add benchmark of example

lib/src/Control/Arrow/Abstract/Join.hs

+{-# LANGUAGE Arrows #-}
 module Control.Arrow.Abstract.Join where
 
 import Prelude hiding ((.))
 
 import Control.Arrow
+import Control.Arrow.Utils
+import Data.Order(Complete(..))
 
 class Arrow c => ArrowJoin c where
   -- | Join two arrow computation with the provided upper bound operator.
@@ -11,7 +14,25 @@ class Arrow c => ArrowJoin c where
   -- @
   --   joinWith (⊔) f g = joined f g
   -- @
-  joinWith :: (z -> z -> z) -> c x z -> c y z -> c (x,y) z
+  joinWith :: (y -> y -> y) -> c x y -> c x y -> c x y
+
+joinWith' :: ArrowJoin c => (y -> y -> y) -> c x y -> c x' y -> c (x,x') y
+joinWith' lub f g = joinWith lub (f <<< pi1) (g <<< pi2)
+
+
+(<⊔>) :: (ArrowJoin c, Complete y) => c x y -> c x y -> c x y
+(<⊔>) = joinWith (⊔)
+
+-- | Joins a list of arguments. Use it with idiom brackets:
+-- @
+--   let a = ...; b = ...; xs = ...
+--   (| joinList (returnA -< a) (\x -> f -< x+b) |) xs
+-- @
+joinList :: (ArrowChoice c, ArrowJoin c, Complete y) => c (e,s) y -> c (e,(x,s)) y -> c (e,([x],s)) y
+joinList empty f = proc (e,(l,s)) -> case l of
+  [] -> empty -< (e,s)
+  [x] -> f -< (e,(x,s))
+  (x:xs) -> (f -< (e,(x,s))) <⊔> (joinList empty f -< (e,(xs,s)))
 
 instance ArrowJoin (->) where
-  joinWith lub f g = \(x,y) -> lub (f x) (g y)
+  joinWith lub f g = \x -> lub (f x) (g x)

lib/src/Control/Arrow/Conditional.hs

@@ -13,5 +13,6 @@ class Arrow c => ArrowCond v c | c -> v where
   -- | Type class constraint used by the abstract instances to join arrow computations.
   type family Join (c :: * -> * -> *) x y :: Constraint
 
+  -- TODO: Change type to if_ :: Join c (e,s) y => c (e,s) y -> c (e,s) y -> c (e, (v, s)) y
   -- | @'if_' f g -< (v,(x,y))@ performs a case distinction on the given value @v@ and executes either @(f -< x)@ or @(g -< y)@. Abstract instances might join the results of @f@ and @g@.
   if_ :: Join c (x,y) z => c x z -> c y z -> c (v, (x, y)) z

lib/src/Control/Arrow/Environment.hs

@@ -26,6 +26,7 @@ class Arrow c => ArrowEnv var val env c | c -> var, c -> val, c -> env where
   -- | Type class constraint used by the abstract instances to join arrow computations.
   type family Join (c :: * -> * -> *) x y :: Constraint
 
+  -- TODO: Change type to lookup (Join c x y) => c (e,(val,s)) y -> c (e,s) y -> c (e,(var,s)) y
   -- | Lookup a variable in the current environment. If the
   -- environment contains a binding of the variable, the first
   -- continuation is called and the second computation otherwise.

lib/src/Control/Arrow/Fix.hs

@@ -24,3 +24,4 @@ instance ArrowFix x y (->) where
 
 liftFix :: (ArrowFix (Dom t x y) (Cod t x y) c,ArrowTrans t) => (t c x y -> t c x y) -> t c x y
 liftFix f = lift $ fix (unlift . f . lift)
+{-# INLINE liftFix #-}

lib/src/Control/Arrow/Transformer/Abstract/BoundedEnvironment.hs

@@ -20,6 +20,7 @@ import           Control.Arrow.Fix
 import           Control.Arrow.Trans
 import           Control.Arrow.Reader
 import           Control.Arrow.State
+import           Control.Arrow.Abstract.Join
 import           Control.Arrow.Transformer.Const
 import           Control.Arrow.Transformer.Static
 import           Control.Arrow.Transformer.Reader
@@ -89,6 +90,7 @@ deriving instance ArrowChoice c => ArrowChoice (EnvT var addr val c)
 deriving instance ArrowState s c => ArrowState s (EnvT var addr val c)
 deriving instance ArrowFail e c => ArrowFail e (EnvT var addr val c)
 deriving instance ArrowExcept e c => ArrowExcept e (EnvT var addr val c)
+deriving instance ArrowJoin c => ArrowJoin (EnvT var addr val c)
 
