Related papers: A Probabilistic Call-by-Need Lambda-Calculus -- Ex…
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 classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
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…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
We aim to reason about the correctness of behaviour-preserving transformations of Erlang programs. Behaviour preservation is characterised by semantic equivalence. Based upon our existing formal semantics for Core Erlang, we investigate…
Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…
Test-time compute scaling, the practice of spending extra computation during inference via repeated sampling, search, or extended reasoning, has become a powerful lever for improving large language model performance. Yet deploying these…
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…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…
Quantum lambda calculus has been studied mainly as an idealized programming language -- the evaluation essentially corresponds to a deterministic abstract machine. Very little work has been done to develop a rewriting theory for quantum…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
This paper formalizes and proves correct a compilation scheme for mutually-recursive definitions in call-by-value functional languages. This scheme supports a wider range of recursive definitions than previous methods. We formalize our…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…