o[x_][x_]x[x]
In[]:=
SKEvolveList[s[s][s][s[s]][s][s],30];
In[]:=
Extract[#,{First[Sort[Position[#,s[_][_][_],{0,Infinity},HeadsTrue]]]}]&/@SKEvolveList[s[s][s][s[s]][s][s],30];
In[]:=
Position[%,s[s][s][s[s]]]
Out[]=
{{1,1},{6,1}}
In[]:=
ee50=Extract[#,{First[Sort[Position[#,s[_][_][_],{0,Infinity},HeadsTrue]]]}]&/@SKEvolveList[s[s][s][s[s]][s][s],50];
In[]:=
Table[Select[Groupings[Table[s,n],Construct2],MatchQ[#,s[_][_][_]]&],{n,6}]
Out[]=
{{},{},{},{s[s][s][s]},{s[s[s]][s][s],s[s][s[s]][s],s[s][s][s[s]]},{s[s[s][s]][s][s],s[s[s[s]]][s][s],s[s][s[s][s]][s],s[s[s]][s[s]][s],s[s][s[s[s]]][s],s[s[s]][s][s[s]],s[s][s[s]][s[s]],s[s][s][s[s][s]],s[s][s][s[s[s]]]}}
In[]:=
Position[ee50,#]&/@Flatten[%91]
Out[]=
{{},{{5,1}},{},{{1,1},{6,1}},{},{},{},{},{},{},{},{},{}}
[[ For s alone, either terminates completely or is non-terminating ]]
In[]:=
SKFixedPointEvolveList[s[s[s[s][s]][s[s]][s][s][s][s]]];
In[]:=
Length[%]
Out[]=
895
In[]:=
Position[%87,s[s[s[s][s]][s[s]][s][s][s][s]],HeadsTrue]
Out[]=
{{1}}
s[s[s[s][s]][s[s]][s][s][s][s]]
If it has a copy, then it explodes....
Does an X exist s.t. : Given X and Nest[f,X,t], then X appears in it
1. Does the redex reproduce itself?
2. Does the redex appear in a particular evaluation sequence?
2. Does the redex appear in a particular evaluation sequence?
Generalized case: rewrite sequence repeats, but specific redex does not....
Self similarity in the MW graph ... and in MW causal graph
Self similarity in the MW graph ... and in MW causal graph
In[]:=
SKEvolveList[s[s][s][s[s]][s][s],10]
Out[]=
{s[s][s][s[s]][s][s],s[s[s]][s[s[s]]][s][s],s[s][s][s[s[s]][s]][s],s[s[s[s]][s]][s[s[s[s]][s]]][s],s[s[s]][s][s][s[s[s[s]][s]][s]],s[s][s][s[s]][s[s[s[s]][s]][s]],s[s[s]][s[s[s]]][s[s[s[s]][s]][s]],s[s][s[s[s[s]][s]][s]][s[s[s]][s[s[s[s]][s]][s]]],s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s]][s]][s][s[s[s]][s[s[s[s]][s]][s]]]],s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s]][s][s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s]][s[s[s[s]][s]][s]]]]],s[s[s[s]][s[s[s[s]][s]][s]]][s[s][s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]}
c[XXXX][x[z][y[z]]]
Tag expr tree...
In[]:=
LeafCount/@SKFixedPointEvolveList[s[s][s[s]][s[s[s[s]]]][s]]
Out[]=
{9,12,12,18,25,39,39,46,53,61,77,77,77,84,91,99,115,115,115,115,115,115,115,115,115,115,115,115,115}
LeafCount/@SKFixedPointEvolveList[s[s][s[s]][s[s[s[s]]]][s]]
In[]:=
Graph[MWCombinatorGraphMinimal[s[s][s[s]][s[s[s[s]]]][s],11,"LeftmostOutermost",NodeSizeMultiplier2.5],AspectRatio1]
Out[]=
In[]:=
Table[Graph[MWCombinatorGraphMinimal[s[s[s[s]]][s][s][s],t,"LeftmostOutermost",NodeSizeMultiplier.4],AspectRatio1],{t,15}]
Out[]=
,
,
,
,
,
,
,
,
,
,
,
,
,
,
In[]:=
Table[Graph[MWCombinatorGraphMinimal[s[s[s[s]]][s][s][s],t,NodeSizeMultiplier.4],AspectRatio1],{t,15}]
Out[]=
,
,
,
,
,
,
,
,
,
,
,
,
,
,
Proof of Non-Termination
Proof of Non-Termination
Recursion Testing
Recursion Testing
Causal Graph
Causal Graph
Each piece is an expression fragment:
In this case, the output from an event gets copied many times, to be used in many subtrees....
Non-Termination Test
Non-Termination Test
If any subexpression X at any stage has the feature that the evolution from X contains X then it recurses.....
On the initial state, all possible subtrees of the initial expressions are used.
Most promising...
Most promising...
Simpler case:
Simpler case: