git.iko.soy/type-level-sets
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11 files changed+252−567
since splitsnapshots
unifiedsplit
README+42−21 TySet.hs−355 changelog.md+5 example-new.hs−61 example-set.hs−39 example.hs+12−11 example2.hs+9 src/Data/Type/Map.hs+82−25 src/Data/Type/Set.hs+70−29 stack.yaml+1−1 type-level-sets.cabal+31−25
README+42−21
@@ -1,35 +1,56 @@
1−This library provides type-level sets to Haskell, with a value level counterpart, and operations for taking the union, computing
2−subsets, and split sets. Also included is a "mapping" type constructor that pairs symbols with types. This can be used to represent
3−sets of variable-type pairs, which is used in the paper "Embedding effect systems in Haskell" (Dominic Orchard,
1+This library provides type-level sets and finite maps to Haskell, with a value level counterpart, and operations for taking the union, computing
2+subsets/submaps, and splitting sets/maps. This library was originally built based on
3+"Embedding effect systems in Haskell" (Dominic Orchard,
44Tomas Petricek <http://www.cl.cam.ac.uk/~dao29/publ/haskell14-effects.pdf>) to embed effect sets.
55
66The following shows an example:
77
8− {-# LANGUAGE DataKinds, TypeOperators #-}
8+ {-# LANGUAGE DataKinds, TypeOperators, TypeFamilies, MultiParamTypeClasses #-}
9+ import Data.Type.Map
10+
11+ -- Specifies how to combine duplicate key-value pairs for Int values
12+ type instance Combine Int Int = Int
13+ instance Combinable Int Int where
14+ combine x y = x + y
15+
16+ foo :: Map '["x" :-> Int, "z" :-> Bool, "w" :-> Int]
17+ foo = Ext (Var :: (Var "x")) 2
18+ $ Ext (Var :: (Var "z")) True
19+ $ Ext (Var :: (Var "w")) 5
20+ Empty
21+
22+ bar :: Map '["y" :-> Int, "w" :-> Int]
23+ bar = Ext (Var :: (Var "y")) 3
24+ $ Ext (Var :: (Var "w")) 1
25+ $ Empty
26+
27+ -- foobar :: Map '["w" :-> Int, "x" :-> Int, "y" :-> Int, "z" :-> Bool]
28+ foobar = foo `union` bar
29+
30+The 'Map' type for 'foobar' here shows the normalised form (sorted with no duplicates).
31+The type signatures is commented out as it can be infered. Running the example we get:
932
10− import Data.Type.Set
33+ *Main> foobar
34+ {w :-> 6, x :-> 2, y :-> 3, z :-> True}
1135
12− foo :: Set '["x" :-> Int, "z" :-> Int, "w" :-> Int]
13− foo = Ext ((Var :: (Var "x")) :-> 2) $
14− Ext ((Var :: (Var "z")) :-> 4) $
15− Ext ((Var :: (Var "w")) :-> 5) $
16− Empty
36+Thus, we see that values for 'w' are added.
1737
18− bar :: Set '["y" :-> Int, "w" :-> Int]
19− bar = Ext ((Var :: (Var "y")) :-> 3) $
20− Ext ((Var :: (Var "w")) :-> 1) $
21− Empty
38+ import GHC.TypeLits
39+ import Data.Type.Set
40+ type instance Cmp (Natural n) (Natural m) = CmpNat n m
2241
23− -- foobar :: Set '["w" :-> Int, "x" :-> Int, "y" :-> Int, "z" :-> Int]
24− foobar = foo `union` bar
42+ data Natural (a :: Nat) where
43+ Z :: Natural 0
44+ S :: Natural n -> Natural (n + 1)
2545
26−The 'Set' type for 'foobar' here shows the normalised form (sorted with no duplicates).
27−The type signatures is commented out as it can be infered. Running the example we get:
46+ -- foo :: Set '[Natural 0, Natural 1, Natural 3]
47+ foo = asSet $ Ext (S Z) (Ext (S (S (S Z))) (Ext Z Empty))
2848
29− *Main> foobar
30− {(Var :-> 1), (Var :-> 2), (Var :-> 3), (Var :-> 4)}
49+ -- bar :: Set '[Natural 1, Natural 2]
50+ bar = asSet $ Ext (S (S Z)) (Ext (S Z) (Ext (S Z) Empty))
3151
32−Thus, we see that the first value paired with the "w" variable is dropped.
52+ -- foobar :: Set '[Natural 0, Natural 1, Natural 2, Natural 3]
53+ foobar = foo `union` bar
3354
3455
3556
TySet.hsdeleted−355
@@ -1,355 +0,0 @@
1−-- {-# OPTIONS_GHC -package=ghc-7.10.1 #-}
2−{-# LANGUAGE TypeFamilies, DataKinds, PolyKinds, StandaloneDeriving, TypeOperators, FlexibleInstances, ScopedTypeVariables, ImplicitParams, MultiParamTypeClasses #-}
3−
4−module TySet(plugin, Set, Union, dropPrefix, ppr) where
5−
6−import TypeRep
7−import Type
8−import Kind
9−import TcEvidence
10−import CoAxiom
11−import Name
12−import OccName
13−import Var
14−import TyCon
15−import BasicTypes
16−
17−-- friends:
18−import Var
19−import VarEnv
20−import VarSet
21−import Name
22−import BasicTypes
23−import TyCon
24−import Class
25−import CoAxiom
26−
27−-- others
28−import PrelNames
29−import Outputable
30−import FastString
31−import Util
32−import DynFlags
33−
34−import TcPluginM ( TcPluginM, tcPluginIO, tcPluginTrace )
35−import TcRnMonad ( TcPlugin(..), TcPluginResult(..)
