10 Functions

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► | 10 | Functions

10.1 | Simple Functions
10.2 | Higher Order Predicates
10.3 | Currying and (Partial) Application
10.4 | Eta Expansion
10.5 | Parameter Arguments

On this page:

10.1`` Simple Functions
identity
thunk
10.2`` Higher Order Predicates
negate
conjoin
disjoin
10.3`` Currying and (Partial) Application
call
papply
papplyr
curryn
currynr
10.4`` Eta Expansion
eta
eta*
10.5`` Parameter Arguments
lambda/ parameter

Version: 5.0.1.5
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### 10`` Functions

Carl Eastlund <cce@racket-lang.org>

( require unstable/function)

This library is unstable; compatibility will not be maintained. See Unstable for more information.

This module provides tools for higher-order programming and creating functions.

#### 10.1`` Simple Functions

( identity x) → ( one-of/c x)
x : any/c

Returns x.

( thunk body ...)

Creates a function that ignores its inputs and evaluates the given body. Useful for creating event handlers with no (or irrelevant) arguments.

Examples:

( define f ( thunk ( define x 1) ( printf "~a\n" x)))

> (f)
1
> (f 'x)
1
> (f #:y 'z)
1

#### 10.2`` Higher Order Predicates

(( negate f) x ...) → boolean?
f : (-> A ... boolean?)
x : A

Negates the results of f; equivalent to ( not (f x ...)).

This function is reprovided from scheme/function.

Examples:

( define f ( negate exact-integer?))

> (f 1)
#f
> (f 'one)
#t

(( conjoin f ...) x ...) → boolean?
f : (-> A ... boolean?)
x : A

Combines calls to each function with and. Equivalent to ( and (f x ...) ...)

Examples:

( define f ( conjoin exact? integer?))

> (f 1)
#t
> (f 1.0)
#f
> (f 1/2)
#f
> (f 0.5)
#f

(( disjoin f ...) x ...) → boolean?
f : (-> A ... boolean?)
x : A

Combines calls to each function with or. Equivalent to ( or (f x ...) ...)

Examples:

( define f ( disjoin exact? integer?))

> (f 1)
#t
> (f 1.0)
#t
> (f 1/2)
#t
> (f 0.5)
#f

#### 10.3`` Currying and (Partial) Application

( call f x ...) → B
f : (-> A ... B)
x : A

Passes x ... to f. Keyword arguments are allowed. Equivalent to (f x ...). Useful for application in higher-order contexts.

Examples:

> ( map call
( list + - * /)
( list 1 2 3 4)
( list 5 6 7 8))

'(6 -4 21 1/2)

( define count 0)

( define (inc)
( set! count (+ count 1)))

( define (reset)
( set! count 0))

( define (show)
( printf "~a\n" count))

> ( for-each call ( list inc inc show reset show))

2
0

( papply f x ...) → (B ... -> C)
f : (A ... B ... -> C)
x : A

( papplyr f x ...) → (A ... -> C)
f : (A ... B ... -> C)
x : B

The papply and papplyr functions partially apply f to x ..., which may include keyword arguments. They obey the following equations:

(( papply f x ...) y ...) = (f x ... y ...)
(( papplyr f x ...) y ...) = (f y ... x ...)

Examples:

( define reciprocal ( papply / 1))

> (reciprocal 3)
1/3
> (reciprocal 4)
1/4

( define halve ( papplyr / 2))

> (halve 3)
3/2
> (halve 4)
2

( curryn n f x ...) → (A1 ... -> ooo -> An ... -> B)
n : exact-nonnegative-integer?
f : (A0 ... A1 ... ooo An ... -> B)
x : A0

( currynr n f x ...) → (An ... -> ooo -> A1 ... -> B)
n : exact-nonnegative-integer?
f : (A1 ... ooo An ... An+1 ... -> B)
x : An+1

Note: The ooo above denotes a loosely associating ellipsis.

The curryn and currynr functions construct a curried version of f, specialized at x ..., that produces a result after n further applications. Arguments at any stage of application may include keyword arguments, so long as no keyword is duplicated. These curried functions obey the following equations:

( curryn 0 f x ...) = (f x ...)
(( curryn (+ n 1) f x ...) y ...) = ( curryn n f x ... y ...)
( currynr 0 f x ...) = (f x ...)
(( currynr (+ n 1) f x ...) y ...) = ( currynr n f y ... x ...)

The call, papply, and papplyr utilities are related to curryn and currynr in the following manner:

( call f x ...) = ( curryn 0 f x ...) = ( currynr 0 f x ...)
( papply f x ...) = ( curryn 1 f x ...)
( papplyr f x ...) = ( currynr 1 f x ...)

Examples:

( define reciprocal ( curryn 1 / 1))

> (reciprocal 3)
1/3
> (reciprocal 4)
1/4

( define subtract-from ( curryn 2 -))

( define from-10 (subtract-from 10))

> (from-10 5)
5
> (from-10 10)
0

( define from-0 (subtract-from 0))

> (from-0 5)
-5
> (from-0 10)
-10

( define halve ( currynr 1 / 2))

> (halve 3)
3/2
> (halve 4)
2

( define subtract ( currynr 2 -))

( define minus-10 (subtract 10))

> (minus-10 5)
-5
> (minus-10 10)
0

( define minus-0 (subtract 0))

> (minus-0 5)
5
> (minus-0 10)
10

#### 10.4`` Eta Expansion

( eta f)

Produces a function equivalent to f, except that f is evaluated every time it is called.

This is useful for function expressions that may be run, but not called, before f is defined. The eta expression will produce a function without evaluating f.

Examples:

( define f ( eta g))

> f
#<procedure:eta>

( define g ( lambda (x) (+ x 1)))

> (f 1)
2

( eta* f x ...)

Produces a function equivalent to f, with argument list x .... In simple cases, this is equivalent to ( lambda (x ...) (f x ...)). Optional (positional or keyword) arguments are not allowed.

This macro behaves similarly to eta, but produces a function with statically known arity which may improve efficiency and error reporting.

Examples:

( define f ( eta* g x))

> f
#<procedure:f>
> ( procedure-arity f)
1

( define g ( lambda (x) (+ x 1)))

> (f 1)
2

#### 10.5`` Parameter Arguments

( lambda/parameter (param-arg ...) body ...)

param-arg |  | = |  | param-arg-spec
|  | | |  | keyword param-spec
param-arg-spec |  | = |  | id
|  | | |  | [id default-expr]
|  | | |  | [id #:param param-expr]

Constructs a function much like lambda, except that some optional arguments correspond to the value of a parameter. For each clause of the form [id #:param param-expr], param-expr must evaluate to a value param satisfying parameter?. The default value of the argument id is (param); param is bound to id via parameterize during the function call.

Examples:

( define p ( open-output-string))

( define hello-world
( lambda/parameter ([port #:param current-output-port])
( display "Hello, World!")
( newline port)))

> (hello-world p)
> ( get-output-string p)
"Hello, World!\n"

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