 deriving instance PreOrd (c ((Map var addr val),x) y) => PreOrd (EnvT var addr val c x y)
 deriving instance Complete (c ((Map var addr val),x) y) => Complete (EnvT var addr val c x y)

lib/src/Control/Arrow/Transformer/Abstract/Contour.hs

@@ -19,6 +19,7 @@ import           Control.Arrow.Fix
 import           Control.Arrow.Trans
 import           Control.Arrow.Reader
 import           Control.Arrow.State
+import           Control.Arrow.Abstract.Join
 import           Control.Arrow.Transformer.Reader
 
 import           Control.Category
@@ -69,6 +70,7 @@ deriving instance ArrowState s c => ArrowState s (ContourT lab c)
 deriving instance ArrowEnv x y env c => ArrowEnv x y env (ContourT lab c)
 deriving instance ArrowFail e c => ArrowFail e (ContourT lab c)
 deriving instance ArrowExcept e c => ArrowExcept e (ContourT lab c)
+deriving instance ArrowJoin c => ArrowJoin (ContourT lab c)
 
 deriving instance PreOrd (c (CallString lab,x) y) => PreOrd (ContourT lab c x y)
 deriving instance LowerBounded (c (CallString lab,x) y) => LowerBounded (ContourT lab c x y)

lib/src/Control/Arrow/Transformer/Abstract/Except.hs

@@ -49,22 +49,22 @@ instance (ArrowChoice c, ArrowJoin c, Complete e) => Category (ExceptT e c) wher
       SuccessOrFail e y' -> do
         -- Ideally we would like to write '(returnA -< Fail e) ⊔ (f -< y)',
         -- however this is not possible, because the result type of
-        -- 'f', 'UncertainError e z', is not 'Complete' because 'z' is not
+        -- 'f', 'Error e z', is not 'Complete' because 'z' is not
         -- 'Complete'. However, in '(returnA -< Fail e) ⊔ (f -< y)' we
         -- actually never join to values of type 'z'.
-        joinWith (\(Fail e) er -> case er of
+        joinWith' (\(Fail e) er -> case er of
             Success z          -> SuccessOrFail e z
             Fail e'            -> Fail (e ⊔ e')
             SuccessOrFail e' z -> SuccessOrFail (e ⊔ e') z)
           id (unlift f) -< (Fail e,y')
 
 instance (ArrowChoice c, ArrowJoin c, Complete e) => Arrow (ExceptT e c) where
-  arr f = lift' (arr f)
-  first f = lift $ first (unlift f) >>^ strength1
+  arr f    = lift' (arr f)
+  first f  = lift $ first (unlift f) >>^ strength1
   second f = lift $ second (unlift f) >>^ strength2
 
 instance (Complete e, ArrowJoin c, ArrowChoice c) => ArrowChoice (ExceptT e c) where
-  left f = lift $ left (unlift f) >>^ strength1
+  left f  = lift $ left (unlift f) >>^ strength1
   right f = lift $ right (unlift f) >>^ strength2
 
 instance (Complete e, ArrowJoin c, ArrowApply c, ArrowChoice c) => ArrowApply (ExceptT e c) where

lib/src/Control/Arrow/Transformer/Abstract/Fixpoint.hs

@@ -85,21 +85,21 @@ liftFixT f = FixT $ \_ -> ((\((_,o),x) -> (o,x)) ^>> second (f >>^ Terminating))
 #ifndef TRACE
 instance (Identifiable x, PreOrd y, ArrowChoice c) => ArrowFix x y (FixT s x y c) where
   fix f = proc x -> do
-    old <- getOutCache -< ()
+    old <- getCache -< ()
     -- reset the current fixpoint cache
-    setOutCache -< bottom
+    setCache -< bottom
 