36− , Ct(..), CtEvidence(..), CtLoc, ctLoc, ctPred
37− , mkNonCanonical, isTouchableTcM, unsafeTcPluginTcM)
38−import Plugins ( CommandLineOption, defaultPlugin, Plugin(..) )
39−import GHC.TcPluginM.Extra
40−
41−import Debug.Trace
42−import Outputable
43−import DynFlags
44−
45−import Control.Monad
46−import Control.Monad.Trans.Maybe
47−import Control.Applicative
48−import qualified Data.Typeable as DT
49−import Data.List
50−
51−import Test.QuickCheck
52−import Test.QuickCheck.Property
53−
54−{- Set constructor -}
55−data Set (a :: [k])
56−{- Union operation -}
57−type family Union (a :: [k]) (b :: [k]) :: [k]
58−
59−type family Member (a :: k) (b :: [k]) :: Bool where
60− Member x '[] = False
61− Member x (x ': xs) = True
62− Member x (y ': xs) = Member x xs
63−
64−{- Plugin setup -}
65−plugin :: Plugin
66−plugin = defaultPlugin { tcPlugin = Just . thePlugin }
67−
68−thePlugin :: [CommandLineOption] -> TcPlugin
69−thePlugin opts = TcPlugin
70− { tcPluginInit = pluginInit opts
71− , tcPluginSolve = pluginSolve
72− , tcPluginStop = pluginStop
73− }
74−
75−class Debug t m where
76− debug :: (?ifDebug :: Bool) => t -> m ()
77−instance Debug SDoc TcPluginM where
78− debug x = tcPluginTrace "TySet" x
79−instance Debug String IO where
80− debug x = putStrLn x
81−
82−pluginInit :: [CommandLineOption] -> TcPluginM ()
83−pluginInit _ = return ()
84−
85−printerS = let ?ifDebug = True in tcPluginIO . debug . showSDocUnsafe . ppCts
86−printer = let ?ifDebug = True in tcPluginIO . debug
87−
88−pluginSolve :: () -> [Ct] -> [Ct] -> [Ct] -> TcPluginM TcPluginResult
89−pluginSolve () given derived wanted =
90− let ?ifDebug = True in
91−
92− do tcPluginIO $ debug "*****************************"
93− tcPluginIO $ debug "Running TySet equality plugin"
94− --debug $ ppCts wanted
95− tcPluginIO $ debug $ showSDocUnsafe $ ppCts wanted
96− tcPluginIO $ debug "Givens"
97− --debug $ ppCts given
98− tcPluginIO $ debug $ showSDocUnsafe $ ppCts given
99− tcPluginIO $ debug "Derived"
100− -- debug $ ppCts derived
101− tcPluginIO $ debug $ showSDocUnsafe $ ppCts derived
102− -- debug $ ppr $ head $ wanted
103−
104− --solved <- findEmptySetEquality wanted
105− (solved, generated) <- findSetEquality wanted
106− printer "Done - solved"
107− printerS (map snd solved)
108− printer "DOne - generated"
109− printerS generated
110−
111− return $ TcPluginOk solved generated
112−
113−pluginStop :: () -> TcPluginM ()
114−pluginStop _ = return ()
115−
116−-- Pretty print constraints
117−ppCts [] = text "(empty)"
118−ppCts cs = vcat (map ppr cs)
119−
120−{- Some debugging Show instances to help me understand what is coming in and out of GHC -}
121−deriving instance Show TyLit
122−deriving instance Show Type
123−instance Show Var where
124− show v = showSDocUnsafe $ ppr v
125−instance Show TyCon where
126− show tycon = showSDocUnsafe $ ppr tycon
127−instance Show Ct where
128− show ct = showSDocUnsafe $ ppr ct
129−
130−{-
131−-- Prediacate one whether a type is = Set '[]
132−isEmptySetType t = do (x, tcs) <- splitTyConApp_maybe t
133− guard $ length tcs == 2
134− guard $ getOccString (tyConName x) == "Set"
135− case tcs of [TyVarTy k, TyConApp con [TyVarTy k']] ->
136− do guard $ k == k'
137− guard $ (getOccString . tyConName $ con) == "[]"
138− _ -> Nothing
139−-}
140−
141−getNameStr = getOccString . tyConName
142−
143−liftTc :: Maybe a -> MaybeT TcPluginM a
144−liftTc = MaybeT . return
145−
146−liftMt :: TcPluginM a -> MaybeT TcPluginM a
147−liftMt x = MaybeT (fmap Just x)
148−
149−findSetEquality :: [Ct] -> TcPluginM ([(EvTerm, Ct)], [Ct])
150−findSetEquality [] = return ([], [])
151−findSetEquality (ct : xs) =
152− do x <- runMaybeT $
153− do (Nominal, t1, t2) <- liftTc $ getEqPredTys_maybe (ctPred ct)
154− a <- liftTc $ listTypeToTerm t1
155− b <- "sofar sogood" `trace` liftTc $ listTypeToTerm t2
156− (show (t1, a, t2, b)) `trace`
157− if (a == b) then
158− "are equal" `trace` return $ Left (EvCoercion $ TcRefl Nominal t1, ct)
159− else -- not equal, try to find an mgu and generate conditions on that
160− let ?ctLoc = ctLoc ct in
161− do unifiers <- "not equal" `trace` mgu a b
162− case unifiers of
163− Left unifiers -> ("L unifiers: \n" ++ show unifiers) `trace` return $ Right []
164− Right (dataUnifiers, unsolvedExtra) -> ("data unifiers:" ++ (show $ dataUnifiers)) `trace` return $ Right $ (EvCoercion $ TcRefl Nominal t1, ct) : map (\c -> (EvCoercion $ TcRefl Nominal undefined, c)) dataUnifiers
165−
166− (solved, generated) <- findSetEquality xs
167− case x of
168− Just y -> case y of
169− Left (ev, ct) -> return $ ((ev, ct) : solved, generated)
170− Right cts -> return $ (solved ++ cts, generated)
171− Nothing -> return (solved, generated)
172−
173−listTypeToTerm :: Type -> Maybe (TermTree Type)
174−listTypeToTerm t = case (splitTyConApp_maybe t) of
175− Just (tcon, args) ->
176− case getNameStr tcon of
177− "Union" -> do guard $ (length args) >= 3
178− (_ : (t1 : (t2 : ts))) <- return args
179− t1' <- listTypeToTerm t1
180− t2' <- listTypeToTerm t2
181− return $ Union t1' t2'
182− -- this case is probably temporary [see SessionListE.hs]
183− ":++" -> do guard $ (length args) >= 3
184− (_ : (t1 : (t2 : ts))) <- return args
185− t1' <- listTypeToTerm t1
186− t2' <- listTypeToTerm t2
187− return $ Union t1' t2'
188− ":" -> do guard $ (length args >= 2)
189− (t1 : (t2 : ts)) <- return args
190− (kind, args) <- splitTyConApp_maybe $ t1
191− ts' <- listTypeToTerm $ head ts -- possible bug here
192− return $ Union (Data [t2]) ts'
193− "[]" -> do guard $ (length args == 1)
194− [t] <- return args
195− (kind, args) <- splitTyConApp_maybe $ t
196− return $ Empty
197−
198− _ -> return $ Empty -- Data [t]
199− _ -> case t of
200− TyVarTy v -> return $ Var $ v
201−
202−-- Representation for solving equalities on terms comprising union, data, and variables
203−
204−data TermTree a = Union (TermTree a) (TermTree a) | Empty | Var Var | Data [a] deriving Show
205−
