Abstract
This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time reasoning, and less pessimistic execution time estimation using amortized analysis. We define a Hoare logic for the three cases and prove its soundness with respect to an annotated cost-aware operational semantics. Finally, we define a verification conditions (VC) generator that generates the goals needed to prove program correctness, cost, and termination. Those goals are then sent to the Easycrypt toolset for validation. The practicality of the proof system is demonstrated with an implementation in OCaml of the different modules needed to apply it to example programs. Our case studies are motivated by real-time and cryptographic software.

Abstract
In this work, we enhance the EasyCrypt proof assistant to reason about the computational complexity of adversaries. The key technical tool is a Hoare logic for reasoning about computational complexity (execution time and oracle calls) of adversarial computations. Our Hoare logic is built on top of the module system used by EasyCrypt for modeling adversaries. We prove that our logic is sound w.r.t. the semantics of EasyCrypt programs-we also provide full semantics for the EasyCrypt module system, which was lacking previously. We showcase (for the first time in EasyCrypt and in other computer-aided cryptographic tools) how our approach can express precise relationships between the probability of adversarial success and their execution time. In particular, we can quantify existentially over adversaries in a complexity class and express general composition statements in simulation-based frameworks. Moreover, such statements can be composed to derive standard concrete security bounds for cryptographic constructions whose security is proved in a modular way. As a main benefit of our approach, we revisit security proofs of some well-known cryptographic constructions and present a new formalization of universal composability.

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Abstract
We study principles and models for reasoning inductively about properties of distributed systems, based on programmed atomic handlers equipped with contracts. We present the Why3-do library, leveraging a state of the art software verifier for reasoning about distributed systems based on our models. A number of examples involving invariants containing existential and nested quantifiers (including Dijsktra's self-stabilizing systems) illustrate how the library promotes contract-based modular development, abstraction barriers, and automated proofs.

Abstract
The present Special Issue of the Journal of Logical and Algebraic Methods in Programming was planned as a tribute to Jose Manuel Esgalhado Valenca on the occasion of his Jubilation. A tribute to a professor, in the deepest sense of the word, a colleague and a friend, but above all to a long and inspiring academic journey that has so profoundly shaped the development of Informatics as a scientific area in Portugal. A scientific area that, as he taught us, needs to be understood broadly: not only as an independent research domain, but also as an educational pillar, a strategy for social and economic development, a foundation for a multifaceted professional career. This preface introduces some steps of such a journey. The Special Issue features a selection of scientific papers written by his collaborators, colleagues and friends, covering the different areas Jose Valenca helped to launch and consolidate in Portugal, namely computational logic, verification and mechanized reasoning, and information security. (c) 2022 Published by Elsevier Inc.