     -- recompute the fixpoint cache by calling 'f' and memoize its results.
-    y <- localInCache (F.fix (memoize . f)) -< (old,x)
+    y <- localOldCache (F.fix (memoize . f)) -< (old,x)
 
-    new <- getOutCache -< ()
+    new <- getCache -< ()
 
     -- In case the new fixpoint cache contains less information than
     -- the old cache, we are in the reductive set of `f` and have
     -- overshot the fixpoint and stop recursion.  Otherwise, we have
     -- not reached the fixpoint yet and need to continue improving the
     -- fixpoint cache.
-    if (new ⊑ old)
+    if {-# SCC "Fix.Cache.comparison" #-}(new ⊑ old)
     then returnA -< y
     else fix f -< x
 
@@ -107,29 +107,29 @@ instance (Identifiable x, PreOrd y, ArrowChoice c) => ArrowFix x y (FixT s x y c
 -- has been computed before, the cached value is returned and will not
 -- be recomputed.
 memoize :: (Identifiable x, PreOrd y, ArrowChoice c) => FixT s x y c x y -> FixT s x y c x y
-memoize (FixT f) = FixT $ \(stackWidening,widening) -> proc (((stack,inCache), outCache),x) -> do
-  case M.unsafeLookup x outCache of
+memoize (FixT f) = FixT $ \(stackWidening,widening) -> proc (((stack,oldCache), newCache),x) -> do
+  case M.unsafeLookup x newCache of
     -- In case the input was in the fixpoint cache, short-cut
     -- recursion and return the cached value.
-    Just y -> returnA -< (outCache,y)
+    Just y -> returnA -< (newCache,y)
 
     -- In case the input was not in the fixpoint cache, initialize the
     -- cache with previous knowledge about the result or ⊥, compute
     -- the result of the function and update the fixpoint cache.
     Nothing -> do
-      let yOld = fromMaybe bottom (M.unsafeLookup x inCache)
-          outCache' = M.insert x yOld outCache
+      let yOld = fromMaybe bottom (M.unsafeLookup x oldCache)
+          newCache' = M.insert x yOld newCache
           (x',stack') = runState (stackWidening x) stack 
-      (outCache'',y) <- f (stackWidening,widening) -< (((stack',inCache), outCache'),x')
-      let outCache''' = M.unsafeInsertWith (flip (T.widening widening)) x' y outCache''
-          y' = fromJust (M.unsafeLookup x' outCache''')
-      returnA -< (outCache''',y')
+      (newCache'',y) <- f (stackWidening,widening) -< (((stack',oldCache), newCache'),x')
+      let newCache''' = M.unsafeInsertWith (flip (T.widening widening)) x' y newCache''
+          y' = fromJust (M.unsafeLookup x' newCache''')
+      returnA -< (newCache''',y')
 
 #else
               
 instance (Show x, Show y, Identifiable x, PreOrd y, ArrowChoice c) => ArrowFix x y (FixT s x y c) where
   fix f =  proc x -> do
-    old <- getOutCache -< ()
+    old <- getCache -< ()
     setOutCache -< bottom
     y <- localInCache (F.fix (memoize . f)) -< trace "----- ITERATION -----" $ (old,x)
     new <- getOutCache -< ()
@@ -155,14 +155,14 @@ memoize (FixT f) = FixT $ \(stackWidening,widening) -> proc (((stack,inCache), o
               
 #endif
 
-getOutCache :: Arrow c => FixT s x y c () (Map x (Terminating y))
-getOutCache = FixT $ \_ -> arr $ \((_,o),()) -> (o,return o)
+getCache :: Arrow c => FixT s x y c () (Map x (Terminating y))
+getCache = FixT $ \_ -> arr $ \((_,o),()) -> (o,return o)
 
-setOutCache :: Arrow c => FixT s x y c (Map x (Terminating y)) ()
-setOutCache = FixT $ \_ -> arr $ \((_,_),o) -> (o,return ())
+setCache :: Arrow c => FixT s x y c (Map x (Terminating y)) ()
+setCache = FixT $ \_ -> arr $ \((_,_),o) -> (o,return ())
 
