Unexpected restriction in "let rec" expressions
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Date:   (:) 
From:  PalKristian Engstad <pal_engstad@n...> 
Subject:  Re: [Camllist] Unexpected restriction in "let rec" expressions 
Loup Vaillant wrote: > loop :: ((a,c) > (b,c)) > a > b > loop f a = b > where (b,c) = f (a,c) > Remember that values in Haskell are lazy, which simply means that they are pointers to things that is either a pointer to a function to evaluate it, or the cached value. (This works, since all Haskell values are immutable.) So, what we have here is a specification on how to calculate (b,c) from (a, c), given a function f :: (a,c) > (b, c), and a. In order to evaluate b, we must evaluate the pair (b, c), i.e. evaluate the function call. Here we're using the value c, which is undefined  except that we have one constraint. The second result value is the same as c, and since a value is always immutable, it means that the second result value must be the *same value* as the second input value. In other words, we're telling the compiler: Given a function f :: (a, c) > (b, c) and a value of type a, loop f a will give the result b by evaluating (b, c') = f (a, c) where c' == c always. An example function is: g (a, c) = (c a, (*2)) Here' the constraint is telling us that c == (*2), and since we're returning the first parameter, the result is [c a == (*2) a == a * 2]. Another: g (a, c) = (a + c, 2) Now, c == 2, thus loop g a == a + 2. The other examples are of the same theme. g (a, c) = (c, a : map (+a) c), means that c == a : map (+a) c, which again is a recursive definition, and since everything is lazy this works. The first element in the list is a, when the second element is requested, map (+a) c is requested, but that means requesting c again which equals a : map (+a) c, so we get map (+a) (a : map (+a) c), which requires just the head of the conscell,which is a, so the result is (+a) a : map (+a) (map (+a) c), which is (a + a) : (map (+a) $ map (+a) c) Hope it helps, PKE  PålKristian Engstad (engstad@naughtydog.com), Lead Graphics & Engine Programmer, Naughty Dog, Inc., 1601 Cloverfield Blvd, 6000 North, Santa Monica, CA 90404, USA. Ph.: (310) 6339112. "Most of us would do well to remember that there is a reason Carmack is Carmack, and we are not Carmack.", Jonathan Blow, 2/1/2006, GD Algo Mailing List