This lambda calculus program produces the infinite multiplication table and uses finite parts of it. There are more straightforwrd ways to do that and this is a technical exercise to demonstrate memo-ing.

References

[All89] Lloyd Allison, 'Circular Programs and Self-Referential Structures', Software Practice & Experience, 19(2), pp.99-109, doi:10.1002/spe.4380190202, arxiv:2403.01866, February 1989.

[All93] Lloyd Allison, 'Applications of Recursively Defined Data Structures', Australian Computer Journal, 25(1), pp.14-20, arxiv:2206.12795, 1993.

And other publications.

There are more λ-calculus examples here.