相关论文: The Formal System lambda-delta

In this paper we investigate the Curry-Howard correspondence for constructive modal logic in light of the gap between the proof equivalences enforced by the lambda calculi from the literature and by the recently defined winning strategies…

We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…

We present a full formalization in Martin-L\"of's Constructive Type Theory of the Standardization Theorem for the Lambda Calculus using first-order syntax with one sort of names for both free and bound variables and Stoughton's multiple…

This short note presents a new formal language, lambda dependency-based compositional semantics (lambda DCS) for representing logical forms in semantic parsing. By eliminating variables and making existential quantification implicit, lambda…

We introduce the Delta-framework, LF-Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union.…

The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…

Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…

Tables have gained significant attention in large language models (LLMs) and multimodal large language models (MLLMs) due to their complex and flexible structure. Unlike linear text inputs, tables are two-dimensional, encompassing formats…

The aim of this work is to characterize three fundamental normalization proprieties in lambda-calculus trough the Taylor expansion of $ \lambda$-terms. The general proof strategy consists in stating the dependence of ordinary reduction…

The elementary affine lambda-calculus was introduced as a polyvalent setting for implicit computational complexity, allowing for characterizations of polynomial time and hyperexponential time predicates. But these results rely on type…

We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field…

A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…

The Curry-Howard Correspondence has a long history, and still is a topic of active research. Though there are extensive investigations into the subject, there doesn't seem to be a definitive formulation of this result in the level of…