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Reduce(func, list, right=TRUE) R supports right folding and left or right folding with or without an initial value through the right and init arguments to the Reduce function. Racket (foldl func initval list) (foldr func initval list) Ruby: enum.inject(initval, &block) enum.reduce(initval, &block) enum.reverse_each.inject(initval, &block)
The definition of cata implies, that foldrList is the right fold and not the left fold. As an example: foldrList (+) 1 (Cons 10 ( Cons 100 ( Cons 1000 EmptyList))) will evaluate to 1111 and foldrList (*) 3 (Cons 10 ( Cons 100 ( Cons 1000 EmptyList))) to 3.000.000.
As an alternative to the encoding using Church pairs, a list can be encoded by identifying it with its right fold function. For example, a list of three elements x, y and z can be encoded by a higher-order function that when applied to a combinator c and a value n returns c x (c y (c z n)).
A higher-order function is a function that takes a function as an argument or returns one as a result. This is commonly used to customize the behavior of a generically defined function, often a looping construct or recursion scheme. Anonymous functions are a convenient way to specify such function arguments. The following examples are in Python 3.
In Miranda, this right-fold, from Hughes (1989:5-6), has the same semantics (by example) as the Scheme implementation above, for two arguments. append a b = reduce cons b a Where reduce is Miranda's name for fold, and cons constructs a list from two values or lists. For example,
Q3 is a variant that catenates the three parts enclosed by the function ⊂ instead of the parts per se. The three parts generated at each recursive step are apparent in the structure of the final result. Applying the function derived from Q3 to the same argument multiple times gives different results because the pivots are chosen at random.
Despite the case being dismissed in July, Alec Baldwin says the story surrounding the fatal “Rust” shooting has only begun. On the Dec. 16 episode of David Duchovny’s “Fail Better ...
Note: If f takes its values in a ring (in particular for real or complex-valued f ), there is a risk of confusion, as f n could also stand for the n-fold product of f, e.g. f 2 (x) = f(x) · f(x). [11] For trigonometric functions, usually the latter is meant, at least for positive exponents. [11]