I like the name Algorithmic Induction, or Inductive Programming. Just like how in an (strongly) inductive proof you use facts from Fact(0)..Fact(n) to prove Fa

I like the name Algorithmic Induction, or Inductive Programming. Just like how in an (strongly) inductive proof you use facts from Fact(0)..Fact(n) to prove Fact(n+1), with inductive programming you're using results from Result(0)..Result(n) to compute Result(n+1).