' (MethodN n) = MethodN (nextName n)
811type Term = TT Name
812type Type = Term
814type Env = EnvTT Name
816-- an environment with de Bruijn indices 'normalised' so that they all refer to
817-- this environment
819newtype WkEnvTT n = Wk (EnvTT n)
820type WkEnv = WkEnvTT Name
822instance (Eq n, Show n) => Show (TT n) where
823 show t = showEnv [] t
825itBitsName IT8 = "Bits8"
826itBitsName IT16 = "Bits16"
827itBitsName IT32 = "Bits32"
828itBitsName IT64 = "Bits64"
830instance Show Const where
831 show (I i) = show i
832 show (BI i) = show i
833 show (Fl f) = show f
834 show (Ch c) = show c
835 show (Str s) = show s
836 show (B8 x) = show x
837 show (B16 x) = show x
838 show (B32 x) = show x
839 show (B64 x) = show x
840 show (B8V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
841 show (B16V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
842 show (B32V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
843 show (B64V x) = "<" ++ intercalate "," (map show (V.toList x)) ++ ">"
844 show (AType ATFloat) = "Float"
845 show (AType (ATInt ITBig)) = "Integer"
846 show (AType (ATInt ITNative)) = "Int"
847 show (AType (ATInt ITChar)) = "Char"
848 show (AType (ATInt (ITFixed it))) = itBitsName it
849 show (AType (ATInt (ITVec it c))) = itBitsName it ++ "x" ++ show c
850 show StrType = "String"
851 show PtrType = "Ptr"
852 show VoidType = "Void"
854showEnv env t = showEnv' env t False
855showEnvDbg env t = showEnv' env t True
857prettyEnv env t = prettyEnv' env t False
858 where
859 prettyEnv' env t dbg = prettySe 10 env t dbg
861 bracket outer inner p
862 | inner > outer = lparen <> p <> rparen
863 | otherwise = p
865 prettySe p env (P nt n t) debug =
866 pretty n <+>
867 if debug then
868 lbrack <+> pretty nt <+> colon <+> prettySe 10 env t debug <+> rbrack
869 else
870 empty
871 prettySe p env (V i) debug
872 | i < length env =
873 if debug then
874 text . show . fst $ env!!i
875 else
876 lbrack <+> text (show i) <+> rbrack
877 | otherwise = text "unbound" <+> text (show i) <+> text "!"
878 prettySe p env (Bind n b@(Pi t) sc) debug
879 | noOccurrence n sc && not debug =
880 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
881 prettySe p env (Bind n b sc) debug =
882 bracket p 2 $ prettySb env n b debug <> prettySe 10 ((n, b):env) sc debug
883 prettySe p env (App f a) debug =
884 bracket p 1 $ prettySe 1 env f debug <+> prettySe 0 env a debug
885 prettySe p env (Proj x i) debug =
886 prettySe 1 env x debug <+> text ("!" ++ show i)
887 prettySe p env (Constant c) debug = pretty c
888 prettySe p env Erased debug = text "[_]"
889 prettySe p env (TType i) debug = text "Type" <+> (text . show $ i)
891 prettySb env n (Lam t) = prettyB env "λ" "=>" n t
892 prettySb env n (Hole t) = prettyB env "?defer" "." n t
893 prettySb env n (Pi t) = prettyB env "(" ") ->" n t
894 prettySb env n (PVar t) = prettyB env "pat" "." n t
895 prettySb env n (PVTy t) = prettyB env "pty" "." n t
896 prettySb env n (Let t v) = prettyBv env "let" "in" n t v
897 prettySb env n (Guess t v) = prettyBv env "??" "in" n t v
899 prettyB env op sc n t debug =
900 text op <> pretty n <+> colon <+> prettySe 10 env t debug <> text sc
902 prettyBv env op sc n t v debug =
903 text op <> pretty n <+> colon <+> prettySe 10 env t debug <+> text "=" <+>
904 prettySe 10 env v debug <> text sc
907showEnv' env t dbg = se 10 env t where
908 se p env (P nt n t) = show n
909 ++ if dbg then "{" ++ show nt ++ " : " ++ se 10 env t ++ "}" else ""
910 se p env (V i) | i < length env && i >= 0
911 = (show $ fst $ env!!i) ++
912 if dbg then "{" ++ show i ++ "}" else ""
913 | otherwise = "!!V " ++ show i ++ "!!"
