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Math Help - functions - Iterate and Curry

  1. #1
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    functions - Iterate and Curry

    Folks, I am trying to refresh function...and could not solve a problem...can anyone help..


    LetA be an arbitrary set. For any total function P: A A and any non-negative integer n, iterate(P, n) isdefined as the n-th iteration of f, in other words, the function iterate(f,n)is defined as iterate(p, n) = p ; p ; ... ; p (n times of composition).The sign ; is used for function composition.

    Whatis the signature of iterate?
    Whatis the signature of curry(iterate)?

    Thanks.
    Last edited by sureshcisco; September 14th 2011 at 07:15 AM. Reason: thanks.
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  2. #2
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    Re: functions - Iterate and Curry

    Quote Originally Posted by sureshcisco View Post
    For any total function P: A A
    Bonjour et bienvenue!

    iterate : (A -> A) x nat -> (A -> A)

    The function iterate takes a function and a number and returns a function. The right pair of parentheses is optional because -> associates to the right. (I would even say that iterate is polymorphic because it can probably work for any type A.)

    curry(iterate) : (A -> A) -> nat -> (A -> A)

    but this may depend on the precise definition of currying that you have.
    Last edited by Ackbeet; September 14th 2011 at 08:33 AM. Reason: Last sentence no longer relevant.
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