-localInCache :: Arrow c => FixT s x y c x y -> FixT s x y c (Map x (Terminating y),x) y
-localInCache (FixT f) = FixT $ \w -> proc (((s,_),o),(i,x)) -> f w -< (((s,i),o),x)
+localOldCache :: Arrow c => FixT s x y c x y -> FixT s x y c (Map x (Terminating y),x) y
+localOldCache (FixT f) = FixT $ \w -> proc (((s,_),o),(i,x)) -> f w -< (((s,i),o),x)
 
 instance ArrowChoice c => Category (FixT s i o c) where
   id = liftFixT id
@@ -191,9 +191,9 @@ instance (ArrowChoice c, ArrowApply c) => ArrowApply (FixT s i o c) where
   app = FixT $ \w -> (\(io,(FixT f,x)) -> (f w,(io,x))) ^>> app
 
 instance (Identifiable i, Complete o, ArrowJoin c, ArrowChoice c) => ArrowJoin (FixT s i o c) where
-  joinWith lub (FixT f) (FixT g) = FixT $ \w -> proc ((i,o),(x,y)) -> do
+  joinWith lub (FixT f) (FixT g) = FixT $ \w -> proc ((i,o),x) -> do
     (o',t1) <- f w -< ((i,o),x)
-    (o'',t2) <- g w -< ((i,o'),y)
+    (o'',t2) <- g w -< ((i,o'),x)
     returnA -< (o'',case (t1,t2) of
       (Terminating y',Terminating v') -> Terminating (lub y' v')
       (Terminating y',NonTerminating) -> Terminating y'

lib/src/Control/Arrow/Transformer/Abstract/ReachingDefinitions.hs

@@ -31,6 +31,7 @@ import           Control.Arrow.Fail
 import           Control.Arrow.Random
 import           Control.Arrow.Store as Store
 import           Control.Arrow.Environment
+import           Control.Arrow.Abstract.Join
 import           Control.Arrow.Transformer.Reader
 
 import           Data.Identifiable
@@ -88,6 +89,7 @@ deriving instance ArrowExcept e c => ArrowExcept e (ReachingDefsT lab c)
 deriving instance ArrowState s c => ArrowState s (ReachingDefsT lab c)
 deriving instance ArrowEnv x y env c => ArrowEnv x y env (ReachingDefsT lab c)
 deriving instance ArrowCond val c => ArrowCond val (ReachingDefsT lab c)
+deriving instance ArrowJoin c => ArrowJoin (ReachingDefsT lab c)
 
 deriving instance PreOrd (c (Dom (ReachingDefsT lab) x y) (Cod (ReachingDefsT lab) x y)) => PreOrd (ReachingDefsT lab c x y)
 deriving instance LowerBounded (c (Dom (ReachingDefsT lab) x y) (Cod (ReachingDefsT lab) x y)) => LowerBounded (ReachingDefsT lab c x y)

lib/src/Control/Arrow/Transformer/Abstract/Stack.hs

+{-# LANGUAGE Arrows #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE TypeFamilies #-}
+module Control.Arrow.Transformer.Abstract.Stack(StackT,runStackT,runStackT') where
+
+import           Prelude hiding ((.))
+
+import           Control.Category
+import           Control.Arrow
+import           Control.Arrow.Fix
+import           Control.Arrow.Trans
+import           Control.Arrow.Abstract.Join
+import           Control.Arrow.Transformer.Const
+import           Control.Arrow.Transformer.Static
+
+import qualified Control.Monad.State as M
+
+import           Data.Order
+import           Data.Abstract.StackWidening (StackWidening)
+
+newtype StackT s a c x y = StackT (ConstT (StackWidening s a,s a) c x y)
+  deriving (Category,Arrow,ArrowChoice,ArrowLift,ArrowJoin,PreOrd,Complete)
+instance ArrowApply c => ArrowApply (StackT s a c) where app = StackT ((\(StackT f,x) -> (f,x)) ^>> app)
+
+runStackT :: Arrow c => (StackWidening s a,s a) -> StackT s a c x y -> c x y
+runStackT s (StackT f) = runConstT s f
+
+runStackT' :: (Arrow c, Monoid (s a)) => StackWidening s a -> StackT s a c x y -> c x y
+runStackT' s = runStackT (s,mempty)
+
+stackT :: ((StackWidening s a,s a) -> c x y) -> StackT s a c x y
+stackT f = StackT $ ConstT $ StaticT $ f
+
+type instance Fix x y (StackT s () c) = StackT s x (Fix x y c)
+instance (ArrowApply c, ArrowFix x y c) => ArrowFix x y (StackT s x c) where
+  fix f = stackT $ \(stackWidening,stack) -> proc x -> do
+    let (x',stack') = M.runState (stackWidening x) stack
+    fix (runStackT (stackWidening,stack') . f . lift') -<< x'
+