206−-- if the second argument is a prefix of the first argument, then return Just of the suffix, else Nothing
207−dropPrefix :: Eq a => [a] -> [a] -> Maybe [a]
208−dropPrefix [] xs = Just []
209−dropPrefix xs [] = Just xs
210−dropPrefix (x:xs) (y:ys) | x == y = dropPrefix xs ys
211− | otherwise = Nothing
212−
213−mguDataVars :: [a] -> [Var] -> Maybe [(Var, TermTree a)]
214−mguDataVars suffix [] = Nothing -- No variables to unify with
215−mguDataVars suffix (v:vs) = Just $ [(v, Data suffix)] ++ map (\v' -> (v', Var v)) vs
216−
217−mgu :: (?ctLoc :: CtLoc) => TermTree Type -> TermTree Type -> MaybeT TcPluginM (Either [(Var, TermTree Type)] ([Ct], ([Type], [Type]))) -- last component should be some equalities
218−mgu t1 t2 = let (vs1, ds1) = normalisedRep t1
219− (vs2, ds2) = normalisedRep t2
220− in ("----> " ++ show (ds1, ds2)) `trace`
221− (show $ dropPrefix ds1 ds2) `trace`
222− case (dropPrefix ds1 ds2) of
223− Nothing -> case (dropPrefix ds2 ds1) of
224− Nothing -> "el zilcho primo" `trace` do x <- liftMt (zipMatch ds1 ds2)
225− return $ Right x -- ([], ([], []))
226− Just suffix_ds2 -> "suffix_ds2" `trace`
227− do x <- liftTc $ mguDataVars suffix_ds2 vs1
228− return $ Left x
229− Just suffix_ds1 -> ("suffix_ds1 " ++ (show suffix_ds1))
230− `trace`
231− if (suffix_ds1 == []) then
232− do x <- liftMt (zipMatch ds1 ds2)
233− ("zipm: ds1 = " ++ (show ds1) ++ " ds2 = " ++ (show ds2) ++ ": " ++ (show x)) `trace` return $ Right x -- ([], ([], []))
234− else
235− do x <- liftTc $ mguDataVars suffix_ds1 vs2
236− return $ Left x
237−
238−mkEqualities :: (?ctLoc :: CtLoc) => [(Type, Type)] -> TcPluginM [Ct]
239−mkEqualities xs = (mapM (\(x, y) -> mkCt x y) xs) -- >>= (return . concat)
240−
241−mkCt t t' = fmap mkNonCanonical (newDerived ?ctLoc (uncurry mkPrimEqPred (t,t')))
242−
243−mkEqualities' (AppTy t1 t2) (AppTy t1' t2') = do ct <- mkCt t1 t1'
244− ct' <- mkCt t2 t2'
245− return [ct, ct']
246−mkEqualities' (TyConApp con kt) (TyConApp con' kt') | con == con' = mapM (uncurry mkCt) (zip kt kt')
247−mkEqualities' (FunTy t1 t2) (FunTy t1' t2') = do ct <- mkCt t1 t1'
248− ct' <- mkCt t2 t2'
249− return [ct, ct']
250−mkEqualities' (ForAllTy v t) (ForAllTy v' t') | v == v' = do ct <- mkCt t t'
251− return [ct]
252−mkEqualities' t t' = do ct <- mkCt t t'
253− return [ct]
254−
255−
256−
257−
258−zipMatch :: (?ctLoc :: CtLoc) => [Type] -> [Type] -> TcPluginM ([Ct], ([Type], [Type]))
259−zipMatch xs ys = let (unifiers, restL, restR) = zipMatch' xs ys
260− in do unifiers' <- mkEqualities unifiers
261− return $ (unifiers', (restL, restR))
262−
263−zipMatch' :: [a] -> [a] -> ([(a, a)], [a], [a])
264−zipMatch' [] xs = ([], [], xs)
265−zipMatch' xs [] = ([], xs, [])
266−zipMatch' (x:xs) (y:ys) = let (zips, l, r) = zipMatch' xs ys
267− in ((x, y) : zips, l, r)
268−
269−
270−
271−
272−
273−
274−subst :: TermTree a -> [(Var, TermTree a)] -> TermTree a
275−subst (Union s t) theta = Union (subst s theta) (subst t theta)
276−subst (Var a) theta = case (lookup a theta) of
277− Just t -> t
278− Nothing -> Var a
279−subst t theta = t
280−
281−instance Eq a => Eq (TermTree a) where
282− t1 == t2 = let (vs1, ds1) = normalisedRep t1
283− (vs2, ds2) = normalisedRep t2
284− in ("vars = " ++ (show (vs1, vs2)) ++ " eq = " ++ (show (vs1 == vs2)))
285− `trace` (vs1 == vs2) && (all (flip elem $ ds2) ds1) && (all (flip elem $ ds1) ds2)
286−
287−normalisedRep :: Eq a => TermTree a -> ([Var], [a])
288−normalisedRep t = let (vs, ds) = separate t
289− in (nub . sort $ vs, nub ds)
290−
291−separate :: TermTree a -> ([Var], [a])
292−separate Empty = ([], [])
293−separate (Var s) = ([s], [])
294−separate (Data xs) = ([], xs)
295−separate (Union a b) = let (vs1, ds1) = separate a
296− (vs2, ds2) = separate b
297− in (vs1++vs2, ds1++ds2)
298−
299−{-- Unit testing of normaliser and set equality --}
300−testSetTermEquality :: IO ()
301−testSetTermEquality = quickCheck (\((n, m) :: (TermTree Int, TermTree Int)) -> n == m)
302−
303−mkVar :: String -> Var
304−mkVar = undefined
305−
306−instance {-# OVERLAPS #-} Arbitrary (TermTree Int, TermTree Int) where
307− arbitrary = sized $ \vars ->
308− sized $ \datums ->
309− do v0 <- (vector vars)::(Gen [String])
310− v <- return $ map mkVar v0
311− dat <- (vector datums)::(Gen [Int])
312− v' <- shuffle v
313− dat' <- shuffle dat
314− g1 <- gen v dat
315− g2 <- gen v' dat'
316−
317− -- Soundness check on generated tree
318− let (v0, dat0) = separate g1
319− (v1, dat1) = separate g2
320− norm :: (Ord a) => [a] -> [a]
321− norm = nub . sort
322−
323− if and [(norm v0) == (norm v), (norm v1) == (norm v),
324− (norm dat) == (norm dat0), (norm dat) == (norm dat1)]
325− then return ()
326− else error $ "Generated trees failed soundness check: " ++ (show g1) ++ " " ++ (show g2)
327− return (g1, g2)
328−
329−-- Arbitrarily permute a union of two generators
330−unionPerm x y = do x' <- x
331− y' <- y
332− elements [Union x' y', Union y' x']
333−
334−-- Generates arbitrary terms from a list of variables and list of Int adtums
335−gen :: [Var] -> [Int] -> Gen (TermTree Int)
336−gen [] [] = return $ Empty
337−gen vs ds = do -- Choose between 0 and 1 if 'vs' is empty, or 0-2 if 'vs' has elements
338− choose <- suchThat arbitrary (\x -> x<=(2 - if vs == [] then 1 else 0) && x>=0)
339− case choose::Int of
340− -- Union with Empty
341− 0 -> unionPerm (gen vs ds) (return $ Empty)
342−
343− -- Pick some number of elements (maybe none) and create a data leaf
344− 1 -> do i <- suchThat arbitrary (<= (length ds))
345− unionPerm (gen vs (drop i ds)) (return $ Data (take i ds))
346−
347− -- Case where vs is non-empty, create a variable node, and either remove that
348− -- variable, or keep it around as a possibility again to test idempotency
349− 2 -> oneof [unionPerm (gen (tail vs) ds) (return $ Var (head vs)),
350− unionPerm (gen vs ds) (return $ Var (head vs))]
351− _ -> error "unpossible"
352−
353−
354−
355−
changelog.mdnew file+5
@@ -0,0 +1,5 @@
1+ # v0.8.9.0
2+
3+ - GHC 8.4 and 8.6 support.
