Related papers: Type-Based Termination for Futures
We present a novel general resource analysis for logic programs based on sized types. Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of…
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…
We show how systems of sessions types can enforce interactions to be bounded for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
We consider prescriptive type systems for logic programs (as in Goedel or Mercury). In such systems, the typing is static, but it guarantees an operational property: if a program is "well-typed", then all derivations starting in a…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
Large language models (LLMs) achieve strong performance by generating long chains of thought, but longer traces always introduce redundant or ineffective reasoning steps. One typical behavior is that they often perform unnecessary…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We…
Computational efficiency has remained a critical consideration in scaling high-capacity language models, with inference latency and resource consumption presenting significant constraints on real-time applications. The study has introduced…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to…
We study termination of higher-order probabilistic functional programs with recursion, stochastic conditioning and sampling from continuous distributions. Reasoning about the termination probability of programs with continuous distributions…
We introduce a method of verifying termination of logic programs with respect to concrete queries (instead of abstract query patterns). A necessary and sufficient condition is established and an algorithm for automatic verification is…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This type theory can be used as a metalanguage for synthetic guarded domain theory in which one can…
There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a…
We present a new characterization of termination of general logic programs. Most existing termination analysis approaches rely on some static information about the structure of the source code of a logic program, such as modes/types,…