相关论文: Initiality for Typed Syntax and Semantics
Recently we presented a concise survey of the formulation of the induction and coinduction principles, and some concepts related to them, in programming languages type theory and four other mathematical disciplines. The presentation in type…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
Abstracting Gradual Typing (AGT) is an approach to systematically deriving gradual counterparts to static type disciplines. The approach consists of defining the semantics of gradual types by interpreting them as sets of static types, and…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
In this paper, we present a typed lambda calculus ${\bf SILL}(\lambda)_{\Sigma}$, a type-theoretic version of intuitionistic linear logic with subexponentials, that is, we have many resource comonadic modalities with some interconnections…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
Working with the simple types over a base type of natural numbers (including product types), we consider the question of when a type $\sigma$ is encodable as a definable retract of $\tau$: that is, when there are $\lambda$-terms…
Modeling interoperability between programs in different languages is a key problem when modeling verified and secure compilation, which has been successfully addressed using multi-language semantics. Unfortunately, existing models of…
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…
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…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
In this paper we provide a semantic and syntactic analysis of parametrised natural numbers object in coherent categories, or pr-coherent categories. Semantically, we show the definable functions in the initial pr-coherent category are…
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…
Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Gradually typed programming languages, which allow for soundly mixing static and dynamically typed programming styles, present a strong challenge for metatheorists. Even the simplest sound gradually typed languages feature at least…
The aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In…
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…