Related papers: Representing Isabelle in LF
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Isabelle is an interactive theorem prover that supports a variety of logics. It represents rules as propositions (not as functions) and builds proofs by combining rules. These operations constitute a meta-logic (or `logical framework') in…
We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
This is an overview of the Isabelle technology behind the Archive of Formal Proofs (AFP). Interactive development and quasi-interactive build jobs impose significant demands of scalability on the logic (usually Isabelle/HOL), on Isabelle/ML…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
We describe the development of a logic for reasoning about specifications in the Edinburgh Logical Framework (LF). In this logic, typing judgments in LF serve as atomic formulas, and quantification is permitted over contexts and terms that…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have…
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…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…