Related papers: Case Studies in Formal Reasoning About Lambda-Calc…
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…
Verifying a real-world program's functional correctness can be decomposed into (1) a refinement proof showing that the program implements a more abstract high-level program and (2) an algorithm correctness proof at the high level.…
In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…
Formal programming language semantics are imperative when trying to verify properties of programs in an automated manner. Using a new approach, Din et al. strengthen the ability of reasoning about concurrent programs by proposing a modular…
This thesis presents a formalization of martingales in arbitrary Banach spaces using Isabelle/HOL. We begin by examining formalizations in prominent proof repositories and extend the definition of the conditional expectation operator from…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…
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…
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…
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda…
Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different tools are being increasingly used in…
We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…
Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding…
We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global…
We present fully abstract encodings of the call-by-name and call-by-value $\lambda$-calculus into HOcore, a minimal higher-order process calculus with no name restriction. We consider several equivalences on the $\lambda$-calculus side --…
A comprehensive model of natural language processing in the brain must accommodate four components: representations, operations, structures and encoding. It further requires a principled account of how these components mechanistically, and…
We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…
We present a variant of the calculus of deductive systems developed in (Lambek 1972, 1974), and give a generalization of the Curry-Howard-Lambek theorem giving an equivalence between the category of typed lambda-calculi and the category of…
Type annotations are essential when printing terms in a way that preserves their meaning under reparsing and type inference. We study the problem of complete and minimal type annotations for rank-one polymorphic $\lambda$-calculus terms, as…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…