Below is an attempt I've made to create a procedure that returns the function composition given a list of functions in scheme. I've reached an impasse; What I've written tried makes sense on paper but I don't see where I am going wrong, can anyone give some tips?
; (compose-all-rec fs) -> procedure
; fs: listof procedure
; return the function composition of all functions in fs:
; if fs = (f0 f1 ... fN), the result is f0(f1(...(fN(x))...))
; implement this procedure recursively
(define compose-all-rec (lambda (fs)
(if (empty? fs) empty
(lambda (fs)
(apply (first fs) (compose-all-rec (rest fs)))
))))
where ((compose-all-rec (list abs inc)) -2) should equal 1
I'd try a different approach:
(define (compose-all-rec fs)
(define (apply-all fs x)
(if (empty? fs)
x
((first fs) (apply-all (rest fs) x))))
(λ (x) (apply-all fs x)))
Notice that a single lambda needs to be returned at the end, and it's inside that lambda (which captures the x parameter and the fs list) that happens the actual application of all the functions - using the apply-all helper procedure. Also notice that (apply f x) can be expressed more succinctly as (f x).
If higher-order procedures are allowed, an even shorter solution can be expressed in terms of foldr and a bit of syntactic sugar for returning a curried function:
(define ((compose-all-rec fs) x)
(foldr (λ (f a) (f a)) x fs))
Either way the proposed solutions work as expected:
((compose-all-rec (list abs inc)) -2)
=> 1
Post check-mark, but what the heck:
(define (compose-all fns)
(assert (not (null? fns)))
(let ((fn (car fns)))
(if (null? (cdr fns))
fn
(let ((fnr (compose-all (cdr fns))))
(lambda (x) (fn (fnr x)))))))
