▼Unstable: May Change Without Warning
►15 Functions
On this page:
15.1 Simple Functions
15.2 Higher Order Predicates
negate
conjoin
disjoin
15.3 Currying and (Partial) Application
call
papply
papplyr
curryn
currynr
15.4 Eta Expansion
eta
eta*
15.5 Parameter Arguments
lambda/ parameter
Version: 5.2
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15 Functions

Carl Eastlund <cce@racket-lang.org>

 (require unstable/function)

This library is unstable; compatibility will not be maintained. See Unstable: May Change Without Warning for more information.

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

15.1 Simple Functions

15.2 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?))

reference to undefined identifier: negate

> (f 1)

reference to undefined identifier: f

> (f 'one)

reference to undefined identifier: f

((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

15.3 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

15.4 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

15.5 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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