Related papers: Call-by-value, call-by-name and the vectorial beha…
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…
The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
Abella is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and…
The $\lambda\mu$-calculus plays a central role in the theory of programming languages as it extends the Curry-Howard correspondence to classical logic. A major drawback is that it does not satisfy B\"ohm's Theorem and it lacks the…
Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. for hardware synthesis or for…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
We present an elegant design of the core language in a dependently-typed lambda calculus with $\delta$-reduction and an elaboration algorithm.
Pitts and Stark's $\nu$-calculus is a paradigmatic total language for studying the problem of contextual equivalence in higher-order languages with name generation. Models for the $\nu$-calculus that validate basic equivalences concerning…
Large language models (LLMs) often encode word-form variation (e.g., walk vs. walked) as linear directions in the embedding space. However, standard tokenization algorithms treat such variants as distinct words with different vocabulary…
Multilingual pre-trained Large Language Models (LLMs) are incredibly effective at Question Answering (QA), a core task in Natural Language Understanding, achieving high accuracies on several multilingual benchmarks. However, little is known…
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
Approximation semantics capture the observable behaviour of {\lambda}-terms, with B\"ohm Trees and Taylor Expansion standing as two central paradigms. Although conceptually different, these notions are related via the Commutation Theorem,…
LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet…
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…