Thank you. That's just what I needed. And your second version shows that I needn't use an anonymous function (lambda expression) at all, something that got lost in translation from Lisp to Haskell. First, yes, there was a typo. I couldn't find the original message so had to rewrite. Second, the reason I switched to a tuple argument in the first place is that I read somewhere, "Real World Haskell" I think, that Haskell anonymous functions could only have a single parameter (\ n -> ...). Maybe I didn't read far enough or Haskell has since been updated. Then, one poster didn't like the use of a (tuple) argument because it couldn't be partially applied, but the whole point of anonymous functions is for one off stuff, like these verifiers, where one doesn't want to create a named function that's used just once. In any case, the function we pass to makeVerifier, whether anonymous or in the WHERE of your clarified version, is a function that only appears in the definition of a particular verifier, so what difference can it possibly make whether or not it can be partially applied? That's what I can't get my head around. Thanks again. Michael --- On Sun, 4/12/09, Ross Mellgren wrote: From: Ross Mellgren Subject: Re: [Haskell-cafe] Functions that return functions To: "michael rice" Cc: "Daniel Fischer" , haskell-cafe@haskell.org Date: Sunday, April 12, 2009, 11:59 PM On Apr 12, 2009, at 11:50 PM, michael rice wrote:

I'm not sure what you're trying to tell me, so let's try a specific case.

Here's the makeVerifier function that expects its function f to have a single arg, a pair (i,d):

makeVerifier :: ((Int,Int) -> Int) -> Int -> (Int -> Bool) makeVerifier f m = divides m . foldl (+) 0 . map f . zip [1 .. ] . digits

And usage: let checkCc = makeVerifier (\ (i d) -> if odd i then d else if d < 5 then 2*d else 2*d + 1) 10

This looks like it has a typo -- did you mean \ (i, d) -> rather than \ (i d) -> ?

And here's the old makeVerifier function that expects its function f to have two integer arguments, i & d:

makeVerifier :: (Int -> Int -> Int) -> Int -> (Int -> Bool) makeVerifier f m = divides m . foldl (+) 0 . zipWith f [1 .. ] . digits

And usage: let checkCc = makeVerifier (\ ....    <== Complete this  ) 10

let checkCc = makeVerifier (\ i d -> if odd i then d else if d < 5 then 2*d else 2*d + 1) 10 though I find it a bit nicer to expand it a bit for clarity: checkCc :: Int -> Bool checkCc = makeVerifier f 10     where         f i d | odd i     = d               | d < 5     = 2*d               | otherwise = 2*d + 1 -Ross

--- On Sun, 4/12/09, Ross Mellgren wrote:

From: Ross Mellgren Subject: Re: [Haskell-cafe] Functions that return functions To: "michael rice" Cc: "Daniel Fischer" , haskell-cafe@haskell.org Date: Sunday, April 12, 2009, 9:23 PM

Under the covers of syntax they only have one parameter, but you can write curried lambdas or functions easily:

\ a b -> a + b

which is equivalent to

\ a -> \ b -> a + b

and also equivalent to the "normal" function syntax

f a b = a + b

or

f a = \ b -> a + b

-Ross

On Apr 12, 2009, at 9:09 PM, michael rice wrote:

...

My question was meant in the context of the makeVerifier function, which is passed a lambda expression. It's my understanding that Haskell lambda expressions can have only a single parameter, which is why I changed the function parameter to a pair, (i,d).

How would it be done otherwise?

Michael

--- On Sun, 4/12/09, Daniel Fischer wrote:

From: Daniel Fischer Subject: Re: [Haskell-cafe] Functions that return functions To: "michael rice" Cc: haskell-cafe@haskell.org Date: Sunday, April 12, 2009, 7:20 PM

Am Montag 13 April 2009 01:09:22 schrieb michael rice:

...

Example please.

Michael

Curried:

f :: a -> b -> c

amenable to partial application.

Uncurried:

g :: (a,b) -> c

not easy to apply partially.

The Prelude contains

curry :: ((a,b) -> c) -> (a -> b -> c)

uncurry :: (a -> b -> c) -> ((a,b) -> c)

to convert if needed.

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