相关论文: Well-Scoped Locally Nameless Representation of Syn…

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…

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,…

In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming,…

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…

Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…

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,…

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 define "Locally Nameless Permutation Types", which fuse permutation types as used in Nominal Isabelle with the locally nameless representation. We show that this combination is particularly useful when formalizing programming languages…

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…

By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore,…

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…

Agda is a dependently-typed programming language and a proof assistant, pivotal in proof formalization and programming language theory. This paper extends the Agda ecosystem into machine learning territory, and, vice versa, makes…

We present a lightweight, open source Agda framework for manually verifying effectful programs using predicate transformer semantics. We represent the abstract syntax trees (AST) of effectful programs with a generalized algebraic datatype…

In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…

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…

Nominal techniques provide a mathematically principled approach to dealing with names and variable binding in programming languages. This paper explores an attempt to make nominal techniques accessible as an Agda library. We aim for a…

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 develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…

We employ the dependently-typed programming language Agda2 to explore formalisation of untyped and typed term graphs directly as set-based graph structures, via the gs-monoidal categories of Corradini and Gadducci, and as nested…

Sign Language (SL) linguistic is dependent on the expensive task of annotating. Some automation is already available for low-level information (eg. body part tracking) and the lexical level has shown significant progresses. The syntactic…