Lists are central constructs in the Wolfram Language, used to represent collections, arrays, sets, and sequences of all kinds. Lists can have any structure and size and can routinely involve even millions of elements. Well over a thousand built-in functions throughout the Wolfram Language operate directly on lists, making lists a powerful vehicle for interoperability.

Constructing Lists »

{a,b,…} (List ) — specify a list explicitly

Table — make a table of values of an expression

Array — make an array of any dimension from a function

Range   ▪ Subdivide   ▪ SparseArray   ▪ NumericArray   ▪ Tuples   ▪ NestList   ▪ ...

Elements of Lists »

list[[…]] — parts or sequences of parts (;;), resettable with =

First   ▪ Last   ▪ Take   ▪ Drop   ▪ TakeList   ▪ Extract   ▪ Append   ▪ ReplacePart   ▪ ...

Select — select according to a function

Cases — give cases matching a pattern

Length   ▪ Position   ▪ MemberQ   ▪ DeleteDuplicates   ▪ ...

Nothing — an element automatically removed from lists

Splice — sequence of elements to automatically be spliced into a list

Rearranging & Restructuring Lists »

Flatten — flatten out nested lists

Join   ▪ Partition   ▪ Transpose   ▪ Reverse   ▪ Sort   ▪ Split   ▪ Gather   ▪ Riffle   ▪ ...

Applying Functions to Lists »

Map (/@ ) — map a function over a list: f/@{a,b,c}⟶{f[a],f[b],f[c]}

Apply (@@ ) — apply to a list: f@@{x,y,z}⟶f[x,y,z]

MapApply (@@@ ) — apply to a list: f@@@{x,y,z}⟶{f@@x,f@@y,f@@z}

MapIndexed   ▪ Scan   ▪ Thread   ▪ MapThread   ▪ Outer   ▪ FoldList   ▪ ...

Threaded — thread listable functions at the deepest levels of array arguments

Elementwise — make a function behave as if it were listable

Predicates on Lists

AllTrue   ▪ AnyTrue   ▪ NoneTrue

ContainsAll   ▪ ContainsNone   ▪ ContainsAny   ▪ ContainsOnly   ▪ ContainsExactly

Math & Counting Operations »

{…}+{…}, etc. — automatically operate in parallel on list elements

Total   ▪ Differences   ▪ Count   ▪ CountDistinct   ▪ Counts   ▪ BinCounts   ▪ SequenceCount   ▪ ...

Displaying & Visualizing Lists »

Column   ▪ Row   ▪ Grid   ▪ ListPlot   ▪ ArrayPlot   ▪ ...

Importing & Exporting Lists »

Import   ▪ Export   ▪ "Table"   ▪ "Text"   ▪ "CSV"   ▪ ...

Creating Associations from Lists »

Counts   ▪ GroupBy   ▪ PositionIndex   ▪ ...

Related Tech Notes

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• Making Lists of Objects
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• Getting Pieces of Lists
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• Combining Lists
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• Adding, Removing, and Modifying List Elements
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• Manipulating Lists by Their Indices
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• Nested Lists
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• Applying Functions to Parts of Expressions
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• Testing and Searching List Elements

Related Workflow Guides

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• Importing and Analyzing Data

Related Guides

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• Handling Arrays of Data
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• Handling Numerical Data
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• Operations on Vectors
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• Matrix Operations
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• Tensors
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• General Expressions
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• Associations
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• Structured Datasets

Related Links

• Fast Introduction for Programmers: Lists