Affiliation:
1. University of Sheffield, Sheffield, UK
Abstract
We study nominal recursors from the literature on syntax with bindings and compare them with respect to expressiveness. The term "nominal" refers to the fact that these recursors operate on a syntax representation where the names of bound variables appear explicitly, as in nominal logic. We argue that nominal recursors can be viewed as epi-recursors, a concept that captures abstractly the distinction between the constructors on which one actually recurses, and other operators and properties that further underpin recursion. We develop an abstract framework for comparing epi-recursors and instantiate it to the existing nominal recursors, and also to several recursors obtained from them by cross-pollination. The resulted expressiveness hierarchies depend on how strictly we perform this comparison, and bring insight into the relative merits of different axiomatizations of syntax. We also apply our methodology to produce an expressiveness hierarchy of nominal corecursors, which are principles for defining functions targeting infinitary non-well-founded terms (which underlie lambda-calculus semantics concepts such as Böhm trees). Our results are validated with the Isabelle/HOL theorem prover.
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Reference58 articles.
1. Andreas Abel, Alberto Momigliano, and Brigitte Pientka. 2017. POPLMark Reloaded. In Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP) 2017, Marino Miculan and Florian Rabe (Eds.). https://lfmtp.org/workshops/2017/inc/papers/paper_8_abel.pdf
2. Infinite trees and completely iterative theories: a coalgebraic view
3. Type-and-scope safe programs and their proofs
4. Monadic Presentations of Lambda Terms Using Generalized Inductive Types
5. A definitional approach to primitivexs recursion over higher order abstract syntax