Hudak state emulation discussion - can you give me some idea? - Beginners

Hudak state emulation discussion - can you give me some idea?

Girish Bhat

17 Mar 2009 17 Mar '09

5:02 a.m.

Hi Everyone, I was going through the classic Hudak paper "Conception, Evolution, and Application of Functional Programming". Probably the most valuable part is towards the end where he talks about how state is represented in Haskell. On Page 48 of the PDF (page 406 of the ACM Computing survey volume), he gives the following equations "For expository purposes we would like to make the state as implicit as possible, and thus we express the result as a composition of higher-order functions. To facilitate this and to make the result look as much like the original program as possible, we define the following higher-order infix operators and functions": 1 f:=g =\s -> +fs(gs) 2 f;g =\s -> g(fs)=\s-+fs(gs) 3 f;g =\s -> g(fs) 4 goto f = f 5 f+‘g=\s-+fs+gs 6 f<‘g=\s-+fs

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Benjamin L.Russell

17 Mar 17 Mar

10:49 p.m.

New subject: Hudak state emulation discussion - can you give me some idea?

On Tue, 17 Mar 2009 14:32:24 +0530, Girish Bhat wrote:

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Hi Everyone,

I was going through the classic Hudak paper "Conception, Evolution, and Application of Functional Programming". Probably the most valuable part is towards the end where he talks about how state is represented in Haskell. On Page 48 of the PDF (page 406 of the ACM Computing survey volume), he gives the following equations "For expository purposes we would like to make the state as implicit as possible, and thus we express the result as a composition of higher-order functions. To facilitate this and to make the result look as much like the original program as possible, we define the following higher-order infix operators and functions":

1 f:=g =\s -> +fs(gs)

2? ?f;g =\s -> g(fs)=\s-+fs(gs)

3? ?f;g =\s -> g(fs)

4 goto f = f

5 f+‘g=\s-+fs+gs

6 f<‘g=\s-+fs
7 if’ p c = \s + (if (p s) then (c s) else s)

Unfortunately I am unable to parse/understand what he is doing here. My closure understanding too seems to be wonky. :) Would someone be kind enough to translate each of the above into plain english and explain how to read such eqns in the future?

(FYI, there is a copy of the above-mentioned paper that doesn't require an ACM account available at http://www.cs.berkeley.edu/~jcondit/pl-prelim/hudak89functional.pdf.) Hudak is just defining a series of higher-order infix operators and functions. (You have made some notational errors in the above-mentioned notation, so I am revising it to match the paper as below.) A backslash denotes a lambda symbol; i.e., whatever immediately follows the lambda is a parameter in the following equation. Specifically:

...

1 f := g =\s -> f s (g s)

In other words, the infix operator ':=' works between functions f and g such that lambda s -> f s (g s).

...

2 f ; g = \s -> g (f s)

In other words, the infix operator ';' works between functions f and g such that lambda s -> g (f s).

...

3? ?f;g =\s -> g(fs)

I couldn't find this equation on p. 406 of the volume; where did you find it?

...

4 goto f = f

In other words, the function "goto" applied to f is defined as simply f.

...

5 f +' g = \s -> f s + g s

In other words, the infix operator '+'' works between functions f and g such that lambda s -> f s + g s.

...

6 f <' g = \s -> f s < g s

In other words, the infix operator '<'' works between functions f and g such that lambda s -> f s < g s.

...

7 if' p c = \s -> (if (p s) then (c s) else s)

In other words, the function "if'" applied to functions p and c is such that lambda p c -> (if (p s) then (c s) else s). Hope this helps.... -- Benjamin L. Russell -- Benjamin L. Russell / DekuDekuplex at Yahoo dot com http://dekudekuplex.wordpress.com/ Translator/Interpreter / Mobile: +011 81 80-3603-6725 "Furuike ya, kawazu tobikomu mizu no oto." -- Matsuo Basho^

Girish Bhat

18 Mar 18 Mar

3:32 a.m.

New subject: Hudak state emulation discussion - can you give me some idea?

...

(FYI, there is a copy of the above-mentioned paper that doesn't require an ACM account available at http://www.cs.berkeley.edu/~jcondit/pl-prelim/hudak89functional.pdf.)

Hudak is just defining a series of higher-order infix operators and functions. (You have made some notational errors in the above-mentioned notation, so I am revising it to match the paper as below.) A backslash denotes a lambda symbol; i.e., whatever

Sorry about that.

...

