Results 1 
6 of
6
A coalgebraic approach to the semantics of the ambient calculus
 ALGEBRA AND COALGEBRA IN COMPUTER SCIENCE
, 2005
"... Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is — in contrast to the situatio ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is — in contrast to the situation in standard process algebra — up to now no satisfying coalgebraic representation of a mobile process calculus. Here, we discuss a coalgebraic denotational semantics for the ambient calculus, viewed as a step towards a generic coalgebraic framework for modelling mobile systems. Crucial features of our modelling are a set of GSOS style transition rules for the ambient calculus, a hardwiring of the socalled hardening relation in the functorial signature, and a setbased treatment of hidden name sharing. The formal representation of this framework is cast in the algebraiccoalgebraic specification language CoCasl.
The Power of Parameterization in Coinductive Proof
"... Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonlyknown latticetheoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e., breaking proofs into se ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonlyknown latticetheoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e., breaking proofs into separate pieces that can be developed in isolation), and they do not support incremental reasoning (i.e., developing proofs interactively by starting from the goal and generalizing the coinduction hypothesis repeatedly as necessary). In this paper, we show how to support coinductive proofs that are both compositional and incremental, using a dead simple construction we call the parameterized greatest fixed point. The basic idea is to parameterize the greatest fixed point of interest over the accumulated knowledge of “the proof so far”. While this idea has been proposed before, by Winskel in 1989 and by Moss in 2001, neither of the previous accounts suggests its general applicability to improving the state of the art in interactive coinductive proof. In addition to presenting the latticetheoretic foundations of parameterized coinduction, demonstrating its utility on representative examples, and studying its composition with “upto ” techniques, we also explore its mechanization in proof assistants like Coq and Isabelle. Unlike traditional approaches to mechanizing coinduction (e.g., Coq’s cofix), which employ syntactic “guardedness checking”, parameterized coinduction offers a semantic account of guardedness. This leads to faster and more robust proof development, as we demonstrate using our new Coq library, Paco.
Coinduction in an AutoActive Program Verifier
, 2013
"... Abstract. Program verification relies heavily on induction, which has received decades of attention in mechanical verification tools. When program correctness is best described by infinite structures, program verification is usefully aided also by coinduction, which has not benefited from the same ..."
Abstract
 Add to MetaCart
Abstract. Program verification relies heavily on induction, which has received decades of attention in mechanical verification tools. When program correctness is best described by infinite structures, program verification is usefully aided also by coinduction, which has not benefited from the same degree of tool support. Coinduction is complicated to work with in interactive proof assistants and has had no previous support in autoactive program verifiers. This paper shows that an autoactive program verifier can support reasoning about coinduction—handling infinite data structures, lazy function calls, and userdefined properties defined as greatest fixpoints, as well as letting users write coinductive proofs. Moreover, the support can be packaged to provide a simple user experience. The paper describes the features for coinduction in the language and verifier Dafny, defines their translation into input for a firstorder SMT solver, and reports on some encouraging initial experience. 0
Automatic Equivalence Proofs for Nondeterministic
, 1303
"... A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene’s theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata, M ..."
Abstract
 Add to MetaCart
A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene’s theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata, Mealy machines and labelled transition systems. In this paper, we present a novel algorithm to decide whether two expressions are bisimilar or not. The procedure is implemented in the automatic theorem prover CIRC, by reducing coinduction to an entailment relation between an algebraic specification and an appropriate set of equations. We illustrate the generality of the tool with three examples: infinite streams of real numbers, Mealy machines and labelled transition systems. 1.