Related papers: Representing operational semantics with enriched L…
Yoshida demonstrated how to eliminate the bound names coming from the input prefix in the asynchronous pi calculus, but her combinators still depend on the "new" operator to bind names. We modify Yoshida's combinators by replacing "new" and…
Enriched Lawvere theories are a generalization of Lawvere theories that allow us to describe the operational semantics of formal systems. For example, a graph enriched Lawvere theory describes structures that have a graph of operations of…
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
We give an exposition of the semantics of the simply-typed lambda-calculus, and its linear and ordered variants, using multi-ary structures. We define universal properties for multicategories, and use these to derive familiar rules for…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
This article is devoted to the presentation of lambda_rex, an explicit substitution calculus with de Bruijn indexes and a simple notation. By being isomorphic to lambda_ex - a recent formalism with variable names -, lambda_rex accomplishes…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
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…
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…
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…
We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…
In 1990 J-L. Krivine introduced the notion of storage operators. They are $\lambda$-terms which simulate call-by-value in the call-by-name strategy and they can be used in order to modelize assignment instructions. J-L. Krivine has shown…
We provide an explicit combinatorial realization of all simple and injective (hence, and projective) modules in the category of bounded $\mathfrak{sp}(2n)$-modules. This realization is defined via a natural tableaux 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…
We set up a left ring of fractions over a certain ring of boundary problems for linear ordinary differential equations. The fraction ring acts naturally on a new module of generalized functions. The latter includes an isomorphic copy of the…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
We give a modern computational introduction to the S,K combinators invented by Moses Sch\"onfinkel in 1920, and present a variety of new results and ideas about combinators. We explore the spectrum of behavior obtained with small combinator…
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…