5 research outputs found
Closed nominal rewriting and efficiently computable nominal algebra equality
We analyse the relationship between nominal algebra and nominal rewriting,
giving a new and concise presentation of equational deduction in nominal
theories. With some new results, we characterise a subclass of equational
theories for which nominal rewriting provides a complete procedure to check
nominal algebra equality. This subclass includes specifications of the
lambda-calculus and first-order logic.Comment: In Proceedings LFMTP 2010, arXiv:1009.218
Algorithms for Extended Alpha-Equivalence and Complexity
Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-binding “let ” may make alpha-equivalence as hard as finding graph-isomorphisms, and that the replication operator in the pi-calculus may lead to an EXPSPACE-hard alpha-equivalence problem
From nominal to higher-order rewriting and back again
We present a translation function from nominal rewriting systems (NRSs) to
combinatory reduction systems (CRSs), transforming closed nominal rules and
ground nominal terms to CRSs rules and terms, respectively, while preserving
the rewriting relation. We also provide a reduction-preserving translation in
the other direction, from CRSs to NRSs, improving over a previously defined
translation. These tools, together with existing translations between CRSs and
other higher-order rewriting formalisms, open up the path for a transfer of
results between higher-order and nominal rewriting. In particular, techniques
and properties of the rewriting relation, such as termination, can be exported
from one formalism to the other.Comment: 41 pages, journa
Matching and alpha-equivalence check for nominal terms
AbstractNominal terms generalise first-order terms by including abstraction and name swapping constructs. α-equivalence can be easily axiomatised using name swappings and a freshness relation, which makes the nominal approach well adapted to the specification of systems that involve binders. Nominal matching is matching modulo α-equivalence and has applications in programming languages, rewriting, and theorem proving. In this paper, we describe efficient algorithms to check the validity of equations involving binders and to solve matching problems modulo α-equivalence, using the nominal approach