what is the fastest way to extract variables from a proposition?

Cetin Sert

20 Feb 2008 20 Feb '08

9:29 p.m.

-- proposition data Prp a = Var a | Not (Prp a) | Or (Prp a) (Prp a) | And (Prp a) (Prp a) | Imp (Prp a) (Prp a) | Xor (Prp a) (Prp a) | Eqv (Prp a) (Prp a) | Cns Bool deriving (Show, Eq) -- Here are to variable extraction methods -- variable extraction reference imp. -- Graham Hutton: Programming in Haskell, 107 vars_ :: Prp a → [a] vars_ (Cns _) = [] vars_ (Var x) = [x] vars_ (Not p) = vars_ p vars_ (Or p q) = vars_ p ++ vars_ q vars_ (And p q) = vars_ p ++ vars_ q vars_ (Imp p q) = vars_ p ++ vars_ q vars_ (Xor p q) = vars_ p ++ vars_ q vars_ (Eqv p q) = vars_ p ++ vars_ q -- variable extraction new * this is faster vars :: Prp a → [a] vars p = evs [p] where evs [] = [] evs (Cns _ :ps) = [] evs (Var x :ps) = x:evs ps evs (Not p :ps) = evs (p:ps) evs (Or p q:ps) = evs (p:q:ps) evs (And p q:ps) = evs (p:q:ps) evs (Imp p q:ps) = evs (p:q:ps) evs (Xor p q:ps) = evs (p:q:ps) evs (Eqv p q:ps) = evs (p:q:ps) -- for : Not (Imp (Or (Var 'p') (Var 'q')) (Var p)) -- vars_: ['p','q','p'] -- vars : ['p','q','p'] -- order and the fact that 'p' appears twice being irrelevant: -- is there an even faster way to do this? -- -- Cetin Sert -- www.corsis.de

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Ryan Ingram

21 Feb 21 Feb

2:51 a.m.

New subject: what is the fastest way to extract variables from a proposition?

It depends what you mean by "faster"; more efficient (runtime) or less typing (programmer time!) For the former, you have basically the best implementation there is; you are basically encoding the continuation of (++) into the accumulating list of arguments to evs. You might want to consider difference lists to simplify the definition, however; the performance should be comparable: newtype DList a = DL ([a] -> [a]) dlToList :: DList a -> [a] dlToList (DL l) = l [] dlSingleton :: a -> DList a dlSingleton = DL . (:) dlConcat :: DList a -> DList a -> DList a dlConcat (DL l1) (DL l2) = DL (l1 . l2) varsDL :: Prp a -> DList a varsDL (Var a) = dlSingleton a varsDL (Not a) = varsDL a varsDL (Or a b) = varsDL a `dlConcat` varsDL b -- etc. If you want less typing, consider some form of generics programming such as using "Scrap your Boilerplate"; see http://www.cs.vu.nl/boilerplate/ data Prp a = ... deriving (Eq, Show, Data, Typeable) -- note that this gives the wrong result for Prp Bool because of Cns. -- this is fixable, see http://www.cs.vu.nl/boilerplate/testsuite/foldTree.hs varsGeneric :: forall a. Typeable a => Prp a -> [a] varsGeneric = listify (\x -> case (x :: a) of _ -> True) -- ryan On 2/20/08, Cetin Sert wrote:

...

-- proposition data Prp a = Var a | Not (Prp a) | Or (Prp a) (Prp a) | And (Prp a) (Prp a) | Imp (Prp a) (Prp a) | Xor (Prp a) (Prp a) | Eqv (Prp a) (Prp a) | Cns Bool deriving (Show, Eq)

-- Here are to variable extraction methods

-- variable extraction reference imp. -- Graham Hutton: Programming in Haskell, 107 vars_ :: Prp a → [a] vars_ (Cns _) = [] vars_ (Var x) = [x] vars_ (Not p) = vars_ p vars_ (Or p q) = vars_ p ++ vars_ q vars_ (And p q) = vars_ p ++ vars_ q vars_ (Imp p q) = vars_ p ++ vars_ q vars_ (Xor p q) = vars_ p ++ vars_ q vars_ (Eqv p q) = vars_ p ++ vars_ q