4+ - Fixed bug in the delete operation.
5+ - Non-membership predicates
example-new.hsdeleted−61
@@ -1,61 +0,0 @@
1−{-# LANGUAGE DataKinds, KindSignatures, GADTs, TypeOperators, TypeFamilies, PolyKinds, EmptyDataDecls #-}
2−
3−{-# OPTIONS_GHC -fplugin=TyMap #-}
4−import TyMap
5−
6−import GHC.TypeLits
7−
8−
9−data Proxy (s :: Map * (Session *)) = Proxy
10−
11−data Container (a :: *) where
12− Empty :: Container (Set '[])
13− Ext :: a -> Container (Set s) -> Container (Set (Union '[a] s))
14− ExtP :: Proxy a -> Container (Set s) -> Container (Set (Union '[a] s))
15−
16−data Natural (a :: Nat) where
17− Z :: Natural 0
18− S :: Natural n -> Natural (n + 1)
19−
20−-- Should be typeable with the plugin
21−foo :: Container (Set '[Natural 1, Natural 2, Natural 3])
22−foo = Ext (S $ S Z) (Ext (S Z) (Ext (S $ S $ S Z) Empty))
23−
24−
25−
26−
27−
28−
29−
30−
31−
32−
33−
34−
35−
36−
37−
38−
39−
40−
41−
42−
43−
44−
45−
46−infixr 4 :->
47−data Map a b = a :-> b
48−
49−data X
50−data Y
51−
52−mkA :: Proxy (Y :-> A)
53−mkA = Proxy
54−
55−mkB :: Proxy (X :-> B)
56−mkB = Proxy
57−
58−data Session a = A | B | C a
59−
60−bar :: Container (Set '[Y :-> A, X :-> B])
61−bar = ExtP mkB (ExtP mkA Empty)
example-set.hsdeleted−39
@@ -1,39 +0,0 @@
1−{-# LANGUAGE DataKinds, KindSignatures, GADTs, TypeOperators, TypeFamilies, PolyKinds, EmptyDataDecls, StandaloneDeriving #-}
2−{-# OPTIONS_GHC -fplugin=TySet #-}
3−
4−import GHC.TypeLits
5−import TySet
6−
7−data Container (a :: *) where
8− Empty :: Container (Set '[])
9− Ext :: Show a => a -> Container (Set s) -> Container (Set (Union '[a] s))
10−
11−instance Show (Container a) where
12− show Empty = "Empty"
13− show (Ext x xs) = "Ext " ++ show x ++ " " ++ show xs
14−
15−data Natural (a :: Nat) where
16− Z :: Natural 0
17− S :: Natural n -> Natural (n + 1)
18−
19−instance Show (Natural a) where
20− show Z = "Z"
21− show (S n) = "S " ++ (show n)
22−
23−-- Should be typeable with the plugin
24−
25−foo :: Container (Set '[Natural 3, Natural 2, Natural 1])
26−foo = Ext (S $ S Z) (Ext (S Z) (Ext (S $ S $ S Z) Empty))
27−
28−foo2 :: Container (Set '[Natural 2, Natural 1])
29−foo2 = Ext (S $ S Z) (Ext (S Z) Empty)
30−
31−bar :: (Container (Set '[Natural 2, Natural 1])) -> Container (Set '[Natural 1])
32−bar (Ext (S (S Z)) (Ext (S Z) Empty)) = Ext (S Z) Empty
33−bar (Ext (S Z) (Ext (S (S Z)) Empty)) = Ext (S Z) Empty
34−
35−{-
36−dup :: Container (Set s) -> Container (Set (Union s s))
37−dup Empty = Empty
38−dup (Ext x xs) = Ext x (Ext x (dup xs))
39−-}
example.hs+12−11
@@ -1,7 +1,6 @@
1−{-# LANGUAGE DataKinds, TypeOperators, KindSignatures, TypeFamilies, MultiParamTypeClasses #-}
1+{-# LANGUAGE DataKinds, TypeOperators, TypeFamilies, MultiParamTypeClasses #-}
22
33import GHC.TypeLits
4−import Data.Type.Set (subset)
54import Data.Type.Map
65
76-- Specify that key-value pairs on Ints combine to an Int
@@ -9,22 +8,24 @@ type instance Combine Int Int = Int
98-- Specify that Int values for matching keys should be added
109instance Combinable Int Int where
1110 combine x y = x + y
12−
13−foo :: Map '["x" :-> Int, "z" :-> Int, "w" :-> Int]
14−foo = Ext (Var :: (Var "x")) 2 $
15− Ext (Var :: (Var "z")) 4 $
16− Ext (Var :: (Var "w")) 5 $
17− Empty
1811
12+foo :: Map '["x" :-> Int, "z" :-> Bool, "w" :-> Int]
13+foo = Ext (Var :: (Var "x")) 2
14+ $ Ext (Var :: (Var "z")) True
15+ $ Ext (Var :: (Var "w")) 5
16+ $ Empty
17+
18+foo' :: Map (AsMap '["z" :-> Bool, "x" :-> Int, "w" :-> Int])
19+foo' = asMap foo
1920
2021bar :: Map '["y" :-> Int, "w" :-> Int]
2122bar = Ext (Var :: (Var "y")) 3 $
2223 Ext (Var :: (Var "w")) 1 $
23− Empty
24+ Empty
2425
2526-- GHC can easily infer this type, so an explicit signature not necessary
2627-- foobar :: Map '["w" :-> Int, "x" :-> Int, "y" :-> Integer, "z" :-> Int]
2728foobar = foo `union` bar
2829
29−foobarToFoo :: Map '["x" :-> Int, "z" :-> Int, "w" :-> Int]
30−foobarToFoo = subset foobar
30+foobarToFoo :: Map '["w" :-> Int, "x" :-> Int, "z" :-> Bool]
31+foobarToFoo = submap foobar
example2.hs+9
@@ -1,4 +1,5 @@
11{-# LANGUAGE DataKinds, TypeOperators, TypeFamilies, GADTs, StandaloneDeriving #-}
2+{-# LANGUAGE FlexibleContexts #-}
23
34import GHC.TypeLits
45import Data.Type.Set
@@ -19,3 +20,11 @@ bar = asSet $ Ext (S (S Z)) (Ext (S Z) (Ext (S Z) Empty))
1920
2021-- foobar :: Set '[Natural 0, Natural 1, Natural 2, Natural 3]
2122foobar = foo `union` bar
23+
24+nonMemberTest :: NonMember (Natural 0) as => Set as -> ()
25+nonMemberTest set = ()
26+
27+-- nonMemberTest meep is well typed
28+meep = asSet $ Ext (S Z) (Ext (S (S Z)) Empty)
29+-- nonMemberTest morp is ill typed
30+morp = asSet $ Ext (S Z) (Ext (S (S Z)) (Ext Z Empty))
src/Data/Type/Map.hs+82−25
@@ -5,12 +5,14 @@ The implementation is similar to that shown in the paper.