...
3? ?f;g =\s -> g(fs)

I couldn't find this equation on p. 406 of the volume; where did you find it?

Again my transcription error.

...

In other words, the function "if'" applied to functions p and c is such that lambda p c -> (if (p s) then (c s) else s).

Hope this helps....

Thanks! It does. I think what threw me was that while there is enough redundancy in what he states for someone more clever than me, he would have explicitly stated before hand that he was defining the operators [:=], [+'], ['if] etc.:) thanks again.

Benjamin L.Russell

5:59 a.m.

New subject: Hudak state emulation discussion - can you give me some idea?

On Wed, 18 Mar 2009 13:02:34 +0530, Girish Bhat wrote:

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...
[...]

Hope this helps....

Thanks! It does. I think what threw me was that while there is enough redundancy in what he states for someone more clever than me, he would have explicitly stated before hand that he was defining the operators [:=], [+'], ['if] etc.:)

But he did; specifically, on pages 405 (the previous page) to 406 of the volume, Hudak writes as follows:

...

For expository purposes we would like to make the state as implicit as possible, and thus we express the result as a composition of higher-order functions. To facilitate this and to make the result look as much like the original program as possible, we define the following higher-order infix operators and functions(22):

So he did in fact explicitly state beforehand that he was defining those operators. -- Benjamin L. Russell -- Benjamin L. Russell / DekuDekuplex at Yahoo dot com http://dekudekuplex.wordpress.com/ Translator/Interpreter / Mobile: +011 81 80-3603-6725 "Furuike ya, kawazu tobikomu mizu no oto." -- Matsuo Basho^

Will Ness

10:45 a.m.

New subject: Hudak state emulation discussion - can you give me some idea?

Benjamin L. Russell writes:

...

On Wed, 18 Mar 2009 13:02:34 +0530, Girish Bhat wrote:

...
...
[...]

Thanks! It does. I think what threw me was that while there is enough redundancy in what he states for someone more clever than me, he would have explicitly stated before hand that he was defining the operators [:=], [+'], ['if] etc.:)

But he did; specifically, on pages 405 (the previous page) to 406 of

So he did in fact explicitly state beforehand that he was defining those operators.

What he didn't do, is specify the precedences associativities of these operators. It seems that for the definitions to make sense, together with the code that follows them in the article, the fixity declarations ought to be as e.g. infixl 8 +' infix 8 <' infix 7 := infixl 6 ; -- infixr is good too (p; q) s = q (p s) -- (;) = CB -- flip (.) (x:=f) s = x s (f s) -- (:=) = S goto f s = f s -- id = I (f+'g) s = f s + g s (f<'g) s = f s < g s if' p c s = if (p s) then (c s) else s x' (a,b) = a i' (a,b) = b so that ( x:=f ; i:=g ; x:=h ) would parse as ( ( (x:=f) ; (i:=g) ) ; (x:=h) ) , so that ( x:=f ; i:=g ; x:=h ) s = (x:=h) . (i:=g) . (x:=f) $ s The types involved would be as follows. 's' denotes state; (_:=_) denote state transformers of type (s -> s) (for them to be composable). 'x' and 'f' in (x:=f) are f :: s -> v -- value producer (including x' and i') x :: s v -> s -- state updater (with the new value) so that the combination (x:=f) s = x s (f s) has 'f' produce a new value and 'x' update its supplied state with it: (x:=f) s = s' where v = f s; s' = x s v The whole combination as presented in the article actually defines a new function to perform all these activities, and would be defined as prog = x := const 1 ; i := const 0 ; loop where loop = x := f ; i := i' +' const 1 ; if' (i' <' const 10) (goto loop) and used as prog initState where initState = (0,0) or something like that. Which is all very reminiscent of monad, a "programmable semicolon". Cheers,

Will Ness

11:36 a.m.

New subject: Hudak state emulation discussion - can you give me some idea?

Will Ness writes:

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infixl 8 +' infix 8 <' infix 7 := infixl 6 ; -- infixr is good too

(p; q) s = q (p s) -- (;) = CB -- flip (.) (x:=f) s = x s (f s) -- (:=) = S goto f s = f s -- id = I (f+'g) s = f s + g s (f<'g) s = f s < g s if' p c s = if (p s) then (c s) else s x' (a,b) = a i' (a,b) = b

Er, forgot to include the two state updaters of the article, x (a,b) v = (v,b) i (a,b) v = (a,v)

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Benjamin L.Russell
Girish Bhat
Will Ness