lib/src/Control/Arrow/Transformer/Reader.hs

@@ -93,23 +93,23 @@ instance ArrowFix (Dom (ReaderT r) x y) (Cod (ReaderT r) x y) c => ArrowFix x y
   fix = liftFix
 
 instance ArrowExcept e c => ArrowExcept e (ReaderT r c) where
-  type instance Join (ReaderT r c) (x,(x,e)) y = Exc.Join c ((r,x),((r,x),e)) y
+  type instance Join (ReaderT r c) (x,(x,e)) y = Exc.Join c (Dom (ReaderT r) x y,(Dom (ReaderT r) x y,e)) (Cod (ReaderT r) x y)
   throw = lift' throw
-  catch (ReaderT f) (ReaderT g) = ReaderT $ catch f (from assoc ^>> g)
-  finally (ReaderT f) (ReaderT g) = ReaderT $ finally f g
+  catch f g = lift $ catch (unlift f) (from assoc ^>> unlift g)
+  finally f g = lift $ finally (unlift f) (unlift g)
 
 instance ArrowDeduplicate (r, x) y c => ArrowDeduplicate x y (ReaderT r c) where
-  dedup (ReaderT f) = ReaderT (dedup f)
+  dedup f = lift (dedup (unlift f))
 
 instance ArrowJoin c => ArrowJoin (ReaderT r c) where
-  joinWith lub (ReaderT f) (ReaderT g) = ReaderT $ (\(r,(x,y)) -> ((r,x),(r,y))) ^>> joinWith lub f g
+  joinWith lub f g = lift $ joinWith lub (unlift f) (unlift g)
 
 instance ArrowConst x c => ArrowConst x (ReaderT r c) where
   askConst = lift' askConst
 
 instance ArrowCond v c => ArrowCond v (ReaderT r c) where
-  type instance Join (ReaderT r c) (x,y) z = Cond.Join c ((r,x),(r,y)) z
-  if_ (ReaderT f) (ReaderT g) = ReaderT $ (\(r,(v,(x,y))) -> (v,((r,x),(r,y)))) ^>> if_ f g
+  type instance Join (ReaderT r c) (x,y) z = Cond.Join c (Dom (ReaderT r) x z,Dom (ReaderT r) y z) (Cod (ReaderT r) (x,y) z)
+  if_ f g = lift $ (\(r,(v,(x,y))) -> (v,((r,x),(r,y)))) ^>> if_ (unlift f) (unlift g)
 
 deriving instance PreOrd (c (r,x) y) => PreOrd (ReaderT r c x y)
 deriving instance LowerBounded (c (r,x) y) => LowerBounded (ReaderT r c x y)

lib/src/Control/Arrow/Transformer/State.hs

@@ -113,7 +113,7 @@ instance (Eq s, Hashable s, ArrowDeduplicate (Dom (StateT s) x y) (Cod (StateT s
 
 instance (ArrowJoin c, Complete s) => ArrowJoin (StateT s c) where
   joinWith lub f g =
-    lift $ (\(s,(x,y)) -> ((s,x),(s,y))) ^>> joinWith (\(s1,z1) (s2,z2) -> (s1⊔s2,lub z1 z2)) (unlift f) (unlift g)
+    lift $ joinWith (\(s1,z1) (s2,z2) -> (s1⊔s2,lub z1 z2)) (unlift f) (unlift g)
 
 instance ArrowConst x c => ArrowConst x (StateT s c) where
   askConst = lift' askConst

lib/src/Data/Abstract/FreeCompletion.hs

 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE DeriveGeneric #-}
 {-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE DeriveTraversable #-}
 {-# LANGUAGE TypeFamilies #-}
@@ -7,16 +8,20 @@ module Data.Abstract.FreeCompletion where
 
 import Control.Applicative
 import Control.Monad
+import Control.DeepSeq
 import Data.Abstract.Widening
 import Data.Hashable
 import Data.Order
+import GHC.Generics(Generic)
 
