57 research outputs found
Resource-Bound Quantification for Graph Transformation
Graph transformation has been used to model concurrent systems in software
engineering, as well as in biochemistry and life sciences. The application of a
transformation rule can be characterised algebraically as construction of a
double-pushout (DPO) diagram in the category of graphs. We show how
intuitionistic linear logic can be extended with resource-bound quantification,
allowing for an implicit handling of the DPO conditions, and how resource logic
can be used to reason about graph transformation systems
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 an embedding of Graph Transformation in Intuitionistic Linear Logic
Linear logics have been shown to be able to embed both rewriting-based
approaches and process calculi in a single, declarative framework. In this
paper we are exploring the embedding of double-pushout graph transformations
into quantified linear logic, leading to a Curry-Howard style isomorphism
between graphs and transformations on one hand, formulas and proof terms on the
other. With linear implication representing rules and reachability of graphs,
and the tensor modelling parallel composition of graphs and transformations, we
obtain a language able to encode graph transformation systems and their
computations as well as reason about their properties
Redundancy Elimination for LF
AbstractWe present a type system extending the dependent type theory LF, whose terms are more amenable to compact representation. This is achieved by carefully omitting certain subterms which are redundant in the sense that they can be recovered from the types of other subterms. This system is capable of omitting more redundant information than previous work in the same vein, because of its uniform treatment of higher-order and first-order terms. Moreover the ‘recipe’ for reconstruction of omitted information is encoded directly into annotations on the types in a signature. This brings to light connections between bidirectional (synthesis vs. checking) typing algorithms of the object language on the one hand, and the bidirectional flow of information in the ambient encoding language. The resulting system is a compromise seeking to retain both the effectiveness of full unification-based term reconstruction such as is found in implementation practice, and the logical simplicity of pure LF
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