is a list of elements.


  • Lists are very general objects that represent collections of expressions.
  • Functions with attribute Listable are automatically "threaded" over lists, so that they act separately on each list element. Most builtin mathematical functions are Listable.
  • {a,b,c} represents a vector.
  • {{a,b},{c,d}} represents a matrix.
  • Nested lists can be used to represent tensors.
  • If Nothing appears in a list, it is automatically removed.

Background & Context

  • List is a very general construct used to represent collections of expressions. Lists may have any length or depth. The expression List[a,b,c,] is commonly written and displayed using the shorthand syntax {a,b,c,}. Lists are particularly important in the Wolfram Language, which does not define explicit vector, matrix, tensor, etc. objects but rather uses (possibly nested) lists to represent such structures. For example, {a,b,c,} can represent a vector, {{a,b},{c,d}} a matrix, and so on.
  • Functions with attribute Listable are automatically threaded over lists, meaning they act separately on each list element. Most builtin mathematical functions are Listable.
  • Apply replaces the head of a List (or any other expression) with a new head, while Map applies a function to elements on the first level of a List (or any other expression).
  • SparseArray may be used to efficiently represent and compute with lists (or nested lists) that have a constant (often 0) background value. A SparseArray can be expanded to a full-dimensional List using Normal.
  • Values of a list can be efficiently modified in place using Set, e.g. list[[k]]=newValue. Common operations to access, insert, or delete elements of a list include Part, Take, Drop, Extract, Insert, Delete, PadLeft/PadRight, Append/AppendTo, and Prepend/PrependTo.
  • A flat list of values (i.e. a vector) may be plotted using ListPlot, and an array of values given by a rectangular list of lists may be plotted using ArrayPlot, MatrixPlot, ListDensityPlot, or related functions. Other important and useful functions commonly applied to lists include Total, Accumulate, Mean, and ListConvolve.
  • Association provides a generalization of symbolically indexed lists, associative arrays, dictionaries, hashmaps, structs, and a variety of other powerful data structures. An Association is so named because it associates keys with values, allowing highly efficient lookup and updating even with millions of elements.
  • A list can be converted to a sequence of expressions by applying Sequence to it. This can be particularly useful since functions in the Wolfram Language often take a flat sequence of arguments instead of an argument list, so use of Sequence allows list-represented data to be easily spliced into other functions.


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Basic Examples  (1)

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Click for copyable input

Scope  (26)

Generalizations & Extensions  (2)

Properties & Relations  (1)

See Also

Association  Dataset  Sequence  ListPlot  Listable  CompoundElement  DelimitedSequence


Introduced in 1988