On this page:
1.1 Simple Functions
identity
thunk
constant
const
1.2 Higher Order Predicates
negate
conjoin
disjoin
1.3 Currying and (Partial) Application
call
papply
papplyr
curryn
currynr
1.4 Eta Expansion
eta
eta*
1.5 Parameter Arguments
lambda/ parameter

1 Functions

 (require (planet cce/scheme:6:1/function))

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

1.1 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

(constant x)  (unconstrained-domain-> (one-of/c x))
  x : any/c
Deprecated: This function from previous versions of this package has been subsumed by const from scheme/function; see below.

(const x)  (unconstrained-domain-> (one-of/c x))
  x : any/c
Produces a function that returns x regardless of input.

This function is reprovided from scheme/function. In versions of PLT Scheme before const was implemented, this module provides its own definition.

Examples:

  (define f (const 5))
  > (f)

  5

  > (f 'x)

  5

  > (f #:y 'z)

  5

1.2 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

1.3 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

1.4 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

1.5 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"