Span

A range of positions i;;j;;step used as a part specification.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageSpan✓↗

Span(i, j, step?)positions $i, i+step, \dots$ up to $j$; a negative position counts from the end. Never evaluated on its own — read by At.

Typed signatures

Type	Package	Applies
(integer, integer, integer?) -> unknown	combinatorics	always

Domain: Collections

Details

• Never reduces by itself: it is a part specification other heads read, the way $Range$ describes a sequence of numbers. At is the only head here that reads one.
• $step$ defaults to 1; a negative $step$ walks from $i$ down to $j$.
• Negative $i$/$j$ count from the end, exactly as a plain negative index does in At.

Examples

Basic #

Positions 2 through 4 ($2;;4$ in Wolfram)

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(2, 4)]$Out$\bigl\lbrack b, c, d\bigr\rbrack$

Every other element through the last ($1;;-1;;2$)

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(1, -1, 2)]$Out$\bigl\lbrack a, c, f\bigr\rbrack$

live ↗

In$\bigl\lbrack a, b, c, d, k, f, g, h\bigr\rbrack[\mathrm{Span}(2, 5)]$Out$\bigl\lbrack b, c, d, k\bigr\rbrack$

live ↗

In$\bigl\lbrack a, b, c, d, k, f, g, h\bigr\rbrack[\mathrm{Span}(1, -1, 3)]$Out$\bigl\lbrack a, d, g\bigr\rbrack$

Scope #

A negative step walks backwards ($-1;;1;;-1$)

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(-1, 1, -1)]$Out$\bigl\lbrack f, d, c, b, a\bigr\rbrack$

Negative bounds: the last two elements

live ↗

In$\bigl\lbrack a, b, c, d, f\bigr\rbrack[\mathrm{Span}(-2, -1)]$Out$\bigl\lbrack d, f\bigr\rbrack$

Spans at two levels cut out a submatrix

live ↗

In$\bigl\lbrack\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack4, 5, 6\bigr\rbrack, \bigl\lbrack7, 8, 9\bigr\rbrack\bigr\rbrack[\mathrm{Span}(2, 3), \mathrm{Span}(1, 2)]$Out$\bigl\lbrack\bigl\lbrack4, 5\bigr\rbrack, \bigl\lbrack7, 8\bigr\rbrack\bigr\rbrack$

The first five letters

live ↗

In$\mathrm{CharacterRange}(\text{a}, \text{z})[\mathrm{Span}(1, 5)]$Out$\bigl\lbrack\text{a}, \text{b}, \text{c}, \text{d}, \text{e}\bigr\rbrack$

A negative end counts from the last element, so the slice runs to the end

live ↗

In$(1..10)[\mathrm{Span}(3, -1)]$Out$\bigl\lbrack3, 4, 5, 6, 7, 8, 9, 10\bigr\rbrack$

A step of $2$ takes every other element

live ↗

In$(1..10)[\mathrm{Span}(1, -1, 2)]$Out$\bigl\lbrack1, 3, 5, 7, 9\bigr\rbrack$

live ↗

In$\bigl\lbrack a, b, c, d, k, f, g, h\bigr\rbrack[\mathrm{Span}(2, -3)]$Out$\bigl\lbrack b, c, d, k, f\bigr\rbrack$

About

Examples	11
Checked against	Wolfram Language 11 agree
Crosswalk	Wolfram Language

See also: At, UpTo