-- variable extraction new * this is faster vars :: Prp a → [a] vars p = evs [p] where evs [] = [] evs (Cns _ :ps) = [] evs (Var x :ps) = x:evs ps evs (Not p :ps) = evs (p:ps) evs (Or p q:ps) = evs (p:q:ps) evs (And p q:ps) = evs (p:q:ps) evs (Imp p q:ps) = evs (p:q:ps) evs (Xor p q:ps) = evs (p:q:ps) evs (Eqv p q:ps) = evs (p:q:ps)

-- for : Not (Imp (Or (Var 'p') (Var 'q')) (Var p)) -- vars_: ['p','q','p'] -- vars : ['p','q','p']

-- order and the fact that 'p' appears twice being irrelevant: -- is there an even faster way to do this? -- -- Cetin Sert -- www.corsis.de

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

ajb＠spamcop.net

2:59 a.m.

New subject: what is the fastest way to extract variables from a proposition?

G'day all. Quoting Cetin Sert :

...

-- proposition data Prp a = Var a | Not (Prp a) | Or (Prp a) (Prp a) | And (Prp a) (Prp a) | Imp (Prp a) (Prp a) | Xor (Prp a) (Prp a) | Eqv (Prp a) (Prp a) | Cns Bool deriving (Show, Eq)

This is probably the fastest: vars :: Prp a -> [a] vars p = vars' p [] where vars' (Var a) = (a:) vars' (Not p) = vars' p vars' (Or l r) = vars' l . vars' r {- etc -} vars' (Cns _) = id Cheers, Andrew Bromage

Cetin Sert

4:10 a.m.

New subject: what is the fastest way to extract variables from a proposition?

plong 0 = Var 0 plong n | even n = Or (Var n) (plong (n-1)) | otherwise = And (Var n) (plong (n-1)) main = do print ((length ∘ vars) (plong 10000000)) real 0m3.290s user 0m3.152s sys 0m0.020s main = do print ((length ∘ vars_) (plong 10000000)) real 0m3.732s user 0m3.680s sys 0m0.024s -- vrsn=varsBromage main = do print ((length ∘ vrsn) (plong 10000000)) real 0m4.164s user 0m4.128s sys 0m0.008s ghc -fglasgow-exts -O2 ghc 6.8.2 @Andrew: It is astonishing to see that your version actually performs the worst (at least on my machine). By looking at your code I had also thought that yours would be the fastest in terms of runtime performance, it was also exactly what I tried but failed to get to here on my own. Maybe future ghc versions will change this in favour of your version. I would like to have someone test it on another machine though: fetch: svn co https://okitsune.svn.sourceforge.net/svnroot/okitsune . build: ghc -fglasgow-exts -O2 Common.hs Propositions.hs Test.hs testS: time ./a.out sert testH: time ./a.out hutton testB: time ./a.out bromage Best regards, Cetin Sert. On 21/02/2008, ajb@spamcop.net wrote:

...

G'day all.

Quoting Cetin Sert :

...
-- proposition data Prp a = Var a | Not (Prp a) | Or (Prp a) (Prp a) | And (Prp a) (Prp a) | Imp (Prp a) (Prp a) | Xor (Prp a) (Prp a) | Eqv (Prp a) (Prp a) | Cns Bool deriving (Show, Eq)

This is probably the fastest:

vars :: Prp a -> [a] vars p = vars' p [] where vars' (Var a) = (a:)

vars' (Not p) = vars' p

vars' (Or l r) = vars' l . vars' r {- etc -} vars' (Cns _) = id

Cheers, Andrew Bromage

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

Derek Elkins

4:30 a.m.

New subject: what is the fastest way to extract variables from a proposition?

