9 research outputs found
A practical module system for LF
Module systems for proof assistants provide administrative support for large developments when mechanizing the meta-theory of programming languages and logics. In this paper we describe a module system for the logical framework LF. It is based on two main primitives: signatures and signature morphisms, which provide a semantically transparent module level and permit to represent logic translations as homomorphisms. Modular LF is a conservative extension over LF, and defines an elaboration of modular into core LF signatures. We have implemented our design in the Twelf system and used it to modularize large parts of the Twelf example library
Representing Isabelle in LF
LF has been designed and successfully used as a meta-logical framework to
represent and reason about object logics. Here we design a representation of
the Isabelle logical framework in LF using the recently introduced module
system for LF. The major novelty of our approach is that we can naturally
represent the advanced Isabelle features of type classes and locales.
Our representation of type classes relies on a feature so far lacking in the
LF module system: morphism variables and abstraction over them. While
conservative over the present system in terms of expressivity, this feature is
needed for a representation of type classes that preserves the modular
structure. Therefore, we also design the necessary extension of the LF module
system.Comment: In Proceedings LFMTP 2010, arXiv:1009.218
Towards MKM in the Large: Modular Representation and Scalable Software Architecture
MKM has been defined as the quest for technologies to manage mathematical
knowledge. MKM "in the small" is well-studied, so the real problem is to scale
up to large, highly interconnected corpora: "MKM in the large". We contend that
advances in two areas are needed to reach this goal. We need representation
languages that support incremental processing of all primitive MKM operations,
and we need software architectures and implementations that implement these
operations scalably on large knowledge bases.
We present instances of both in this paper: the MMT framework for modular
theory-graphs that integrates meta-logical foundations, which forms the base of
the next OMDoc version; and TNTBase, a versioned storage system for XML-based
document formats. TNTBase becomes an MMT database by instantiating it with
special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
An Open Challenge Problem Repository for Systems Supporting Binders
A variety of logical frameworks support the use of higher-order abstract
syntax in representing formal systems; however, each system has its own set of
benchmarks. Even worse, general proof assistants that provide special libraries
for dealing with binders offer a very limited evaluation of such libraries, and
the examples given often do not exercise and stress-test key aspects that arise
in the presence of binders. In this paper we design an open repository ORBI
(Open challenge problem Repository for systems supporting reasoning with
BInders). We believe the field of reasoning about languages with binders has
matured, and a common set of benchmarks provides an important basis for
evaluation and qualitative comparison of different systems and libraries that
support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759
Representing Model Theory in a Type-Theoretical Logical Framework
AbstractWe give a comprehensive formal representation of first-order logic using the recently developed module system for the Twelf implementation of the Edinburgh Logical Framework LF. The module system places strong emphasis on signature morphisms as the main primitive concept, which makes it particularly useful to reason about structural translations, which occur frequently in proof and model theory.Syntax and proof theory are encoded in the usual way using LF's higher order abstract syntax and judgments-as-types paradigm, but using the module system to treat all connectives and quantifiers independently. The difficulty is to reason about the model theory, for which the mathematical foundation in which the models are expressed must be encoded itself. We choose a variant of Martin-Löf's type theory as this foundation and use it to axiomatize first-order model theoretic semantics. Then we can encode the soundness proof as a signature morphism from the proof theory to the model theory. We extend our results to models given in terms of set theory using an encoding of Zermelo-Fraenkel set theory in LF and giving a signature morphism from Martin-Löf type theory into it. These encodings can be checked mechanically by Twelf.Our results demonstrate the feasibility of comprehensively formalizing large scale representation theorems and thus promise significant future applications
Architectural Refinement in HETS
The main objective of this work is to bring a number of improvements to the Heterogeneous Tool Set HETS, both from a theoretical and an implementation point of view. In the first part of the thesis we present a number of recent extensions of the tool, among which declarative specifications of logics, generalized theoroidal comorphisms, heterogeneous colimits and integration of the logic of the term rewriting system Maude. In the second part we concentrate on the CASL architectural refinement language, that we equip with a notion of refinement tree and with calculi for checking correctness and consistency of refinements. Soundness and completeness of these calculi is also investigated. Finally, we present the integration of the VSE refinement method in HETS as an institution comorphism. Thus, the proof manangement component of HETS remains unmodified