In[]:=
FindLambdas[n_,vars_]:=ResourceFunction["ParallelMapMonitored"][Function[c,If[FreeQ[Last[#],s|k],If[Head[#]===Failure,Nothing,#]&[#],Nothing]&[c->CombinatorFixedPoint[Fold[#[#2]&,c,Range[vars]],"MaxSize"10000,"MaxSteps"1000]]],EnumerateCombinators[n]]
In[]:=
With[{n=3,vars=2},Export[StringTemplate["/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-``-``.wxf"][n,vars],FindLambdas[n,vars]]]
Out[]=
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-3-2.wxf
In[]:=
Import[%]
Out[]=
{s[s][k]1[2][1],s[s[k]]1[2],s[k][s]1[2],s[k][k]1[2],k[k][s]1,k[k][k]1}
In[]:=
Table[With[{res=FindLambdas[n,vars]},Echo[Export[StringTemplate["/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-``-``.wxf"][n,vars],res]];Echo[{n,vars}->KeySort[Counts[LeafCount[Last[#]]&/@First/@GatherBy[res,Last]]]]],{n,5},{vars,2,2}]
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-1-2.wxf
»
{1,2}11
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-2-2.wxf
»
{2,2}11
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-3-2.wxf
»
{3,2}11,21,31
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-4-2.wxf
»
{4,2}12,21,32,41
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-5-2.wxf
»
{5,2}12,21,32,41,53,71
Out[]=
{{{1,2}11},{{2,2}11},{{3,2}11,21,31},{{4,2}12,21,32,41},{{5,2}12,21,32,41,53,71}}
In[]:=
Table[With[{res=FindLambdas[n,vars]},Echo[Now];Echo[Export[StringTemplate["/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-``-``.wxf"][n,vars],res]];Echo[{n,vars}->KeySort[Counts[LeafCount[Last[#]]&/@First/@GatherBy[res,Last]]]]],{n,12},{vars,2,4}]
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-1-2.wxf
»
{1,2}11
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-1-3.wxf
»
{1,3}21,41
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-1-4.wxf
»
{1,4}31,51
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-2-2.wxf
»
{2,2}11
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-2-3.wxf
»
{2,3}11,21,51
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-2-4.wxf
»
{2,4}21,31,41,61
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-3-2.wxf
»
{3,2}11,21,31
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-3-3.wxf
»
{3,3}11,22,31,42,71
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-3-4.wxf
»
{3,4}11,21,32,41,54,81
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-4-2.wxf
»
{4,2}12,21,32,41
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-4-3.wxf
»
{4,3}13,22,34,43,52,61,101
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-4-4.wxf
»
{4,4}12,24,32,46,53,64,72,111
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-5-2.wxf
»
{5,2}12,21,32,41,53,71
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-5-3.wxf
»
{5,3}12,23,33,46,54,64,72,82,151
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-5-4.wxf
»
{5,4}13,23,37,44,59,66,75,83,93,101,161
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-6-2.wxf
»
{6,2}12,22,34,43,53,62,71,82,111
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-6-3.wxf
»
{6,3}13,23,37,49,511,65,76,84,94,101,111,121,231
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-6-4.wxf
»
{6,4}13,26,36,416,513,616,710,87,95,104,113,121,132,151,241
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-7-2.wxf
»
{7,2}12,24,37,48,56,63,76,82,91,102,121,132,181
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-7-3.wxf
»
{7,3}13,25,313,416,520,617,711,810,96,104,117,122,132,142,151,161,191,361
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-7-4.wxf
»
{7,4}14,26,317,418,533,628,729,819,914,109,115,128,132,142,153,163,171,202,231,371
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-8-2.wxf
»
{8,2}12,24,310,414,513,67,712,85,95,105,113,121,133,141,162,181,191,212,291
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-8-3.wxf
»
{8,3}13,27,320,425,539,634,729,824,921,1011,1112,127,135,146,154,162,175,181,191,201,211,222,231,241,301,571
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-8-4.wxf
»
{8,4}14,28,322,436,549,665,757,841,939,1029,1122,1218,139,147,158,165,173,185,191,201,212,222,232,242,252,312,361,581
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-9-2.wxf
»
{9,2}12,24,311,425,530,618,720,817,913,1011,117,126,134,142,156,164,173,184,192,201,213,231,262,311,342,471
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-9-3.wxf
»
{9,3}13,28,324,443,566,673,765,855,945,1037,1131,1217,1322,1415,157,1610,178,186,1910,202,215,224,231,243,253,273,291,321,341,352,361,371,481,911
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-9-4.wxf
»
{9,4}14,210,334,451,593,6112,7125,899,989,1067,1156,1242,1333,1431,1524,1613,1715,1812,196,2011,214,225,236,242,254,263,283,301,312,331,352,362,372,381,391,492,571,921
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-10-2.wxf
»
{10,2}12,24,316,435,551,653,747,841,940,1026,1120,1220,1315,149,1510,168,179,189,197,201,216,222,235,245,252,263,271,293,312,321,344,361,372,422,501,552,761,2191
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-10-3.wxf
»
{10,3}13,29,332,467,5115,6126,7151,8122,9115,1095,1175,1253,1358,1442,1529,1625,1722,1824,1923,2016,218,2210,239,246,257,269,276,282,293,303,312,324,331,342,355,361,373,384,401,433,471,511,551,562,571,581,771,1461,2201
»
»
/Users/sw/Dropbox/Physics/Data/Combinators/LambdaSearch/lambda-10-4.wxf
»
{10,4}14,214,340,495,5144,6210,7237,8232,9197,10177,11155,12102,1394,1482,1561,1642,1740,1834,1939,2026,2124,2214,2316,2412,2513,268,2710,287,294,303,314,323,334,342,352,367,372,384,394,411,443,461,471,481,501,521,551,561,572,582,591,621,782,911,1471,2211