On Thu, 2008-02-21 at 05:10 +0100, Cetin Sert wrote:

...

plong 0 = Var 0 plong n | even n = Or (Var n) (plong (n-1)) | otherwise = And (Var n) (plong (n-1))

compare the times again but with plong as follows: plong 0 = Var 0 plong n | even n = Or (plong (n-1)) (Var n) | otherwise = And (plong (n-1)) (Var n)

...

main = do print ((length ∘ vars) (plong 10000000)) real 0m3.290s user 0m3.152s sys 0m0.020s

main = do print ((length ∘ vars_) (plong 10000000)) real 0m3.732s user 0m3.680s sys 0m0.024s

-- vrsn=varsBromage main = do print ((length ∘ vrsn) (plong 10000000)) real 0m4.164s user 0m4.128s sys 0m0.008s

ghc -fglasgow-exts -O2 ghc 6.8.2

@Andrew: It is astonishing to see that your version actually performs the worst (at least on my machine). By looking at your code I had also thought that yours would be the fastest in terms of runtime performance, it was also exactly what I tried but failed to get to here on my own. Maybe future ghc versions will change this in favour of your version.

I would like to have someone test it on another machine though:

fetch: svn co https://okitsune.svn.sourceforge.net/svnroot/okitsune . build: ghc -fglasgow-exts -O2 Common.hs Propositions.hs Test.hs testS: time ./a.out sert testH: time ./a.out hutton testB: time ./a.out bromage

Best regards, Cetin Sert.

On 21/02/2008, ajb@spamcop.net wrote: G'day all.

Quoting Cetin Sert :

> -- proposition > data Prp a = Var a > | Not (Prp a) > | Or (Prp a) (Prp a) > | And (Prp a) (Prp a) > | Imp (Prp a) (Prp a) > | Xor (Prp a) (Prp a) > | Eqv (Prp a) (Prp a) > | Cns Bool > deriving (Show, Eq)

This is probably the fastest:

vars :: Prp a -> [a] vars p = vars' p [] where vars' (Var a) = (a:)

vars' (Not p) = vars' p

vars' (Or l r) = vars' l . vars' r {- etc -} vars' (Cns _) = id

Cheers, Andrew Bromage

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

Cetin Sert

4:54 a.m.

New subject: what is the fastest way to extract variables from a proposition?

sert@elite:~/workspace/Haskell-1/bin$ time ./theResult sert 1000001 real 0m1.384s user 0m1.148s sys 0m0.112s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult bromage 1000001 real 0m2.240s user 0m1.972s sys 0m0.176s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult bromage 10000001 real 0m59.875s user 0m58.080s sys 0m1.656s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult sert 10000001 real 0m32.043s user 0m30.930s sys 0m0.992s Hutton seems to fail miserably in both lengths here o_O I was not aware of the effect of structures on performance. Thanks for reminding me! Best Regards, Cetin Sert On 21/02/2008, Derek Elkins wrote:

...

On Thu, 2008-02-21 at 05:10 +0100, Cetin Sert wrote:

...
plong 0 = Var 0 plong n | even n = Or (Var n) (plong (n-1)) | otherwise = And (Var n) (plong (n-1))

compare the times again but with plong as follows: plong 0 = Var 0 plong n | even n = Or (plong (n-1)) (Var n) | otherwise = And (plong (n-1)) (Var n)

...
main = do print ((length ∘ vars) (plong 10000000)) real 0m3.290s user 0m3.152s sys 0m0.020s

main = do print ((length ∘ vars_) (plong 10000000)) real 0m3.732s user 0m3.680s sys 0m0.024s

-- vrsn=varsBromage main = do print ((length ∘ vrsn) (plong 10000000)) real 0m4.164s user 0m4.128s sys 0m0.008s

ghc -fglasgow-exts -O2 ghc 6.8.2

@Andrew: It is astonishing to see that your version actually performs the worst (at least on my machine). By looking at your code I had also thought that yours would be the fastest in terms of runtime performance, it was also exactly what I tried but failed to get to here on my own. Maybe future ghc versions will change this in favour of your version.

I would like to have someone test it on another machine though:

fetch: svn co https://okitsune.svn.sourceforge.net/svnroot/okitsune . build: ghc -fglasgow-exts -O2 Common.hs Propositions.hs Test.hs testS: time ./a.out sert testH: time ./a.out hutton testB: time ./a.out bromage

Best regards, Cetin Sert.

On 21/02/2008, ajb@spamcop.net wrote: G'day all.

Quoting Cetin Sert :

> -- proposition > data Prp a = Var a > | Not (Prp a) > | Or (Prp a) (Prp a) > | And (Prp a) (Prp a) > | Imp (Prp a) (Prp a) > | Xor (Prp a) (Prp a) > | Eqv (Prp a) (Prp a) > | Cns Bool > deriving (Show, Eq)

This is probably the fastest:

vars :: Prp a -> [a] vars p = vars' p [] where vars' (Var a) = (a:)

vars' (Not p) = vars' p

vars' (Or l r) = vars' l . vars' r {- etc -} vars' (Cns _) = id

Cheers, Andrew Bromage

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

ajb＠spamcop.net

4:53 a.m.

New subject: what is the fastest way to extract variables from a proposition?

G'day all. Quoting Cetin Sert :

...

It is astonishing to see that your version actually performs the worst (at least on my machine).

On your example, I'm not surprised:

...

plong 0 = Var 0 plong n | even n = Or (Var n) (plong (n-1)) | otherwise = And (Var n) (plong (n-1))

This is effectively a singly linked list. I would expect my (well, I didn't invent it) to work better on something that didn't have this unique structure, such as: test 0 = Var 0 test n | even n = Or (Var n) (test (n-1)) | otherwise = And (test (n-1)) (Var n) Cheers, Andrew Bromage

Cetin Sert

5:13 a.m.

New subject: what is the fastest way to extract variables from a proposition?

...

I would expect my (well, I didn't invent it) to work better on something that didn't have this unique structure, such as: test 0 = Var 0 test n | even n = Or (Var n) (test (n-1)) | otherwise = And (test (n-1)) (Var n)

for some reason this still does not perform as well as it should o__O I think function composition might somehow be the bottleneck behind this. --with plong 0 = Var 0 plong n | even n = Or (Var n) (plong (n-1)) | otherwise = And (plong (n-1)) (Var n) --and n = 1000000 sert@elite:~/workspace/Haskell-1/bin$ time ./theResult sert 1000001 real 0m0.692s user 0m0.624s sys 0m0.040s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult sert 1000001 real 0m0.696s user 0m0.644s sys 0m0.036s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult sert 1000001 real 0m0.840s user 0m0.744s sys 0m0.052s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult bromage 1000001 real 0m1.561s user 0m1.360s sys 0m0.100s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult bromage 1000001 real 0m1.692s user 0m1.392s sys 0m0.136s sert@elite:~/workspace/Haskell-1/bin$ time ./theResult bromage 1000001 real 0m1.959s user 0m1.580s sys 0m0.116s Best Regards, Cetin Sert On 21/02/2008, ajb@spamcop.net wrote:

...

G'day all.

Quoting Cetin Sert :

...
It is astonishing to see that your version actually performs the worst (at least on my machine).

On your example, I'm not surprised:

...
plong 0 = Var 0 plong n | even n = Or (Var n) (plong (n-1)) | otherwise = And (Var n) (plong (n-1))

This is effectively a singly linked list. I would expect my (well, I didn't invent it) to work better on something that didn't have this unique structure, such as:

test 0 = Var 0 test n | even n = Or (Var n) (test (n-1)) | otherwise = And (test (n-1)) (Var n)

Cheers, Andrew Bromage _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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ajb＠spamcop.net
Cetin Sert
Derek Elkins
Ryan Ingram