R: Common Higher-Order Functions in Functional Programming...

funprog {base}

R Documentation

Common Higher-Order Functions in Functional Programming Languages

Description

Reduce: uses a binary function to successively combine the elements of a given vector and a possibly given initial value.
Filter: extracts the elements of a vector for which a predicate (logical) function gives true.
Find and Position: give the first or last such element and its position in the vector, respectively.
Map: applies a function to the corresponding elements of given vectors.
Negate: creates the negation of a given function.

Usage

Reduce(f, x, init, right = FALSE, accumulate = FALSE, simplify = TRUE)
Filter(f, x)
Find(f, x, right = FALSE, nomatch = NULL)
Map(f, ...)
Negate(f)
Position(f, x, right = FALSE, nomatch = NA_integer_)

Arguments

`f`	a function of the appropriate arity (binary for `Reduce`, unary for `Filter`, `Find` and `Position`, `k`-ary for `Map` if this is called with `k` arguments). An arbitrary predicate function for `Negate`.
`x`	a vector.
`init`	an R object of the same kind as the elements of `x`.
`right`	a logical indicating whether to proceed from left to right (default) or from right to left.
`accumulate`	a logical indicating whether the successive reduce combinations should be accumulated. By default, only the final combination is used.
`simplify`	a logical indicating whether accumulated results should be simplified (by unlisting) in case they all are length one.
`nomatch`	the value to be returned in the case when “no match” (no element satisfying the predicate) is found.
`...`	vectors to which the function is `Map()`ped, and other arguments of `mapply` passed to it, e.g., `MoreArgs`.

Details

If init is given, Reduce logically adds it to the start (when proceeding left to right) or the end of x, respectively. If this possibly augmented vector v has n > 1 elements, Reduce successively applies f to the elements of v from left to right or right to left, respectively. I.e., a left reduce computes l_1 = f(v_1, v_2), l_2 = f(l_1, v_3), etc., and returns l_{n-1} = f(l_{n-2}, v_n), and a right reduce does r_{n-1} = f(v_{n-1}, v_n), r_{n-2} = f(v_{n-2}, r_{n-1}) and returns r_1 = f(v_1, r_2). (E.g., if v is the sequence (2, 3, 4) and f is division, left and right reduce give (2 / 3) / 4 = 1/6 and 2 / (3 / 4) = 8/3, respectively.) If v has only a single element, this is returned; if there are no elements, NULL is returned. Thus, it is ensured that f is always called with 2 arguments.

The current implementation is non-recursive to ensure stability and scalability.

Reduce is patterned after Common Lisp's reduce. A reduce is also known as a fold (e.g., in Haskell) or an accumulate (e.g., in the C++ Standard Template Library). The accumulative version corresponds to Haskell's scan functions.

Filter applies the unary predicate function f to each element of x, coercing to logical if necessary, and returns the subset of x for which this gives true. Note that possible NA values are currently always taken as false; control over NA handling may be added in the future. Filter corresponds to filter in Haskell or ‘⁠remove-if-not⁠’ in Common Lisp.

Find and Position are patterned after Common Lisp's ‘⁠find-if⁠’ and ‘⁠position-if⁠’, respectively. If there is an element for which the predicate function gives true, then the first or last such element or its position is returned depending on whether right is false (default) or true, respectively. If there is no such element, the value specified by nomatch is returned. The current implementation is not optimized for performance.

Map is a simple wrapper to mapply which does not attempt to simplify the result, similar to Common Lisp's mapcar (with arguments being recycled, however). Future versions may allow some control of the result type.

Negate corresponds to Common Lisp's complement. Given a (predicate) function f, it creates a function which returns the logical negation of what f returns.

Examples

## A general-purpose adder:
add <- function(x) Reduce(`+`, x)
add(list(1, 2, 3))
## Like sum(), but can also used for adding matrices etc., as it will
## use the appropriate '+' method in each reduction step.
## More generally, many generics meant to work on arbitrarily many
## arguments can be defined via reduction:
FOO <- function(...) Reduce(FOO2, list(...))
FOO2 <- function(x, y) UseMethod("FOO2")
## FOO() methods can then be provided via FOO2() methods.

## A general-purpose cumulative adder:
cadd <- function(x) Reduce(`+`, x, accumulate = TRUE)
cadd(seq_len(7))

## A simple function to compute continued fractions:
cfrac <- function(x) Reduce(function(u, v) u + 1 / v, x, right = TRUE)
## Continued fraction approximation for pi:
cfrac(c(3, 7, 15, 1, 292))
## Continued fraction approximation for Euler's number (e):
cfrac(c(2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8))

## Map() now recycles similar to basic Ops:
Map(`+`, 1,         1 : 3) ;         1 + 1:3
Map(`+`, numeric(), 1 : 3) ; numeric() + 1:3

## Iterative function application:
Funcall <- function(f, ...) f(...)
## Compute log(exp(acos(cos(0))))
Reduce(Funcall, list(log, exp, acos, cos), 0, right = TRUE)
## n-fold iterate of a function, functional style:
Iterate <- function(f, n = 1)
    function(x) Reduce(Funcall, rep.int(list(f), n), x, right = TRUE)
## Continued fraction approximation to the golden ratio:
Iterate(function(x) 1 + 1 / x, 30)(1)
## which is the same as
cfrac(rep.int(1, 31))
## Computing square root approximations for x as fixed points of the
## function t |-> (t + x / t) / 2, as a function of the initial value:
asqrt <- function(x, n) Iterate(function(t) (t + x / t) / 2, n)
asqrt(2, 30)(10) # Starting from a positive value => +sqrt(2)
asqrt(2, 30)(-1) # Starting from a negative value => -sqrt(2)

## A list of all functions in the base environment:
funs <- Filter(is.function, sapply(ls(baseenv()), get, baseenv()))
## Functions in base with more than 10 arguments:
names(Filter(function(f) length(formals(f)) > 10, funs))
## Number of functions in base with a '...' argument:
length(Filter(function(f)
              any(names(formals(f)) %in% "..."),
              funs))

## Find all objects in the base environment which are *not* functions:
Filter(Negate(is.function),  sapply(ls(baseenv()), get, baseenv()))