Results 1 
3 of
3
An Overview of the Tatami Project
, 2000
"... This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator fo ..."
Abstract

Cited by 13 (8 self)
 Add to MetaCart
(Show Context)
This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator for documentation websites, a database, an equational proof engine, and a communication protocol to support distributed cooperative work. We believe behavioral specification and verification are important for software development, and for this purpose we use first order hidden logic with equational atoms. The paper also briefly describes some novel user interface design methods that have been developed and applied in the project
Equational reasoning with subtypes
 Iowa State University
, 2002
"... Abstract. Using equational logic as a specification language, we investigate the proof theory of behavioral subtyping for objectoriented abstract data types with immutable objects and deterministic methods that can use multiple dispatch. In particular, we investigate a proof technique for correct b ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Using equational logic as a specification language, we investigate the proof theory of behavioral subtyping for objectoriented abstract data types with immutable objects and deterministic methods that can use multiple dispatch. In particular, we investigate a proof technique for correct behavioral subtyping in which each subtypeâ€™s specification includes terms that can be used to coerce its objects to objects of each of its supertypes. We show that this technique is sound, using our previous work on the model theory of such abstract data types. We also give an example to show that the technique is not complete, even if the methods do not use multiple dispatch, and even if types specified are termgenerated. In preparation for the results on equational subtyping we develop the proof theory of a richer form of equational logic that is suitable for dealing with subtyping and behavioral equivalence. This gives some insight into question of when our proof techniques can be make effectively computable, but in general behavioral consequence is not effectively computable. 1.
Observational Truth as a Categorical Modality
"... Abstract We examine the notion of truthuptoobservability in the setting of categorical logic and show that it can be captured by a modal operator. We view socalled `hidden algebras ' as setvalued functors on a category of observations. Our main results extend the KripkeBethJoyal semantic ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract We examine the notion of truthuptoobservability in the setting of categorical logic and show that it can be captured by a modal operator. We view socalled `hidden algebras ' as setvalued functors on a category of observations. Our main results extend the KripkeBethJoyal semantics for the internal logics of functor toposes to the observational modality. We also give a categorical account of coinduction as a proof technique for establishing observational truth, and give a covariety theorem that characterises a class of algebras as equationally definable up to observability iff the class forms a slice topos over a particular form of subobject.