-data FreeCompletion a = Lower a | Top deriving (Eq,Functor,Traversable,Foldable)
+data FreeCompletion a = Lower a | Top deriving (Eq,Functor,Traversable,Foldable,Generic)
 
 instance Show a => Show (FreeCompletion a) where
   show Top = "⊤"
   show (Lower a) = show a
 
+instance NFData a => NFData (FreeCompletion a)
+
 instance Hashable a => Hashable (FreeCompletion a) where
   hashWithSalt s (Lower a) = s `hashWithSalt` a
   hashWithSalt s Top = s `hashWithSalt` (2::Int)
@@ -52,6 +57,15 @@ instance (PreOrd a, UpperBounded (FreeCompletion a),
     (Lower a, Lower b) -> Lower (a,b)
     (_,_) -> Top
 
+instance (PreOrd x, Complete (FreeCompletion x)) => Complete (FreeCompletion [x]) where
+  Lower xs ⊔ Lower ys | eqLength xs ys = zipWithM (\x y -> Lower x ⊔ Lower y) xs ys
+    where
+      eqLength :: [a] -> [b] -> Bool
+      eqLength [] [] = True
+      eqLength (_:as) (_:bs) = eqLength as bs
+      eqLength _ _ = False
+  _ ⊔ _ = Top
+
 
 instance CoComplete a => CoComplete (FreeCompletion a) where
   Lower a ⊓ Lower b = Lower (a ⊓ b) 

lib/src/Data/Abstract/Map.hs

@@ -10,8 +10,8 @@ import           Prelude hiding (lookup,map,Either(..),(**))
 
 import           Control.Arrow
 
-import           Data.HashMap.Lazy (HashMap)
-import qualified Data.HashMap.Lazy as H
+import           Data.HashMap.Strict (HashMap)
+import qualified Data.HashMap.Strict as H
 import           Data.Hashable
 import           Data.Order
 import           Data.Identifiable
@@ -35,16 +35,19 @@ instance (Show a,Show b) => Show (Map a b) where
     | otherwise = "[" ++ init (unwords [ printf "%s%s -> %s," (show k) (show t) (show v) | (k,(t,v)) <- H.toList h]) ++ "]"
 
 instance (Identifiable a, PreOrd b) => PreOrd (Map a b) where
-  Map m1 ⊑ m2 = all (\(k,(t,v)) -> (case t of Must -> M.Just v; May -> M.JustNothing v) ⊑ lookup k m2) (H.toList m1)
+  Map m1 ⊑ m2 = {-# SCC "Data.Abstract.Map.lt" #-} all (\(k,(t,v)) -> (case t of Must -> M.Just v; May -> M.JustNothing v) ⊑ lookup k m2) (H.toList m1)
 
 instance (Identifiable a, Complete b) => Complete (Map a b) where
-  Map m1 ⊔ Map m2 = Map $ H.map join $ H.unionWith (⊔) (H.map Left m1) (H.map Right m2)
+  m1 ⊔ m2 = {-# SCC "Data.Abstract.Map.join" #-} widening (⊔) m1 m2
+
+widening :: Identifiable a => Widening b -> Widening (Map a b)
+widening w (Map m1) (Map m2) = Map $ H.map join $ H.unionWith (E.widening (finite ** w) (finite ** w)) (H.map Left m1) (H.map Right m2)
     where
-      join :: Complete a => Either (There,a) (There,a) -> (There,a)
       join e = case e of
         Left (_,a) -> (May,a)
         Right (_,b) -> (May,b)
-        LeftRight (t1,a) (t2,b) -> (t1 ⊔ t2,a ⊔ b)
+        LeftRight (t1,a) (t2,b) -> (t1 ⊔ t2,a `w` b)
+{-# SCC widening #-}
 
 instance (Identifiable a, PreOrd b) => LowerBounded (Map a b) where
   bottom = empty
@@ -100,14 +103,6 @@ adjust f a (Map m) = Map (H.adjust (second f) a m)
 compose :: (Identifiable a, Identifiable b, Complete c) => [(a,b)] -> Map b c -> Map a c
 compose f (Map g) = Map $ H.fromListWith (⊔) [ (a,c) | (a,b) <- f, Just c <- return $ H.lookup b g ]
 
