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Meaning of FIX

Pronunciation:  fiks

 
Computing Dictionary
 
 Definition: 
  1. 1. federal information exchange.

    2. financial information exchange.

  2. 1. The fixed point combinator. Called Y in combinatory logic. Fix is a higher-order function which returns a fixed point of its argument (which is a function).

            fix :: (a -> a) -> a
            fix f = f (fix f)

    Which satisfies the equation

            fix f = x such that f x = x.

    Somewhat surprisingly, fix can be defined as the non-recursive lambda abstraction:

            fix = \ h . (\ x . h (x x)) (\ x . h (x x))

    Since this involves self-application, it has an infinite type. A function defined by

            f x1 .. xN = E

    can be expressed as

            f = fix (\ f . \ x1 ... \ xN . E)
              = (\ f . \ x1 ... \xN . E)
                    (fix (\ f . \ x1 ... \ xN . E))
              = let f = (fix (\ f . \ x1 ... \ xN . E))
                in \ x1 ... \xN . E

    If f does not occur free in E (i.e. it is not recursive) then this reduces to simply

            f = \ x1 ... \ xN . E

    In the case where N = 0 and f is free in E, this defines an infinite data object, e.g.

            ones = fix (\ ones . 1 : ones)
                 = (\ ones . 1 : ones) (fix (\ ones . 1 : ones))
                 = 1 : (fix (\ ones . 1 : ones))
                 = 1 : 1 : ...

    Fix f is also sometimes written as mu f where mu is the Greek letter or alternatively, if f = \ x . E, written as mu x . E.

    Compare quine.

    [jargon file]

    2. bug fix.

 
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