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fix
(redirected from fixing upon)

   Also found in: Dictionary/thesaurus, Medical, Legal, Financial, Idioms, Wikipedia 0.01 sec.
fix
Nautical, etc the ascertaining of the navigational position, as of a ship, by radar, observation, etc.

fix [fiks]
(biology)
To kill, harden, or preserve a tissue, organ, or organism by immersion in dilute acids, alcohol, or solutions of coagulants.
(computer science)
A piece of coding that is inserted in a computer program to correct an error.
(navigation)
A position of a vessel or craft determined by its master, pilot, or navigator through the use of some or all of the equipments and techniques available.

1.(networking)FIX - Federal Information Exchange.
2.(business, protocol)FIX - Financial Information eXchange.
3.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.


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