This is less a question and more asking if someone has implemented this already, with more skill.

I need to perform the Outer-like generalized outer product of a list of lists. I need to do it in a lazy way because the lists will become very large (many tens of thousands of elements).

I am using a Module to hold state as iterate over the products

loopOver[list0_]:=Module[ {len0,index,get,increment,isDoneQ,doneB}, len0=Length[list0]; Do[index[j]=1,{j,len0}]; doneB=False; get[]:=Table[list0[[j,index[j]]],{j,len0}]; increment[]:=Block[ {stack,p}, If[doneB,Return[]]; stack={len0}; While[Length[stack]>0, p=First@stack; stack=Rest@stack; index[p]=index[p]+1; If[index[p]>Length[list0[[p]]], ( If[p===1,doneB=True;Return[]]; index[p]=1;stack=Append[stack,p-1] ) ] ] ]; isDoneQ[]:=doneB; { "get"->get, "increment"->increment, "isDoneQ"->isDoneQ } ] 

And you use it as such:

Block[ {a, get, increment, isDoneQ}, a = { {"11", "12", "13"}, {"21", "22"}, {"31"}, {"41", "42"} }; {get,increment,isDoneQ}=loopOver[a][[All,2]]; While[!isDoneQ[], Print[get[]]; increment[] ] ] 

outputting the expected outer of 321*2=12 products:

{11,21,31,41} {11,21,31,42} {11,22,31,41} {11,22,31,42} {12,21,31,41} {12,21,31,42} {12,22,31,41} {12,22,31,42} {13,21,31,41} {13,21,31,42} {13,22,31,41} {13,22,31,42} 

Code review would be appreciated too. I hope my code is high on self documentation where it is low on performance and use of MMA functional coding style.

This is less a question and more asking if someone has implemented this already, with more skill.

I need to perform the Outer-like generalized outer product of a list of lists (also a form of Tuples). I need to do it in a lazy way because the lists will become very large (many tens of thousands of elements).

I am using a Module to hold state as iterate over the products

loopOver[list0_]:=Module[ {len0,index,get,increment,isDoneQ,doneB}, len0=Length[list0]; Do[index[j]=1,{j,len0}]; doneB=False; get[]:=Table[list0[[j,index[j]]],{j,len0}]; increment[]:=Block[ {stack,p}, If[doneB,Return[]]; stack={len0}; While[Length[stack]>0, p=First@stack; stack=Rest@stack; index[p]=index[p]+1; If[index[p]>Length[list0[[p]]], ( If[p===1,doneB=True;Return[]]; index[p]=1;stack=Append[stack,p-1] ) ] ] ]; isDoneQ[]:=doneB; { "get"->get, "increment"->increment, "isDoneQ"->isDoneQ } ] 

And you use it as such:

Block[ {a, get, increment, isDoneQ}, a = { {"11", "12", "13"}, {"21", "22"}, {"31"}, {"41", "42"} }; {get,increment,isDoneQ}=loopOver[a][[All,2]]; While[!isDoneQ[], Print[get[]]; increment[] ] ] 

outputting the expected outer of 321*2=12 products:

{11,21,31,41} {11,21,31,42} {11,22,31,41} {11,22,31,42} {12,21,31,41} {12,21,31,42} {12,22,31,41} {12,22,31,42} {13,21,31,41} {13,21,31,42} {13,22,31,41} {13,22,31,42} 

Code review would be appreciated too. I hope my code is high on self documentation where it is low on performance and use of MMA functional coding style.