fix

n 1: informal terms for a difficult situation; "he got into a

terrible fix"; "he made a muddle of his marriage" [syn:

{hole}, {jam}, {mess}, {muddle}, {pickle}, {kettle of

fish}]

2: (informal) an intravenous injection of a narcotic drug

3: the act of putting something in working order again [syn: {repair},

{fixing}, {mending}, {reparation}]

4: an exemption granted after influence (e.g., money) is

brought to bear; "collusion resulted in tax fixes for

gamblers"

5: a determination of the location of something; "he got a good

fix on the target" [syn: {localization}, {localisation}, {location},

{locating}]

v 1: restore by replacing a part or putting together what is

torn or broken; "She repaired her TV set"; "Repair my

shoes please" [syn: {repair}, {mend}, {bushel}, {doctor},

{furbish up}, {restore}, {touch on}] [ant: {break}]

2: cause to be firmly attached; "fasten the lock onto the

door"; "she fixed her gaze on the man" [syn: {fasten}, {secure}]

[ant: {unfasten}]

3: decide upon, as of variables in math [syn: {specify}, {set},

{determine}]

4: prepare for eating by applying heat; "Cook me dinner,

please"; "can you make me an omelette?" "fix breakfast for

the guests, please" [syn: {cook}, {ready}, {make}, {prepare}]

5: take vengeance on or get even; "We'll get them!" "That'll

fix him good!" "This time I got him" [syn: {pay back}, {pay

off}, {get}]

6: set or place definitely; "Let's fix the date for the party!"

7: kill, preserve, and harden (tissue) in order to prepare for

microscopic study; in cytology

8: make fixed, stable or stationary; "let's fix the picture to

the frame" [syn: {fixate}]

9: make infertile; of both males and females [syn: {sterilize},

{desex}, {unsex}, {desexualize}]

10: place firmly [syn: {situate}, {pose}, {posit}, {deposit}]

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)