-widening :: Identifiable a => Widening b -> Widening (Map a b)
-widening w (Map m1) (Map m2) = Map $ H.map join $ H.unionWith (E.widening (finite ** w) (finite ** w)) (H.map Left m1) (H.map Right m2)
-    where
-      join e = case e of
-        Left (_,a) -> (May,a)
-        Right (_,b) -> (May,b)
-        LeftRight (t1,a) (t2,b) -> (t1 ⊔ t2,a `w` b)
-
 instance Identifiable a => IsList (Map a b) where
   type Item (Map a b) = (a,b)
   toList (Map m) = H.toList (H.map snd m)

lib/src/Data/Abstract/Terminating.hs

+{-# LANGUAGE DeriveGeneric #-}
 {-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE DeriveTraversable #-}
 module Data.Abstract.Terminating where
 
 import Control.Monad
 import Control.Applicative
+import Control.DeepSeq
 
 import Data.Order
 import Data.Abstract.Widening
 
+import GHC.Generics
+
 -- Free cocompletion of a type
-data Terminating a = NonTerminating | Terminating a deriving (Eq,Functor,Traversable,Foldable)
+data Terminating a = NonTerminating | Terminating a deriving (Eq,Functor,Traversable,Foldable,Generic)
+instance NFData a => NFData (Terminating a)
 
 fromTerminating :: a -> Terminating a -> a
 fromTerminating _ (Terminating a) = a

lib/src/Data/Order.hs

@@ -37,23 +37,14 @@ lub = foldr1 (⊔)
 
 joined :: (Arrow c, Complete (c (a1,a2) b)) => c a1 b -> c a2 b -> c (a1,a2) b
 joined f1 f2 = (arr fst >>> f1) ⊔ (arr snd >>> f2)
-
--- What we actually would like to write is this:
--- joined f1 f2 = proc (x1,x2) -> (f1 -< x1) ⊔ (f2 -< x2)
-
--- This is what the compiler desugars it to (we simplified it):
--- joined =
---   (arr (\(x1, x2) -> ((x2, x1), ())) )
---   >>>
---   (op
---         (arr (\((x2,x1), b) -> (x1, b))) >>> arr fst >>> f1   ::  c ((x2,x1,b)) r
---         (arr (\((x2,x1),b) -> (x2,b)) >>> arr fst >>> f2   ::     c ((x2,x1),b) r
+{-# DEPRECATED joined "Use Control.Arrow.Abstract.ArrowJoin.<⊔>" #-}
 
 lubA :: (ArrowChoice c, Complete (c (x,[x]) y), LowerBounded (c () y)) => c x y -> c [x] y
 lubA f = proc l -> case l of
   [] -> bottom -< ()
   -- (x:xs) -> (f -< x) ⊔ (lubA f -< xs) causes an type error.
   (x:xs) -> joined f (lubA f) -< (x, xs)
+{-# DEPRECATED lubA "Use Control.Arrow.Abstract.ArrowJoin.joinList" #-}
 
 -- | Order with all greatest lower bounds
 class PreOrd x => CoComplete x where

pcf/default.nix

-{ pkgs ? import <nixpkgs> {} }:
-
-let
-  hsEnv = pkgs.haskellPackages.ghcWithPackages(p: with p; [
-    Cabal cabal-install hlint text containers hspec mtl numeric-limits criterion fgl
-    (p.callPackage ../lib/default.nix { })
-  ]);
-
-in pkgs.stdenv.mkDerivation {
-  name = "sturdy-pcf";
-  version = "0.0.1";
-  src = ./.;
-  buildInputs = [
-    hsEnv
-  ];
-}

pcf/src/IntervalAnalysis.hs

@@ -28,6 +28,7 @@ import           Control.Arrow.Fix
 import           Control.Arrow.Trans
 import           Control.Arrow.Conditional as Cond
 import           Control.Arrow.Environment
+import           Control.Arrow.Abstract.Join
 import           Control.Arrow.Transformer.Abstract.Contour
 import           Control.Arrow.Transformer.Abstract.BoundedEnvironment
 import           Control.Arrow.Transformer.Abstract.Failure
@@ -96,7 +97,7 @@ evalInterval k env e = -- runInterp eval ?bound k env (generate e)
                $ SW.reuse (\_ l -> head l)
                $ SW.fromWidening (F.widening widenVal)
 
