MapAt

f applied to the part of expr at position n, leaving the rest of expr unchanged.

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MapAt(f, expr, n)f applied at the (1-based, negative counts from the end) position n

MapAt(f, expr, {{n1}, {n2}, …})f applied independently at each of several top-level positions

Typed signatures

Type	Package	Applies
`((any) -> any, any, integer \| list<list<integer>>) -> any`	`combinatorics`	always

Domain: Collections

Details

A position named twice gets f applied twice there.
Only top-level positions are answered here -- a nested path (into a sub-list) is left unevaluated.

Examples

Basic #

\mathrm{MapAt}(f, \bigl\lbrack a, b, c\bigr\rbrack, 2)

Out

\bigl\lbrack a, f(b), c\bigr\rbrack

Applies $f$ at one position only

\mathrm{MapAt}(f, \bigl\lbrack a, b, c, d\bigr\rbrack, 2)

Out

\bigl\lbrack a, f(b), c, d\bigr\rbrack

A list of positions applies $f$ at several places

\mathrm{MapAt}(f, \bigl\lbrack a, b, c, d\bigr\rbrack, \bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack4\bigr\rbrack\bigr\rbrack)

Out

\bigl\lbrack f(a), b, c, f(d)\bigr\rbrack

Scope #

A negative position counts from the end

\mathrm{MapAt}(f, \bigl\lbrack a, b, c\bigr\rbrack, -1)

Out

\bigl\lbrack a, b, f(c)\bigr\rbrack

A list of positions applies f at each independently

\mathrm{MapAt}(f, \bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack3\bigr\rbrack\bigr\rbrack)

Out

\bigl\lbrack f(a), b, f(c)\bigr\rbrack

Works inside a sum, where the result is reordered into canonical form

\mathrm{MapAt}(f, a+b+c+d, 2)

Out

a+c+d+f(b)

Position $2$ is a whole sublist, which $h$ wraps

\mathrm{MapAt}(h, \bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, k\bigr\rbrack, f, g\bigr\rbrack, 2)

Out

\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, h(\bigl\lbrack d, k\bigr\rbrack), f, g\bigr\rbrack

A negative position counts from the end, so $-3$ is the second of four

\mathrm{MapAt}(h, \bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, k\bigr\rbrack, f, g\bigr\rbrack, -3)

Out

\bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, h(\bigl\lbrack d, k\bigr\rbrack), f, g\bigr\rbrack

Several top-level positions applied together

\mathrm{MapAt}(h, \bigl\lbrack\bigl\lbrack a, b, c\bigr\rbrack, \bigl\lbrack d, k\bigr\rbrack, f, g\bigr\rbrack, \bigl\lbrack\bigl\lbrack2\bigr\rbrack, \bigl\lbrack1\bigr\rbrack\bigr\rbrack)

Out

\bigl\lbrack h(\bigl\lbrack a, b, c\bigr\rbrack), h(\bigl\lbrack d, k\bigr\rbrack), f, g\bigr\rbrack

Properties #

\mathrm{MapAt}(f, \bigl\lbrack a, b, c, d\bigr\rbrack, \bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack3\bigr\rbrack, \bigl\lbrack1\bigr\rbrack\bigr\rbrack)

Out

\bigl\lbrack f(f(a)), b, f(c), d\bigr\rbrack

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