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# (lispkit combinator)

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

(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))))))))