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Combines all the elements of list using the binary operation procedure. For example, using
+
one can add up all the elements:(reduce-left + 0 list-of-numbers)The argument initial is used only if list is empty; in this case initial is the result of the call to
reduce-left
. If list has a single argument, it is returned. Otherwise, the arguments are reduced in a left-associative fashion. For example:(reduce-left + 0 '(1 2 3 4)) => 10 (reduce-left + 0 '(1 2)) => 3 (reduce-left + 0 '(1)) => 1 (reduce-left + 0 '()) => 0 (reduce-left + 0 '(foo)) => foo (reduce-left list '() '(1 2 3 4)) => (((1 2) 3) 4)
Like
reduce-left
except that it is right-associative.(reduce-right list '() '(1 2 3 4)) => (1 (2 (3 4)))
Combines all of the elements of list using the binary operation procedure. Unlike
reduce-left
andreduce-right
, initial is always used:(fold-right + 0 '(1 2 3 4)) => 10 (fold-right + 0 '(foo)) error--> Illegal datum (fold-right list '() '(1 2 3 4)) => (1 (2 (3 (4 ()))))
Fold-right
has interesting properties because it establishes a homomorphism between (cons
,()
) and (procedure, initial). It can be thought of as replacing the pairs in the spine of the list with procedure and replacing the()
at the end with initial. Many of the classical list-processing procedures can be expressed in terms offold-right
, at least for the simple versions that take a fixed number of arguments:(define (copy-list list) (fold-right cons '() list)) (define (append list1 list2) (fold-right cons list2 list1)) (define (map p list) (fold-right (lambda (x r) (cons (p x) r)) '() list)) (define (reverse items) (fold-right (lambda (x r) (append r (list x))) '() items))
Combines all the elements of list using the binary operation procedure. Elements are combined starting with initial and then the elements of list from left to right. Whereas
fold-right
is recursive in nature, capturing the essence ofcdr
-ing down a list and then computing a result, fold-left is iterative in nature, combining the elements as the list is traversed.(fold-left list '() '(1 2 3 4)) => ((((() 1) 2) 3) 4) (define (length list) (fold-left (lambda (sum element) (+ sum 1)) 0 list)) (define (reverse items) (fold-left (lambda (x y) (cons y x)) () items))
(SRFI 1) Applies predicate across the lists, returning true if predicate returns true on any application.
If there are n list arguments list1 ... listn, then predicate must be a procedure taking n arguments and returning a boolean result.
any
applies predicate to the first elements of the list parameters. If this application returns a true value,any
immediately returns that value. Otherwise, it iterates, applying predicate to the second elements of the list parameters, then the third, and so forth. The iteration stops when a true value is produced or one of the lists runs out of values; in the latter case,any
returns#f
. The application of predicate to the last element of the lists is a tail call.Note the difference between
find
andany
—find
returns the element that satisfied the predicate;any
returns the true value that the predicate produced.Like
every
,any
's name does not end with a question mark—this is to indicate that it does not return a simple boolean (#t
or#f
), but a general value.(any integer? '(a 3 b 2.7)) => #t (any integer? '(a 3.1 b 2.7)) => #f (any < '(3 1 4 1 5) '(2 7 1 8 2)) => #tThe non-standard procedure
there-exists?
is similar, except that it takes a single list and a predicate argument, in that order.
(SRFI 1) Applies predicate across the lists, returning true if predicate returns true on every application.
If there are n list arguments list1 ... listn, then predicate must be a procedure taking n arguments and returning a boolean result.
every
applies predicate to the first elements of the list parameters. If this application returns false,every
immediately returns false. Otherwise, it iterates, applying predicate to the second elements of the list parameters, then the third, and so forth. The iteration stops when a false value is produced or one of the lists runs out of values. In the latter case,every
returns the true value produced by its final application of predicate. The application of predicate to the last element of the lists is a tail call.If one of the lists has no elements,
every
simply returns#t
.Like
any
,every
's name does not end with a question mark—this is to indicate that it does not return a simple boolean (#t
or#f
), but a general value.The non-standard procedure
for-all?
is similar, except that it takes a single list and a predicate argument, in that order.