An Axiomatization of Linear Temporal Logic in the Calculus of Inductive Constructions

A coinductive semantics of the Unlimited Register Machine

“…As an example, let us consider the abstract program B 1 →J(1, 2, 2), 2 →J(1, 2, 2) . We can prove that the computation under B with the configuration σ (1 →0, 2 →1) converges, while it diverges with τ (1 →0, 2 →0); both the proofs are immediate, the second one is by coinduction 9 :…”

“…There are several contributions in the literature exploiting the potential of coinductive definitions and proofs within CC (Co)Ind to master the fundamental concept of non-terminating computation. Some of these approaches concern transition systems [10, 3], linear temporal logic [9,3] and process algebras [18,20].…”

“Backward” coinduction, Nash equilibrium and the rationality of escalation

“…Interested readers may have a look at Coupet-Grimal [10], Coupet-Grimal and Jakubiec [11], Lescanne [20], Bertot [2,3] and especially Bertot and Castéran [4, chap. 13] for other examples of cofix reasoning.…”

Filters on CoInductive Streams, an Application to Eratosthenes’ Sieve

“…The property that must be repeated for all streams is an always (eventually P). Castéran and Rouillard [4] and Coupet-Grimal [6] have already studied how these linear logic predicates can be encoded as inductive predicates. In our case, we assume that we are working in a context where the predicate P is given, and we encode directly the combination of always and eventually as a predicate on streams, which we call F_infinite (the predicates always, eventually and F_infinite are similar to the ones with the same name in [1], except that our predicates are parameterized by a property on stream elements instead of a property on streams).…”

“…We propose to combine insights coming from reasoning techniques on linear temporal logic [4,6] and on general recursion, essentially the techique advocated by A. Bove [2] in the context of Martin-Löf type theory. We transpose this technique to the Calculus of Inductive Constructions, the underlying theory for the Coq system, with some added difficulties coming from the use of two sorts.…”