Extensively Evolving Combinator Expressions

S combinator expressions of leaf counts 1 through 13 that do not terminate after 10,000 evolution steps

Details

The data is calculated using the method shown in the "Scope & additional elements" subsection.

The default content is a Dataset where the rows are labeled by the leaf count of the S combinator expression and contain the combinator expressions that do not terminate after 10,000 evolution steps.

Examples

Basic Examples

Get the list of non-terminating S combinator expressions of leaf count 7:

In[1]:=

$Normal[ResourceData[\!$\* TagBox["\"\<Extensively Evolving Combinator Expressions\>\"", #& , BoxID -> "ResourceTag-Extensively Evolving Combinator \ Expressions-Input", AutoDelete->True]$]][7]$

Out[1]=

Get the length of the list of non-terminating S combinator expressions of leaf count 13:

In[2]:=

$Length[Normal[ResourceData[\!$\* TagBox["\"\<Extensively Evolving Combinator Expressions\>\"", #& , BoxID -> "ResourceTag-Extensively Evolving Combinator \ Expressions-Input", AutoDelete->True]$]][13]]$

Out[2]=

Scope & Additional Elements

Perform from scratch the enumeration of S combinator expressions of leaf count n that do not terminate in max steps. This method can be used to extend the dataset; however, note that as the leaf count for the combinator expressions and maximum steps for the evolutions increase, this computation will become increasingly expensive:

In[3]:=

$SNT[n_, max_] := With[{all = ResourceFunction["EnumerateCombinators"][n, {s}]}, Select[all, FailureQ[ ResourceFunction["CombinatorFixedPoint"][#, "SKGlyphs" -> {s, k}, "MaxSteps" -> max]] &] ]$

Enumerate S combinator expressions of leaf count 8 that do not terminate within 10 steps:

In[4]:=

Out[4]=

Group S combinator expressions of leaf count 7 that terminate within 10,000 steps in equivalence groups designated by their fixed point form:

In[5]:=

$terminating7 = Complement[ResourceFunction["EnumerateCombinators"][7, {s}], Normal[ResourceData[\!$\* TagBox["\"\<Extensively Evolving Combinator Expressions\>\"", #& , BoxID -> "ResourceTag-Extensively Evolving Combinator \ Expressions-Input", AutoDelete->True]$]][7]];$