914 se p env (Bind n b@(Pi t) sc)
915 | noOccurrence n sc && not dbg = bracket p 2 $ se 1 env t ++ " -> " ++ se 10 ((n,b):env) sc
916 se p env (Bind n b sc) = bracket p 2 $ sb env n b ++ se 10 ((n,b):env) sc
917 se p env (App f a) = bracket p 1 $ se 1 env f ++ " " ++ se 0 env a
918 se p env (Proj x i) = se 1 env x ++ "!" ++ show i
919 se p env (Constant c) = show c
920 se p env Erased = "[__]"
921 se p env Impossible = "[impossible]"
922 se p env (TType i) = "Type " ++ show i
924 sb env n (Lam t) = showb env "\\ " " => " n t
925 sb env n (Hole t) = showb env "? " ". " n t
926 sb env n (GHole t) = showb env "?defer " ". " n t
927 sb env n (Pi t) = showb env "(" ") -> " n t
928 sb env n (PVar t) = showb env "pat " ". " n t
929 sb env n (PVTy t) = showb env "pty " ". " n t
930 sb env n (Let t v) = showbv env "let " " in " n t v
931 sb env n (Guess t v) = showbv env "?? " " in " n t v
933 showb env op sc n t = op ++ show n ++ " : " ++ se 10 env t ++ sc
934 showbv env op sc n t v = op ++ show n ++ " : " ++ se 10 env t ++ " = " ++
935 se 10 env v ++ sc
937 bracket outer inner str | inner > outer = "(" ++ str ++ ")"
938 | otherwise = str
940-- | Check whether a term has any holes in it - impure if so
941pureTerm :: TT Name -> Bool
942pureTerm (App f a) = pureTerm f && pureTerm a
943pureTerm (Bind n b sc) = notClassName n && pureBinder b && pureTerm sc where
944 pureBinder (Hole _) = False
945 pureBinder (Guess _ _) = False
946 pureBinder (Let t v) = pureTerm t && pureTerm v
947 pureBinder t = pureTerm (binderTy t)
949 notClassName (MN _ "class") = False
950 notClassName _ = True
952pureTerm _ = True
954-- | Weaken a term by adding i to each de Bruijn index (i.e. lift it over i bindings)
955weakenTm :: Int -> TT n -> TT n
956weakenTm i t = wk i 0 t
957 where wk i min (V x) | x >= min = V (i + x)
958 wk i m (App f a) = App (wk i m f) (wk i m a)
959 wk i m (Bind x b sc) = Bind x (wkb i m b) (wk i (m + 1) sc)
960 wk i m t = t
961 wkb i m t = fmap (wk i m) t
963-- | Weaken an environment so that all the de Bruijn indices are correct according
964-- to the latest bound variable
966weakenEnv :: EnvTT n -> EnvTT n
967weakenEnv env = wk (length env - 1) env
968 where wk i [] = []
969 wk i ((n, b) : bs) = (n, weakenTmB i b) : wk (i - 1) bs
970 weakenTmB i (Let t v) = Let (weakenTm i t) (weakenTm i v)
971 weakenTmB i (Guess t v) = Guess (weakenTm i t) (weakenTm i v)
972 weakenTmB i t = t { binderTy = weakenTm i (binderTy t) }
974weakenTmEnv :: Int -> EnvTT n -> EnvTT n
975weakenTmEnv i = map (\ (n, b) -> (n, fmap (weakenTm i) b))
977orderPats :: Term -> Term
978orderPats tm = op [] tm
979 where
980 op ps (Bind n (PVar t) sc) = op ((n, PVar t) : ps) sc
981 op ps (Bind n (Hole t) sc) = op ((n, Hole t) : ps) sc
982 op ps sc = bindAll (map (\ (n, t) -> (n, t)) (sortP ps)) sc
984 sortP ps = pick [] (reverse ps)
986 namesIn (P _ n _) = [n]
987 namesIn (Bind n b t) = nub $ nb b ++ (namesIn t \\ [n])
988 where nb (Let t v) = nub (namesIn t) ++ nub (namesIn v)
989 nb (Guess t v) = nub (namesIn t) ++ nub (namesIn v)
990 nb t = namesIn (binderTy t)
991 namesIn (App f a) = nub (namesIn f ++ namesIn a)
992 namesIn _ = []
994 pick acc [] = reverse acc
995 pick acc ((n, t) : ps) = pick (insert n t acc) ps
997 insert n t [] = [(n, t)]
998 insert n t ((n',t') : ps)
999 | n `elem` (namesIn (binderTy t') ++
1000 concatMap namesIn (map (binderTy . snd) ps))
1001 = (n', t') : insert n t ps
1002 | otherwise = (n,t):(n',t'):ps