Related papers: Variable binding and substitution for (nameless) d…

We develop a unified categorical theory of substructural abstract syntax with variable binding and single-variable (capture-avoiding) substitution. This is done for the gamut of context structural rules given by exchange (linear theory)…

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…

The key to any nameless representation of syntax is how it indicates the variables we choose to use and thus, implicitly, those we discard. Standard de Bruijn representations delay discarding maximally till the leaves of terms where one is…

When using interactive theorem provers based on dependent type theory to define and reason about languages involving binding constructs, we advocate the use of a well-scoped version of the locally nameless method of representing syntax.…

Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…

A method is given for obtaining equivalence subgroups of a family of differential equations from the equivalence group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on…

The Bindlib library for OCaml provides a set of tools for the manipulation of data structures with variable binding. It is very well suited for the representation of abstract syntax trees, and has already been used for the implementation of…

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.

I propose a variable-free treatment of dynamic semantics. By "dynamic semantics" I mean analyses of donkey sentences ("Every farmer who owns a donkey beats it") and other binding and anaphora phenomena in natural language where meanings of…

We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…

There are many ways to represent the syntax of a language with binders. In particular, nominal frameworks are metalanguages that feature (among others) name abstraction types, which can be used to specify the type of binders. The resulting…

We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…

It is well-known in the field of programming languages that dealing with variable names and binders may lead to conflicts such as undesired captures when implementing interpreters or compilers. This situation has been overcome by resorting…

Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical…

Matthes and Uustalu (TCS 327(1-2):155-174, 2004) presented a categorical description of substitution systems capable of capturing syntax involving binding which is independent of whether the syntax is made up from least or greatest fixed…

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…

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple,…

Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…

Syntax is a latent hierarchical structure which underpins the robust and compositional nature of human language. In this work, we explore the hypothesis that syntactic dependencies can be represented in language model attention…