55{-# LANGUAGE TypeOperators, PolyKinds, DataKinds, KindSignatures,
66 TypeFamilies, UndecidableInstances, MultiParamTypeClasses,
77 FlexibleInstances, GADTs, FlexibleContexts, ScopedTypeVariables,
8− ConstraintKinds #-}
8+ ConstraintKinds, IncoherentInstances #-}
99
1010module Data.Type.Map (Mapping(..), Union, Unionable, union, Var(..), Map(..),
1111 Combine, Combinable(..), Cmp,
1212 Nubable, nub,
13− Lookup, Member, (:\), Split, split, IsMap,
13+ Lookup, Member, (:\), Split, split,
14+ IsMember, lookp, Updatable, update,
15+ IsMap, AsMap, asMap,
1416 Submap, submap) where
1517
1618import GHC.TypeLits
@@ -44,17 +46,17 @@ type family Combine (a :: v) (b :: v) :: v
4446
4547{-| Delete elements from a map by key -}
4648type family (m :: [Mapping k v]) :\ (c :: k) :: [Mapping k v] where
47− '[] :\ k = '[]
48− ((k :-> v) ': m) :\ k = m :\ k
49− (kvp ': m) :\ k = kvp ': (m :\ k)
49+ '[] :\ k = '[]
50+ ((k :-> v) ': m) :\ k = m :\ k
51+ (kvp ': m) :\ k = kvp ': (m :\ k)
5052
51−{-| Lookup elements from a map -}
53+{-| Type-level lookup of elements from a map -}
5254type family Lookup (m :: [Mapping k v]) (c :: k) :: Maybe v where
5355 Lookup '[] k = Nothing
5456 Lookup ((k :-> v) ': m) k = Just v
5557 Lookup (kvp ': m) k = Lookup m k
5658
57−{-| Membership test -}
59+{-| Membership test as type function -}
5860type family Member (c :: k) (m :: [Mapping k v]) :: Bool where
5961 Member k '[] = False
6062 Member k ((k :-> v) ': m) = True
@@ -74,6 +76,37 @@ data Map (n :: [Mapping Symbol *]) where
7476 Empty :: Map '[]
7577 Ext :: Var k -> v -> Map m -> Map ((k :-> v) ': m)
7678
79+{-| Membership test a type class (predicate) -}
80+class IsMember v t m where
81+ {-| Value-level lookup of elements from a map, via type class predicate -}
82+ lookp :: Var v -> Map m -> t
83+
84+instance {-# OVERLAPS #-} IsMember v t ((v ':-> t) ': m) where
85+ lookp _ (Ext _ x _) = x
86+
87+instance {-# OVERLAPPABLE #-} IsMember v t m => IsMember v t (x ': m) where
88+ lookp v (Ext _ _ m) = lookp v m
89+
90+
91+{-| Updatability as a type class -}
92+class Updatable v t m n where
93+ {-| Update a map with `m` at variable `v` with a value of type `t`
94+ to produce a map of type `n` -}
95+ update :: Map m -> Var v -> t -> Map n
96+
97+instance {-# OVERLAPS #-} Updatable v t ((v ':-> s) ': m) ((v ':-> t) ': m) where
98+ update (Ext v _ m) _ x = Ext v x m
99+
100+instance Updatable v t m n => Updatable v t ((w ':-> y) ': m) ((w ':-> y) ': n) where
101+ update (Ext w y m) v x = Ext w y (update m v x)
102+
103+-- instance Updatable v t '[] '[v ':-> t] where
104+-- update Empty v x = Ext v x Empty
105+
106+instance Updatable v t s ((v ':-> t) ': s) where
107+ update xs v x = Ext v x xs
108+
109+
77110{-| Predicate to check if in normalised map form -}
78111type IsMap s = (s ~ Nub (Sort s))
79112
@@ -88,7 +121,7 @@ instance Show (Map '[]) where
88121 show Empty = "{}"
89122
90123instance (KnownSymbol k, Show v, Show' (Map s)) => Show (Map ((k :-> v) ': s)) where
91− show (Ext k v s) = "{" ++ show k ++ " :-> " ++ show v ++ (show' s) ++ "}"
124+ show (Ext k v s) = "{" ++ show k ++ " :-> " ++ show v ++ show' s ++ "}"
92125
93126class Show' t where
94127 show' :: t -> String
@@ -97,12 +130,25 @@ instance Show' (Map '[]) where
97130instance (KnownSymbol k, Show v, Show' (Map s)) => Show' (Map ((k :-> v) ': s)) where
98131 show' (Ext k v s) = ", " ++ show k ++ " :-> " ++ show v ++ (show' s)
99132
100−{-| Union of two finite maps -}
133+instance Eq (Map '[]) where
134+ Empty == Empty = True
135+
136+instance (Eq v, Eq (Map s)) => Eq (Map ((k :-> v) ': s)) where
137+ (Ext Var v m) == (Ext Var v' m') = v == v' && m == m'
138+
139+instance Ord (Map '[]) where
140+ compare Empty Empty = EQ
141+
142+instance (Ord v, Ord (Map s)) => Ord (Map ((k :-> v) ': s)) where
143+ compare (Ext Var v m) (Ext Var v' m') = compare v v' `mappend` compare m m'
144+
145+{-| Union of two finite maps (normalising) -}
101146union :: (Unionable s t) => Map s -> Map t -> Map (Union s t)
102147union s t = nub (quicksort (append s t))
103148
104149type Unionable s t = (Nubable (Sort (s :++ t)), Sortable (s :++ t))
105150
151+{-| Append of two finite maps (non normalising) -}
106152append :: Map s -> Map t -> Map (s :++ t)
107153append Empty x = x
108154append (Ext k v xs) ys = Ext k v (append xs ys)
@@ -117,11 +163,15 @@ class Sortable xs where
117163instance Sortable '[] where
118164 quicksort Empty = Empty
119165
120−instance (Sortable (Filter FMin (k :-> v) xs),
121− Sortable (Filter FMax (k :-> v) xs), FilterV FMin k v xs, FilterV FMax k v xs) => Sortable ((k :-> v) ': xs) where
122− quicksort (Ext k v xs) = ((quicksort (less k v xs)) `append` (Ext k v Empty)) `append` (quicksort (more k v xs))
123− where less = filterV (Proxy::(Proxy FMin))
124− more = filterV (Proxy::(Proxy FMax))
166+instance (Sortable (Filter FMin (k :-> v) xs)
167+ , Sortable (Filter FMax (k :-> v) xs)
168+ , FilterV FMin k v xs
