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2 definitions found
From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
FIX
1. Federal Information Exchange.
2. Financial Information eXchange.
(2001-05-14)
From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
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)