five year survival rate, FIV protease, fièvre boutonneuse < Prev | Next > fix, fix, fixation

Bookmark with: icon icon icon icon iconword visualiser Go and visit our forums Community Forums

1. <mathematics> 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.

2. bug fix.

(01 Apr 1998)

1. To make firm, stable, or fast; to set or place permanently; to fasten immovably; to establish; to implant; to secure; to make efinite. "An ass's nole I fixed on his head." (Shak) "O, fix thy chair of grace, that all my powers May also fix their reverence." (Herbert) "His heart is fixed, trusting in the Lord." (Ps. Cxii. 7) "And fix far deeper in his head their stings." (Milton)

2. To hold steadily; to direct unwaveringly; to fasten, as the eye on an object, the attention on a speaker. "Sat fixed in thought the mighty Stagirite." (Pope) "One eye on death, and one full fix'd on heaven." (Young)

3. To transfix; to pierce.

4. <photography> To render (an impression) permanent by treating with such applications a will make it insensible to the action of light.

5. To put in prder; to arrange; to dispose of; to adjust; to set to rights; to set or place in the manner desired or most suitable; hence, to repair; as, to fix the clothes; to fix the furniture of a room.

6. To line the hearth of (a puddling furnace) with fettling.

Synonyms: To arrange, prepare, adjust, place, establis, settle, determine.

Origin: Cf. F. Fixer.

(01 Mar 1998)

FIV protease, fièvre boutonneuse, FIX, fix < Prev | Next > fixation, fixational ocular movement

Bookmark with: icon icon icon icon iconword visualiser Go and visit our forums Community Forums