169+ , FilterV FMax k v xs) => Sortable ((k :-> v) ': xs) where
170+ quicksort (Ext k v xs) =
171+ quicksort (less k v xs) `append` Ext k v Empty `append` quicksort (more k v xs)
172+ where
173+ less = filterV (Proxy::(Proxy FMin))
174+ more = filterV (Proxy::(Proxy FMax))
125175
126176{- Filter out the elements less-than or greater-than-or-equal to the pivot -}
127177class FilterV (f::Flag) k v xs where
@@ -130,13 +180,19 @@ class FilterV (f::Flag) k v xs where
130180instance FilterV f k v '[] where
131181 filterV _ k v Empty = Empty
132182
133−instance (Conder ((Cmp x (k :-> v)) == LT), FilterV FMin k v xs) => FilterV FMin k v (x ': xs) where
134− filterV f@Proxy k v (Ext k' v' xs) = cond (Proxy::(Proxy ((Cmp x (k :-> v)) == LT)))
135− (Ext k' v' (filterV f k v xs)) (filterV f k v xs)
183+instance (Conder (Cmp x (k :-> v) == LT), FilterV FMin k v xs) => FilterV FMin k v (x ': xs) where
184+ filterV f@Proxy k v (Ext k' v' xs) =
185+ cond (Proxy::(Proxy (Cmp x (k :-> v) == LT)))
186+ (Ext k' v' (filterV f k v xs))
187+ (filterV f k v xs)
136188
137−instance (Conder (((Cmp x (k :-> v)) == GT) || ((Cmp x (k :-> v)) == EQ)), FilterV FMax k v xs) => FilterV FMax k v (x ': xs) where
138− filterV f@Proxy k v (Ext k' v' xs) = cond (Proxy::(Proxy (((Cmp x (k :-> v)) == GT) || ((Cmp x (k :-> v)) == EQ))))
139− (Ext k' v' (filterV f k v xs)) (filterV f k v xs)
189+instance
190+ (Conder ((Cmp x (k :-> v) == GT) || (Cmp x (k :-> v) == EQ)), FilterV FMax k v xs)
191+ => FilterV FMax k v (x ': xs) where
192+ filterV f@Proxy k v (Ext k' v' xs) =
193+ cond (Proxy::(Proxy ((Cmp x (k :-> v) == GT) || (Cmp x (k :-> v) == EQ))))
194+ (Ext k' v' (filterV f k v xs))
195+ (filterV f k v xs)
140196
141197class Combinable t t' where
142198 combine :: t -> t' -> Combine t t'
@@ -150,15 +206,16 @@ instance Nubable '[] where
150206instance Nubable '[e] where
151207 nub (Ext k v Empty) = Ext k v Empty
152208
153−instance {-# OVERLAPPING #-}
154− (Combinable v v', Nubable ((k :-> Combine v v') ': s)) => Nubable ((k :-> v) ': (k :-> v') ': s) where
155− nub (Ext k v (Ext k' v' s)) = nub (Ext k (combine v v') s)
156−
157−instance {-# OVERLAPPING #-}
209+instance {-# OVERLAPPABLE #-}
158210 (Nub (e ': f ': s) ~ (e ': Nub (f ': s)),
159211 Nubable (f ': s)) => Nubable (e ': f ': s) where
160212 nub (Ext k v (Ext k' v' s)) = Ext k v (nub (Ext k' v' s))
161213
214+instance {-# OVERLAPS #-}
215+ (Combinable v v', Nubable ((k :-> Combine v v') ': s))
216+ => Nubable ((k :-> v) ': (k :-> v') ': s) where
217+ nub (Ext k v (Ext k' v' s)) = nub (Ext k (combine v v') s)
218+
162219
163220class Conder g where
164221 cond :: Proxy g -> Map s -> Map t -> Map (If g s t)
src/Data/Type/Set.hs+70−29
@@ -1,10 +1,13 @@
1−{-# LANGUAGE GADTs, DataKinds, KindSignatures, TypeOperators, TypeFamilies,
2− MultiParamTypeClasses, FlexibleInstances, PolyKinds, FlexibleContexts,
3− UndecidableInstances, ConstraintKinds, ScopedTypeVariables #-}
1+{-# LANGUAGE GADTs, DataKinds, KindSignatures, TypeOperators, TypeFamilies,
2+ MultiParamTypeClasses, FlexibleInstances, PolyKinds,
3+ FlexibleContexts, UndecidableInstances, ConstraintKinds,
4+ ScopedTypeVariables, TypeInType #-}
45
5−module Data.Type.Set (Set(..), Union, Unionable, union, quicksort, append,
6− Sort, Sortable, (:++), Split(..), Cmp, Filter, Flag(..),
7− Nub, Nubable(..), AsSet, asSet, IsSet, Subset(..), Delete(..), Proxy(..)) where
6+module Data.Type.Set (Set(..), Union, Unionable, union, quicksort, append,
7+ Sort, Sortable, (:++), Split(..), Cmp, Filter, Flag(..),
8+ Nub, Nubable(..), AsSet, asSet, IsSet, Subset(..),
9+ Delete(..), Proxy(..), remove, Remove, (:\),
10+ Member(..), NonMember, MemberP(..)) where
811
912import GHC.TypeLits
1013import Data.Type.Bool
@@ -12,10 +15,10 @@ import Data.Type.Equality
1215
1316data Proxy (p :: k) = Proxy
1417
15−-- Value-level 'Set' representation, essentially a list
16−data Set (n :: [*]) where
18+-- Value-level 'Set' representation, essentially a list
19+data Set (n :: [k]) where
1720 {--| Construct an empty set -}
18− Empty :: Set '[]
21+ Empty :: Set '[]
1922 {--| Extend a set with an element -}
2023 Ext :: e -> Set s -> Set (e ': s)
2124
@@ -23,7 +26,7 @@ instance Show (Set '[]) where
2326 show Empty = "{}"
2427
2528instance (Show e, Show' (Set s)) => Show (Set (e ': s)) where
26− show (Ext e s) = "{" ++ show e ++ (show' s) ++ "}"
29+ show (Ext e s) = "{" ++ show e ++ (show' s) ++ "}"
2730
2831class Show' t where
2932 show' :: t -> String
@@ -32,6 +35,10 @@ instance Show' (Set '[]) where
3235instance (Show' (Set s), Show e) => Show' (Set (e ': s)) where
3336 show' (Ext e s) = ", " ++ show e ++ (show' s)
3437
38+instance (Eq e, Eq (Set s)) => Eq (Set (e ': s)) where
39+ (Ext e m) == (Ext e' m') = e == e' && m == m'
40+
41+
3542{-| At the type level, normalise the list form to the set form -}
3643type AsSet s = Nub (Sort s)
3744
@@ -43,8 +50,8 @@ asSet x = nub (quicksort x)
4350type IsSet s = (s ~ Nub (Sort s))
