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Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…

Causal reasoning, the ability to identify cause-and-effect relationship, is crucial in human thinking. Although large language models (LLMs) succeed in many NLP tasks, it is still challenging for them to conduct complex causal reasoning…

Many studies were recently done for investigating the properties of contextual language models but surprisingly, only a few of them consider the properties of these models in terms of semantic similarity. In this article, we first focus on…

We introduce SecRef*, a secure compilation framework protecting stateful programs verified in F* against linked unverified code, with which the program dynamically shares ML-style mutable references. To ease program verification in this…

Component-based synthesis seeks to build programs using the APIs provided by a set of libraries. Oftentimes, these APIs have effects, which make it challenging to reason about the correctness of potential synthesis candidates. This is…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

Deductive verification of hybrid systems (HSs) increasingly attracts more attention in recent years because of its power and scalability, where a powerful specification logic for HSs is the cornerstone. Often, HSs are naturally modelled by…

Thanks to the locality principle, separation logics support modular, scalable analysis of large codebases by relying on local axioms and frame rules to focus only on the heap fragments required for verification. However, depending on the…

Separation logic is a Hoare-style logic for reasoning about programs with heap-allocated mutable data structures. As a step toward extending separation logic to high-level languages with ML-style general (higher-order) storage, we…

Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to…

The C/C++ memory model provides an interface and execution model for programmers of concurrent (shared-variable) code. It provides a range of mechanisms that abstract from underlying hardware memory models -- that govern how multicore…

One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…

Scaling test-time computation--generating and analyzing multiple or sequential outputs for a single input--has become a promising strategy for improving the reliability and quality of large language models (LLMs), as evidenced by advances…

Reasoning about the sensitivity of functions with respect to their inputs has interesting applications in various areas, such as differential privacy. In order to check and enforce sensitivity, several approaches have been developed,…

Deep learning is being used extensively in a variety of software engineering tasks, e.g., program classification and defect prediction. Although the technique eliminates the required process of feature engineering, the construction of…

Programs are more distributed and concurrent today than ever before, and structural communications are at the core. Constructing and debugging such programs are hard due to the lack of formal specification/verification of concurrency. This…

In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling and distributional semantics to probabilistic programs with continuous distributions. Towards this end, we sketch an encoding…

Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…

While the success of semi-supervised learning (SSL) is still not fully understood, Sch\"olkopf et al. (2012) have established a link to the principle of independent causal mechanisms. They conclude that SSL should be impossible when…

Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a…