Related papers: Initial Semantics for Strengthened Signatures
We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as…
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…
Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for…
We give an algebraic characterization of the syntax and semantics of a class of languages with variable binding. We introduce a notion of 2-signature: such a signature specifies not only the terms of a language, but also reduction rules on…
Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general…
Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…
Initial semantics aims to capture inductive structures and their properties as initial objects in suitable categories. We focus on the initial semantics aiming to model the syntax and substitution structure of programming languages with…
The signature of a path can be described as its full non-commutative exponential. Following T. Lyons we regard its expectation, the expected signature, as path space analogue of the classical moment generating function. The logarithm…
In their work on second-order equational logic, Fiore and Hur have studied presentations of simply typed languages by generating binding constructions and equations among them. To each pair consisting of a binding signature and a set of…
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…
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…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Characterizing programming languages with variable binding as initial objects, was first achieved by Fiore, Plotkin, and Turi in their seminal paper published at LICS'99. To do so, in particular to prove initiality theorems, they developed…
Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic…
We present a constructive formalization of Abstract Rewriting Systems (ARS) in the Agda proof assistant, focusing on standard results in term rewriting. We define a taxonomy of concepts related to termination and confluence and investigate…
Abstract Meaning Representation (AMR) is a recently designed semantic representation language intended to capture the meaning of a sentence, which may be represented as a single-rooted directed acyclic graph with labeled nodes and edges.…