2 Functions

(require (planet cce/scheme:4:1/function))

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

2.1 Simple Functions

(identity x) → (one-of/c x)

x : any/c

Returns x.

(constant x) → (unconstrained-> (one-of/c x))

x : any/c

Produces a function that returns x regardless of input.

Examples:

(define f (constant (gensym)))

> (f)

g5027

> (f '(4 5 6))

g5027

> (f #:x 7 #:y 8 #:z 9)

g5027

(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

2.2 Higher Order Predicates

((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

2.3 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

2.4 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"