Strong Normalization as Safe Interaction

Colin Riba
<span title="">2007</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="" style="color: black;">22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)</a> </i> &nbsp;
When enriching the λ-calculus with rewriting, union types may be needed to type all strongly normalizing terms. However, with rewriting, the elimination rule (∨ E) of union types may also allow to type non normalizing terms (in which case we say that (∨ E) is unsafe). This occurs in particular with non-determinism, but also with some confluent systems. It appears that studying the safety of (∨ E) amounts to the characterization, in a term, of safe interactions between some of its subterms. In
more &raquo; ... is paper, we study the safety of (∨ E) for an extension of the λ-calculus with simple rewrite rules. We prove that the union and intersection type discipline without (∨ E) is complete w.r.t. strong normalization. This allows to show that (∨ E) is safe if and only if an interpretation of types based on biorthogonals is sound for it. We also discuss two sufficient conditions for the safety of (∨ E), and study an alternative biorthogonality relation, based on the observation of the least reducibility candidate.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1109/lics.2007.46</a> <a target="_blank" rel="external noopener" href="">dblp:conf/lics/Riba07</a> <a target="_blank" rel="external noopener" href="">fatcat:cw44ovzqkrezlk5fctckz5na4e</a> </span>
<a target="_blank" rel="noopener" href="" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href=""> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> </button> </a>