Related papers: Formal Metatheory of Second-Order Abstract Syntax
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…
We present a framework for the formal meta-theory of lambda calculi in first-order syntax, with two sorts of names, one to represent both free and bound variables, and the other for constants, and by using Stoughton's multiple…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
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…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
Linear typed $\lambda$-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more…
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…
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)…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
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 contribution of this paper is the development of the syntax and semantics of multi-sorted nominal abstract binding trees (abts), an extension of second order universal algebra to support symbol-indexed families of operators. Nominal…
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…
Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model-value beyond mere comprehensible pictures. To…
Among the most general structures extending the framework by Dung are the abstract dialectical frameworks (ADFs). They come equipped with various types of semantics, with the most prominent - the labeling-based one - analyzed in the context…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of $\alpha$-equivalence, capture-avoiding substitution, typing contexts, runtime environments,…
We adapt the technique of type-generic programming via descriptions pointing into a universe to the domain of typed languages with binders and variables, implementing a notion of "syntax-generic programming" in a dependently typed…