4451
4552{-| Useful properties to be able to refer to someties -}
46−type SetProperties f = (Union f '[] ~ f, Split f '[] f,
47− Union '[] f ~ f, Split '[] f f,
53+type SetProperties f = (Union f '[] ~ f, Split f '[] f,
54+ Union '[] f ~ f, Split '[] f f,
4855 Union f f ~ f, Split f f f,
4956 Unionable f '[], Unionable '[] f)
5057
@@ -67,27 +74,44 @@ append :: Set s -> Set t -> Set (s :++ t)
6774append Empty x = x
6875append (Ext e xs) ys = Ext e (append xs ys)
6976
77+{-| Delete elements from a set -}
78+type family (m :: [k]) :\ (x :: k) :: [k] where
79+ '[] :\ x = '[]
80+ (x ': xs) :\ x = xs :\ x
81+ (y ': xs) :\ x = y ': (xs :\ x)
82+
83+class Remove s t where
84+ remove :: Set s -> Proxy t -> Set (s :\ t)
85+
86+instance Remove '[] t where
87+ remove Empty Proxy = Empty
88+
89+instance {-# OVERLAPS #-} Remove xs x => Remove (x ': xs) x where
90+ remove (Ext _ xs) x@Proxy = remove xs x
91+
92+instance {-# OVERLAPPABLE #-} (((y : xs) :\ x) ~ (y : (xs :\ x)), Remove xs x)
93+ => Remove (y ': xs) x where
94+ remove (Ext y xs) (x@Proxy) = Ext y (remove xs x)
95+
7096{-| Splitting a union a set, given the sets we want to split it into -}
7197class Split s t st where
7298 -- where st ~ Union s t
73− split :: Set st -> (Set s, Set t)
99+ split :: Set st -> (Set s, Set t)
74100
75101instance Split '[] '[] '[] where
76102 split Empty = (Empty, Empty)
77103
78−instance Split s t st => Split (x ': s) (x ': t) (x ': st) where
104+instance {-# OVERLAPPABLE #-} Split s t st => Split (x ': s) (x ': t) (x ': st) where
79105 split (Ext x st) = let (s, t) = split st
80106 in (Ext x s, Ext x t)
81107
82−instance Split s t st => Split (x ': s) t (x ': st) where
108+instance {-# OVERLAPS #-} Split s t st => Split (x ': s) t (x ': st) where
83109 split (Ext x st) = let (s, t) = split st
84− in (Ext x s, t)
110+ in (Ext x s, t)
85111
86−instance (Split s t st) => Split s (x ': t) (x ': st) where
112+instance {-# OVERLAPS #-} (Split s t st) => Split s (x ': t) (x ': st) where
87113 split (Ext x st) = let (s, t) = split st
88− in (s, Ext x t)
89−
90−
114+ in (s, Ext x t)
91115
92116{-| Remove duplicates from a sorted list -}
93117type family Nub t where
@@ -97,7 +121,7 @@ type family Nub t where
97121 Nub (e ': f ': s) = e ': Nub (f ': s)
98122
99123{-| Value-level counterpart to the type-level 'Nub'
100− Note: the value-level case for equal types is not define here,
124+ Note: the value-level case for equal types is not define here,
101125 but should be given per-application, e.g., custom 'merging' behaviour may be required -}
102126
103127class Nubable t where
@@ -112,7 +136,7 @@ instance Nubable '[e] where
112136instance Nubable (e ': s) => Nubable (e ': e ': s) where
113137 nub (Ext _ (Ext e s)) = nub (Ext e s)
114138
115−instance {-# OVERLAPS #-} (Nub (e ': f ': s) ~ (e ': Nub (f ': s)),
139+instance {-# OVERLAPS #-} (Nub (e ': f ': s) ~ (e ': Nub (f ': s)),
116140 Nubable (f ': s)) => Nubable (e ': f ': s) where
117141 nub (Ext e (Ext f s)) = Ext e (nub (Ext f s))
118142
@@ -121,13 +145,13 @@ instance {-# OVERLAPS #-} (Nub (e ': f ': s) ~ (e ': Nub (f ': s)),
121145class Subset s t where
122146 subset :: Set t -> Set s
123147
124−instance Subset '[] '[] where
148+instance Subset '[] '[] where
125149 subset xs = Empty
126150
127−instance Subset s t => Subset s (x ': t) where
151+instance {-# OVERLAPPABLE #-} Subset s t => Subset s (x ': t) where
128152 subset (Ext _ xs) = subset xs
129153
130−instance Subset s t => Subset (x ': s) (x ': t) where
154+instance {-# OVERLAPS #-} Subset s t => Subset (x ': s) (x ': t) where
131155 subset (Ext x xs) = Ext x (subset xs)
132156
133157
@@ -140,8 +164,8 @@ data Flag = FMin | FMax
140164
141165type family Filter (f :: Flag) (p :: k) (xs :: [k]) :: [k] where
142166 Filter f p '[] = '[]
143− Filter FMin p (x ': xs) = If (Cmp x p == LT) (x ': (Filter FMin p xs)) (Filter FMin p xs)
144− Filter FMax p (x ': xs) = If (Cmp x p == GT || Cmp x p == EQ) (x ': (Filter FMax p xs)) (Filter FMax p xs)
167+ Filter FMin p (x ': xs) = If (Cmp x p == LT) (x ': (Filter FMin p xs)) (Filter FMin p xs)
168+ Filter FMax p (x ': xs) = If (Cmp x p == GT || Cmp x p == EQ) (x ': (Filter FMax p xs)) (Filter FMax p xs)
145169
146170type family DeleteFromList (e :: elem) (list :: [elem]) where
147171 DeleteFromList elem '[] = '[]
@@ -174,11 +198,11 @@ instance FilterV f p '[] where
174198
175199instance (Conder ((Cmp x p) == LT), FilterV FMin p xs) => FilterV FMin p (x ': xs) where
176200 filterV f@Proxy p (Ext x xs) = cond (Proxy::(Proxy ((Cmp x p) == LT)))
177− (Ext x (filterV f p xs)) (filterV f p xs)
201+ (Ext x (filterV f p xs)) (filterV f p xs)
178202
179203instance (Conder (((Cmp x p) == GT) || ((Cmp x p) == EQ)), FilterV FMax p xs) => FilterV FMax p (x ': xs) where
180204 filterV f@Proxy p (Ext x xs) = cond (Proxy::(Proxy (((Cmp x p) == GT) || ((Cmp x p) == EQ))))
181− (Ext x (filterV f p xs)) (filterV f p xs)
