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Wolfram Language & System Documentation Center
FoldPairList
  • See Also
    • FoldPair
    • FoldList
    • SequenceFoldList
    • TakeList
    • TakeDrop
    • QuotientRemainder
    • SubsetMap
  • Related Guides
    • Functional Iteration
    • See Also
      • FoldPair
      • FoldList
      • SequenceFoldList
      • TakeList
      • TakeDrop
      • QuotientRemainder
      • SubsetMap
    • Related Guides
      • Functional Iteration

FoldPairList[f,y0,{a1,a2,…}]

gives the list of successive xi obtained by applying f to pairs of the form {yi-1,ai}, where at each step f returns {xi,yi}.

FoldPairList[f,y0,list,g]

gives the list of successive values of g[{xi,yi}].

FoldPairList[f,{a0,a1,a2,…}]

is equivalent to FoldPairList[f,a0,{a1,a2,…}].

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • FoldPair
    • FoldList
    • SequenceFoldList
    • TakeList
    • TakeDrop
    • QuotientRemainder
    • SubsetMap
  • Related Guides
    • Functional Iteration
    • See Also
      • FoldPair
      • FoldList
      • SequenceFoldList
      • TakeList
      • TakeDrop
      • QuotientRemainder
      • SubsetMap
    • Related Guides
      • Functional Iteration

FoldPairList

FoldPairList[f,y0,{a1,a2,…}]

gives the list of successive xi obtained by applying f to pairs of the form {yi-1,ai}, where at each step f returns {xi,yi}.

FoldPairList[f,y0,list,g]

gives the list of successive values of g[{xi,yi}].

FoldPairList[f,{a0,a1,a2,…}]

is equivalent to FoldPairList[f,a0,{a1,a2,…}].

Details

  • The function f in FoldPairList[f,y0,list] always takes two arguments and is expected to return a pair {x,y} of expressions.
  • The expression expr in FoldPairList[f,y0,expr] can be any nonatomic expression, with any head.
  • FoldPairList[f,y0,list] is equivalent to FoldPairList[f,y0,list,First].
  • FoldPairList[f,y0,{a1,…,an}] returns a list of length n. FoldPairList[f,y0,{}] returns {}.
  • You can use Throw to exit from FoldPairList before it is finished.

Examples

open all close all

Basic Examples  (6)

Partition a list into sublists of different lengths:

Break an amount of money into bills of given values:

Return both the quotients and the remainders at each step:

Scope  (2)

Use a list in the third argument:

Use an arbitrary head in the third argument:

By default, FoldPairList returns only the first elements of the pairs:

Use FoldPairList with fourth argument Last to get the second element of the successive pairs:

Generalizations & Extensions  (1)

Use Throw to exit a FoldPairList:

Applications  (2)

For each element of a list, return True if it is larger than all previous ones, and False otherwise:

A discrete-time state-space system is represented using a state equation and output equation . Simulate such a system to get the outputs :

Properties & Relations  (4)

Return the seed and all but the last elements of the third argument:

Return the list in the third argument:

Find dimensions of an array up to level 3:

FoldPair returns the last element of the list returned by FoldPairList:

FoldPairList returns one element less than FoldList:

Possible Issues  (2)

The function in the first argument of FoldPairList must return a pair of expressions:

FoldPairList[f,y0,{}] returns an empty list, with no last element:

Therefore FoldPair[f,y0,{}] stays unevaluated:

See Also

FoldPair  FoldList  SequenceFoldList  TakeList  TakeDrop  QuotientRemainder  SubsetMap

Related Guides

    ▪
  • Functional Iteration

History

Introduced in 2015 (10.2)

Wolfram Research (2015), FoldPairList, Wolfram Language function, https://reference.wolfram.com/language/ref/FoldPairList.html.

Text

Wolfram Research (2015), FoldPairList, Wolfram Language function, https://reference.wolfram.com/language/ref/FoldPairList.html.

CMS

Wolfram Language. 2015. "FoldPairList." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FoldPairList.html.

APA

Wolfram Language. (2015). FoldPairList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FoldPairList.html

BibTeX

@misc{reference.wolfram_2025_foldpairlist, author="Wolfram Research", title="{FoldPairList}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FoldPairList.html}", note=[Accessed: 01-March-2026]}

BibLaTeX

@online{reference.wolfram_2025_foldpairlist, organization={Wolfram Research}, title={FoldPairList}, year={2015}, url={https://reference.wolfram.com/language/ref/FoldPairList.html}, note=[Accessed: 01-March-2026]}

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