-newtype IntervalT c x y = IntervalT { runIntervalT :: c x y } deriving (Category,Arrow,ArrowChoice,ArrowFail e, PreOrd, Complete, LowerBounded)
+newtype IntervalT c x y = IntervalT { runIntervalT :: c x y } deriving (Category,Arrow,ArrowChoice,ArrowFail e,ArrowJoin)
 type instance Fix x y (IntervalT c) = IntervalT (Fix x y c)
 deriving instance ArrowFix x y c => ArrowFix x y (IntervalT c)
 deriving instance ArrowEnv var val env c => ArrowEnv var val env (IntervalT c)
@@ -107,35 +108,36 @@ instance ArrowTrans IntervalT where
   lift = IntervalT
   unlift = runIntervalT
 
-instance (ArrowChoice c, ArrowFail String c) => IsVal Val (IntervalT c) where
+instance (ArrowChoice c, ArrowFail String c, ArrowJoin c) => IsVal Val (IntervalT c) where
   succ = proc x -> case x of
-    Top -> returnA -< Top
+    Top -> (returnA -< NumVal top) <⊔> (fail -< "Expected a number as argument for 'succ'")
     NumVal n -> returnA -< NumVal $ n + 1 -- uses the `Num` instance of intervals
     ClosureVal _ -> fail -< "Expected a number as argument for 'succ'"
   pred = proc x -> case x of
-    Top -> returnA -< Top
+    Top -> (returnA -< NumVal top) <⊔> (fail -< "Expected a number as argument for 'pred'")
     NumVal n -> returnA -< NumVal $ n - 1
     ClosureVal _ -> fail -< "Expected a number as argument for 'pred'"
   zero = proc _ -> returnA -< (NumVal 0)
 
-instance (ArrowChoice c, ArrowFail String c) => ArrowCond Val (IntervalT c) where
-  type Join (IntervalT c) x y = Complete (IntervalT c x y)
+instance (ArrowChoice c, ArrowJoin c, ArrowFail String c) => ArrowCond Val (IntervalT c) where
+  type Join (IntervalT c) x y = Complete y
   if_ f g = proc v -> case v of
-    (Top, (x,y)) -> joined f g -< (x,y)
+    (Top, (x,y)) -> (f -< x) <⊔> (g -< y) <⊔> (fail -< "Expected a number as condition for 'ifZero'")
     (NumVal (I.Interval i1 i2), (x, y))
-      | (i1, i2) == (0, 0) -> f -< x              -- case the interval is exactly zero
-      | i1 > 0 || i2 < 0   -> g -< y              -- case the interval does not contain zero
-      | otherwise          -> joined f g -< (x,y) -- case the interval contains zero and other numbers.
-    (ClosureVal _, _) -> fail -< "Expected a number as condition for 'ifZero'"
+      | (i1, i2) == (0, 0) -> f -< x                -- case the interval is exactly zero
+      | i1 > 0 || i2 < 0   -> g -< y                -- case the interval does not contain zero
+      | otherwise          -> (f -< x) <⊔> (g -< y) -- case the interval contains zero and other numbers.
+    (ClosureVal _, _)      -> fail -< "Expected a number as condition for 'ifZero'"
 
-instance (ArrowChoice c, ArrowFail String c, LowerBounded (IntervalT c () Val), Complete (IntervalT c (((Expr, F.Map Text Addr Val),Val),[((Expr, F.Map Text Addr Val), Val)]) Val))
+instance (ArrowChoice c, ArrowFail String c, ArrowJoin c)
     => IsClosure Val (F.Map Text Addr Val) (IntervalT c) where
   closure = arr $ \(e, env) -> ClosureVal (Closure [(e,env)])
   applyClosure f = proc (fun, arg) -> case fun of
     Top -> returnA -< Top
     ClosureVal (Closure cls) ->
       -- Apply the interpreter function `f` on all closures and join their results.
-      lubA (proc ((e,env),arg) -> f -< ((e,env),arg)) -< [ (c,arg) | c <- toList cls]
+      (| joinList (returnA -< Top) (\(e,env) -> f -< ((e,env),arg)) |)