205+ (Ext x (filterV f p xs)) (filterV f p xs)
182206
183207class Conder g where
184208 cond :: Proxy g -> Set s -> Set t -> Set (If g s t)
@@ -193,3 +217,20 @@ instance Conder False where
193217
194218type family Cmp (a :: k) (b :: k) :: Ordering
195219
220+{-| Membership of an element in a set, with an acommanying
221+ value-level function that returns a bool -}
222+class Member a s where
223+ member :: Proxy a -> Set s -> Bool
224+
225+instance {-# OVERLAPS #-} Member a (a ': s) where
226+ member _ (Ext x _) = True
227+
228+instance {-# OVERLAPPABLE #-} Member a s => Member a (b ': s) where
229+ member a (Ext _ xs) = member a xs
230+
231+type family MemberP a s :: Bool where
232+ MemberP a '[] = False
233+ MemberP a (a ': s) = True
234+ MemberP a (b ': s) = MemberP a s
235+
236+type NonMember a s = MemberP a s ~ False
stack.yaml+1−1
@@ -1,7 +1,7 @@
11# For more information, see: https://github.com/commercialhaskell/stack/wiki/stack.yaml
22
33# Specifies the GHC version and set of packages available (e.g., lts-3.5, nightly-2015-09-21, ghc-7.10.2)
4−resolver: lts-3.5
4+resolver: lts-12.7
55
66# Local packages, usually specified by relative directory name
77packages:
type-level-sets.cabal+31−25
@@ -1,39 +1,44 @@
11name: type-level-sets
2−version: 0.7
2+version: 0.8.9.0
33synopsis: Type-level sets and finite maps (with value-level counterparts)
4−description:
4+description:
55 This package provides type-level sets (no duplicates, sorted to provide a normal form) via 'Set' and type-level
66 finite maps via 'Map', with value-level counterparts.
77 .
8− Described in the paper \"Embedding effect systems in Haskell\" by Dominic Orchard
9− and Tomas Petricek <http://www.cl.cam.ac.uk/~dao29/publ/haskell14-effects.pdf> (Haskell Symposium, 2014). This version now uses Quicksort to normalise the representation.
8+ Described in the paper \"Embedding effect systems in Haskell\" by Dominic Orchard
9+ and Tomas Petricek <http://www.cl.cam.ac.uk/~dao29/publ/haskell14-effects.pdf> (Haskell Symposium, 2014). This version now uses Quicksort to normalise the representation.
1010 .
11− Here is a brief example for finite maps.:
11+ Here is a brief example for finite maps:
1212 .
1313 >
1414 > import Data.Type.Map
1515 >
16− > foo :: Map '["x" :-> Int, "z" :-> Int, "w" :-> Int]
17− > foo = Ext ((Var :: (Var "x")) :-> 2) $
18− > Ext ((Var :: (Var "z")) :-> 4) $
19− > Ext ((Var :: (Var "w")) :-> 5) $
20− > Empty
16+ > -- Specify how to combine duplicate key-value pairs for Int values
17+ > type instance Combine Int Int = Int
18+ > instance Combinable Int Int where
19+ > combine x y = x + y
20+ >
21+ > foo :: Map '["x" :-> Int, "z" :-> Bool, "w" :-> Int]
22+ > foo = Ext (Var :: (Var "x")) 2
23+ > $ Ext (Var :: (Var "z")) True
24+ > $ Ext (Var :: (Var "w")) 5
25+ > $ Empty
2126 >
2227 > bar :: Map '["y" :-> Int, "w" :-> Int]
23− > bar = Ext ((Var :: (Var "y")) :-> 3) $
24− > Ext ((Var :: (Var "w")) :-> 1) $
25− > Empty
26− >
27− > -- foobar :: Map '["w" :-> Int, "x" :-> Int, "y" :-> Int, "z" :-> Int]
28+ > bar = Ext (Var :: (Var "y")) 3
29+ > $ Ext (Var :: (Var "w")) 1
30+ > $ Empty
31+ >
32+ > -- foobar :: Map '["w" :-> Int, "x" :-> Int, "y" :-> Int, "z" :-> Bool]
2833 > foobar = foo `union` bar
2934 .
30− The 'Set' type for 'foobar' here shows the normalised form (sorted with no duplicates).
35+ The 'Map' type for 'foobar' here shows the normalised form (sorted with no duplicates).
3136 The type signatures is commented out as it can be infered. Running the example we get:
3237 .
33− > >>> foobar
34− > [(Var :-> 1), (Var :-> 2), (Var :-> 3), (Var :-> 4)]
38+ > >>> foobar
39+ > {w :-> 6, x :-> 2, y :-> 3, z :-> True}
3540 .
36− Thus, we see that the first value paired with the \"w\" variable is dropped.
41+ Thus, we see that the values for \"w\" are added together.
3742 For sets, here is an example:
3843 .
3944 > import GHC.TypeLits
@@ -43,7 +48,7 @@ description:
4348 > data Natural (a :: Nat) where
4449 > Z :: Natural 0
4550 > S :: Natural n -> Natural (n + 1)
46− >
51+ >
4752 > -- foo :: Set '[Natural 0, Natural 1, Natural 3]
4853 > foo = asSet $ Ext (S Z) (Ext (S (S (S Z))) (Ext Z Empty))
4954 >
@@ -58,15 +63,15 @@ description:
5863license: BSD3
5964license-file: LICENSE
6065category: Type System, Data Structures
61−copyright: 2013-16 University of Cambridge
66+copyright: 2013-18 University of Kent
6267author: Dominic Orchard
6368maintainer: Dominic Orchard
6469stability: experimental
6570build-type: Simple
6671cabal-version: >= 1.6
67−tested-with: GHC == 7.10.3
72+tested-with: GHC >= 8.2.2
6873
69−extra-source-files: example.hs
74+extra-source-files: example.hs, example2.hs, changelog.md
7075
7176
7277source-repository head
@@ -75,10 +80,11 @@ source-repository head
7580
7681library
7782 hs-source-dirs: src
83+ other-extensions: TypeInType
7884
7985
8086 exposed-modules: Data.Type.Set
8187 Data.Type.Map
82−
88+
8389 build-depends: base < 5,
84− ghc-prim
90+ ghc-prim