(lispkit combinator)

Library (lispkit combinator) defines abstractions for combinator-style programming. It provides means to create and compose functions.

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(const c ...)

Returns a function accepting any number of arguments and returning the values c ... .

(flip f)

Takes a function with two parameters and returns an equivalent function where the two parameters are swapped.

(define snoc (flip cons))
(snoc (snoc (snoc '() 3) 2) 1)  ⟹  (1 2 3)

(negate f)

Returns a function which invokes f and returns the logical negation.

(define gvector-has-elements? (negate gvector-empty?))
(gvector-has-elements? #g(1 2 3))  ⟹  #t

(partial f arg ...)

Applies arguments arg ... partially to f and returns a new function accepting the remaining arguments. For a function (f a1 a2 a3 ... an), (partial f a1 a2) will return a function (lambda (a3 ... an) (f a1 a2 a3 ... an)).

(compose f ...)

Composes the given functions f ... such that ((compose f1 f2 ... fn) x) is equivalent to (f1 (f2 (... (fn x)))). compose supports functions returning multiple arguments.

(o f ...)

Composes the given functions f ... such that ((o f1 f2 ... fn) x) is equivalent to (f1 (f2 (... (fn x)))). o is a more efficient version of compose which only works if the involved functions only return a single argument. compose is more general and supports functions returning multiple arguments.

(conjoin f ...)

Returns a function invoking all functions f ... and combining the results with and. ((conjoin f1 f2 ...) x ...) is equivalent to (and (f1 x ...) (f2 x ...) ...).

(disjoin f ...)

Returns a function invoking all functions f ... and combining the results with or. ((disjoin f1 f2 ...) x ...) is equivalent to (or (f1 x ...) (f2 x ...) ...).

(list-of? f)

Returns a predicate which takes a list as its argument and returns #t if for every element x of the list (f x) returns true.

(each f ...)

Returns a function which applies the functions f ... each individually to its arguments in the given order, returning the result of the last function application.

(cut f) (cut f <...>) (cut f arg ...) (cut f arg ... <...>)

Special form cut transforms an expression (f arg ...) into a lambda expression with as many formal variables as there are slots <> in the expression (f arg ...). The body of the resulting lambda expression calls procedure f with arguments arg ... in the order they appear. In case there is a rest symbol <...> at the end, the resulting procedure is of variable arity, and the body calls f with all arguments provided to the actual call of the specialized procedure.

(cut cons (+ a 1) <>)   ⟹  (lambda (x2) (cons (+ a 1) x2))
(cut list 1 <> 3 <> 5)  ⟹  (lambda (x2 x4) (list 1 x2 3 x4 5))
(cut list 1 <> 3 <...>) ⟹  (lambda (x2 . xs) (apply list 1 x2 3 xs))

(cute f) (cute f <...>) (cute f arg ...) (cute f arg ... <...>)

Special form cute is similar to cut, except that it first binds new variables to the result of evaluating the non-slot expressions (in an unspecific order) and then substituting the variables for the non-slot expressions. In effect, cut evaluates non-slot expressions at the time the resulting procedure is called, whereas cute evaluates the non-slot expressions at the time the procedure is constructed.

(cute cons (+ a 1) <>)
⟹  (let ((a1 (+ a 1))) (lambda (x2) (cons a1 x2)))

(Y f)

Y combinator for computing a fixed point of a function f. This is a value that is mapped to itself.

; factorial function
(define fac
  (Y (lambda (r)
       (lambda (x) (if (< x 2) 1 (* x (r (- x 1))))))))
; fibonacci numbers
(define fib
  (Y (lambda (f)
       (lambda (x)
         (if (< x 2) x (+ (f (- x 1)) (f (- x 2))))))))