Related papers: A Unified Framework for Initial Semantics
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…
Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial…
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…
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 simply-typed languages, such as the language PCF: we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as…
In this thesis we give an algebraic characterization of the syntax and semantics of simply-typed languages. More precisely, we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the…
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…
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal…
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…
We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a…
We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
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…
Ontologies form the basic interest in various computer science disciplines such as semantic web, information retrieval, database design, etc. They aim at providing a formal, explicit and shared conceptualization and understanding of common…
Presheaves and nominal sets provide alternative abstract models of sets of syntactic objects with free and bound variables, such as lambda-terms. One distinguishing feature of the presheaf-based perspective is its elegant syntax-free…
Mechanisms are a fundamental concept in many areas of science. Nonetheless, there has been little effort to develop structures to represent mechanisms. We explore the issues in developing a basic semantic modeling framework for describing…
The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…