Related papers: A Calculus for Language Transformations
Language transformations are algorithms that take a language specification in input, and return the language specification modified. Language transformations are useful for automatically adding features such as subtyping to programming…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
Coping with ambiguity has recently received a lot of attention in natural language processing. Most work focuses on the semantic representation of ambiguous expressions. In this paper we complement this work in two ways. First, we provide…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
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…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the {\pi}-calculus closely related to linear logic. Decompositions of intuitionistic…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
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…
Situation calculus has been widely applied in Artificial Intelligence related fields. This formalism is considered as a dialect of logic programming language and mostly used in dynamic domain modeling. However, type systems are hardly…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…