Related papers: Unfolding Semantics of the Untyped {\lambda}-Calcu…
Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption and more generally to optimize a given program. Essentially it consists of a sequence of syntactic program manipulations which…
A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no…
$\lambda\upsilon$ is an extension of the $\lambda$-calculus which internalises the calculus of substitutions. In the current paper, we investigate the combinatorial properties of $\lambda\upsilon$ focusing on the quantitative aspects of…
We present several results on counting untyped lambda terms, i.e., on telling how many terms belong to such or such class, according to the size of the terms and/or to the number of free variables.
Unfolding, in the context of high-energy particle physics, refers to the process of removing detector distortions in experimental data. The resulting unfolded measurements are straightforward to use for direct comparisons between…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…
We study the semantics of an untyped lambda-calculus equipped with operators representing read and write operations from and to a global store. We adopt the monadic approach to model side-effects and treat read and write as algebraic…
Large language models (LLMs) represent words through contextual word embeddings encoding different language properties like semantics and syntax. Understanding these properties is crucial, especially for researchers investigating language…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
We study Milner's lambda-calculus with partial substitutions. Particularly, we show confluence on terms and metaterms, preservation of \b{eta}-strong normalisation and characterisation of strongly normalisable terms via an intersection…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
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…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal…
In the previous article we derived a detailed asymptotic expansion of the heat trace for the Laplace-Beltrami operator on functions on manifolds with conic singularities. In this article we investigate how the terms in the expansion reflect…
We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…