相关论文: Strong normalisation for applied lambda calculi

We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…

In each variant of the lambda-calculus, factorization and normalization are two key-properties that show how results are computed. Instead of proving factorization/normalization for the call-by-name (CbN) and call-by-value (CbV) variants…

We give an adequate, concrete, categorical-based model for Lambda-S, which is a typed version of a linear-algebraic lambda calculus, extended with measurements. Lambda-S is an extension to first-order lambda calculus unifying two approaches…

We study the semantics of a resource-sensitive extension of the lambda calculus in a canonical reflexive object of a category of sets and relations, a relational version of Scott's original model of the pure lambda calculus. This calculus…

Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…

One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…

In this paper we prove that any lambda-term that is strongly normalising for beta-reduction is also strongly normalising for beta,assoc-reduction. assoc is a call-by-value rule that has been used in works by Moggi, Joachimsky, Espirito…

In this paper we prove that if $\{\varphi_i(x)=\lambda x+t_i\}$ is an equicontractive iterated function system and $b$ is a positive integer satisfying $\frac{\log b}{\log |\lambda|}\notin\mathbb{Q},$ then almost every $x$ is normal in base…

We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…

It is a common knowledge that the integer functions definable in simply typed lambda-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p->p)->p->p where p is a base type…

In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…

Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further…

We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…

We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…

There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…

In our paper "Uniformity and the Taylor expansion of ordinary lambda-terms" (with Laurent Regnier), we studied a translation of lambda-terms as infinite linear combinations of resource lambda-terms, from a calculus similar to Boudol's…

The strong recurrence is equivalent to the Riemann hypothesis. On the other hand, the generalized strong recurrence holds for any irrational number. In this paper, we show the generalized strong recurrence for all non-zero rational numbers.…

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…

This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional…