FIX

Technology Dictionary -> FIX

FIX

FIX

Technology Dictionary -> FIX

FIX



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]

(1995-04-13)

2. bug fix.

(1998-06-25)


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