Function Repository Resource:

# SKCombinatorLeftmostOutermostLeafCounts

Compute successive leaf counts during leftmost-outermost evolution of an SK combinator expression

Contributed by: Wolfram Research
 ResourceFunction["SKCombinatorLeftmostOutermostLeafCounts"][cmb, t] computes leaf counts of successive expressions during leftmost-outermost evolution of cmb over t steps.

## Details and Options

The argument cmb should be given as a combinator expression in nested bracket form and the argument t should be an integer.
ResourceFunction["SKCombinatorLeftmostOutermostLeafCounts"] has the option "SKGlyphs":
 "SKGlyphs" symbols used to specify S, K combinator transformation rules

## Examples

### Basic Examples (2)

Compute leaf counts associated with states of a leftmost-outermost SK combinator evolution:

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Compare the previous result with the leaf counts found by explicitly generating the combinator evolution:

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The function does not return leaf counts for time steps after the fixed point of the evolution (at which point the combinator will no longer change):

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### Scope (1)

Compare the time efficiency of SKCombinatorLeftmostOutermostLeafCounts to that of taking the leaf counts from the explicit evolution generated by CombinatorEvolveList:

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### Options (1)

Specify the S and K combinator glyphs used in the argument cmb:

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### Applications (1)

Plot the time evolution of a combinator expression by leaf count:

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## Version History

• 1.0.0 – 01 March 2021