A necessary and sufficient condition for cycling reductions to be recurrent is given. A one-step recurrent term is a term in λ-β-calculus whose one-step reductums are all reducible to the term. It is a weakened notion of minimal form or recurrent term in the λ-β-calculus. In this note, a one-step recurrent term which is not recurrent is shown. That term becomes a counter- example for a conjecture presented by Klop. By analysis of the reduction cycles of one-step recurrent terms, a necessary and sufficient condition for a one-step recurrent term to be recurrent is given.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)