CombinatorStep[{s[x_][y_][z_]x[z][y[z]],k[x_][y_]x},s[s[x][y][s[x][y][z]]][y][z][k[x][y][z]],{"Rightmost","Outermost",1}]
In[]:=
s[s[x][y][s[x][y][z]]][y][z][x[z]]
Out[]=
CombinatorMatches[s[s[x][y][s[x][y][z]]][y][z][x[z]]]
In[]:=
{0}1,{0,0,0,1}1,{0,0,0,1,1}1
Out[]=
CombinatorTree[s[s[x][y][s[x][y][z]]][y][z][x[z]]]
In[]:=
Out[]=
CombinatorFixedPointList[s[s][s][s[s[s]]][k][s]]//Column
In[]:=
Out[]=
Length[CombinatorFixedPointList[s[s][s][s[s[s]]][k][s]]]
In[]:=
89
Out[]=
ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s][s][s[s[s]]][k][s]]]
In[]:=
Out[]=
Position[s[s][s][s[s[s]]][k][s],s[_][_][_]|k[_][_]]
In[]:=
{{0,0}}
Out[]=
Position[CombinatorFixedPointList[s[s][s][s[s[s]]][k][s]][[40]],s[_][_][_]|k[_][_]]
In[]:=
{{0,1,1,1,0,0},{0,1,1,1,1,0,1},{0,1,1,1,1,0},{1,0,1,0},{1,1,0,0},{1,1,1,1,0},{1}}
Out[]=
EvaluationOrderSort[%95,{"Leftmost","Outermost"}]
In[]:=
{{0,1,1,1,0,0},{0,1,1,1,1,0},{0,1,1,1,1,0,1},{1},{1,0,1,0},{1,1,0,0},{1,1,1,1,0}}
Out[]=
EvaluationOrderSort[%95,{"Outermost","Leftmost"}]
In[]:=
{{1},{1,0,1,0},{1,1,0,0},{1,1,1,1,0},{0,1,1,1,0,0},{0,1,1,1,1,0},{0,1,1,1,1,0,1}}
Out[]=
EvaluationOrderSort[%95,{"Innermost","Leftmost"}]
In[]:=
{{0,1,1,1,1,0,1},{0,1,1,1,0,0},{0,1,1,1,1,0},{1,1,1,1,0},{1,0,1,0},{1,1,0,0},{1}}
Out[]=
EvaluationOrderSort[%95,{"Leftmost","Innermost"}]
In[]:=
{{0,1,1,1,0,0},{0,1,1,1,1,0,1},{0,1,1,1,1,0},{1,0,1,0},{1,1,0,0},{1,1,1,1,0},{1}}
Out[]=
RelationGraph[ListStrictPrefixQ,{{0,1,1,1,0,0},{0,1,1,1,1,0,1},{0,1,1,1,1,0},{1,0,1,0},{1,1,0,0},{1,1,1,1,0},{1}},VertexLabelsAutomatic]
In[]:=
Out[]=
CombinatorFixedPointList[s[s][s][s[s[s]]][k][s]][[40]]
In[]:=
s[s[s[s[s[s[s[s]]][k]][k[s[s[s[s[s]]][k]]]]][s[s[s[s[s]]][k]]]][k[k[s[s[s[s]]][k]][k[k[s[s[s[s]]][k]]]][s][k[k[s[s[s[s]]][k]]][k[s[s[s[s]]][k]][k[k[s[s[s[s]]][k]]]]][s]]]]][k[s[s[s[s]]][k][k[s[s[s[s]]][k]]][s]][s[s[s[s]]][k][k[s[s[s[s]]][k]]][s][k[s[s[s[s]]][k][k[s[s[s[s]]][k]]][s]]]]]
Out[]=
Column[Extract[%100,#]&/@%95,FrameAll]
In[]:=
k[s[s[s[s]]][k]][k[k[s[s[s[s]]][k]]]] |
k[s[s[s[s]]][k]][k[k[s[s[s[s]]][k]]]] |
k[k[s[s[s[s]]][k]]][k[s[s[s[s]]][k]][k[k[s[s[s[s]]][k]]]]] |
s[s[s[s]]][k][k[s[s[s[s]]][k]]] |
s[s[s[s]]][k][k[s[s[s[s]]][k]]] |
s[s[s[s]]][k][k[s[s[s[s]]][k]]] |
k[s[s[s[s]]][k][k[s[s[s[s]]][k]]][s]][s[s[s[s]]][k][k[s[s[s[s]]][k]]][s][k[s[s[s[s]]][k][k[s[s[s[s]]][k]]][s]]]] |
Out[]=
CombinatorFixedPointList[s[s][s][s[s[s]]][k][s]]
f[g[x],h[y]][[0]]
In[]:=
f
Out[]=
f[g[x],h[y]][[1]]
In[]:=
g[x]
Out[]=
f[g[x],h[y]][[1,1]]
In[]:=
x
Out[]=
f[g[x],h[y]][[1,0]]
In[]:=
g
Out[]=
f[g[x],h[y]]
Total[{Total[{2,3}],Total[{a,b}]}]
In[]:=
5+a+b
Out[]=
Total[{5,a+b}]
x=.
In[]:=
Clear[f]
In[]:=
Set[x,6]
Set[5,6]
Attributes[Set]
In[]:=
{HoldFirst,Protected,SequenceHold}
Out[]=
f[x_Integer,y_Integer]:=x+y
In[]:=
f[f[4,2],f[7,8]]
Clear[f]
In[]:=
Times[Plus[2,3],Plus[4,6]]
Times[5,10]
{Echo[a],Echo[b],Echo[c]}
In[]:=
a
»
b
»
c
»
{a,b,c}
Out[]=
Table[Echo[i],{i,100}]
In[]:=
ParallelTable[Echo[i],{i,100}]
In[]:=
LeafCount/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
In[]:=
{7,8,8,11,11,11,12,17,25,33,41,50,59,87,115,149,187,215,243,272,301}
Out[]=
ListStepPlot[Depth/@CombinatorEvolveList[s[s][s][s[s]][s][s],200]]
In[]:=
Out[]=
Ed’s version
Ed’s version
Ed’s formula:
Ed’s formula: