# LispKit Combinator

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

(const c …) [procedure]

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

(flip f) [procedure]

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) [procedure]

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 …) [procedure]

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 …) [procedure]

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 …) [procedure]

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 …) [procedure]

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 …) [procedure]

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) [procedure]

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 …) [procedure]

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) [syntax]
(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) [syntax]
(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) [procedure]

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))))))))