Results 1 
4 of
4
Pseudodistributive laws
, 2004
"... We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudodistributive law between pseudomonads, and ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudodistributive law between pseudomonads, and we show how the definition and the main theorems about it may be used to model several such structures simultaneously. Specifically, we address the relationship between pseudodistributive laws and the lifting of one pseudomonad to the 2category of algebras and to the Kleisli bicategory of another. This, for instance, sheds light on the preservation of some structures but not others along the Yoneda embedding. Our leading examples are given by the use of open maps to model bisimulation and by the logic of bunched implications.
Local Reasoning about Data Update
 GDP FESTSCHRIFT ENTCS, TO APPEAR
"... We present local Hoare reasoning about data update, using Context Logic for analysing structured data. We apply our reasoning to tree update, heap update which is analogous to local Hoare reasoning using Separation Logic, and term rewriting. ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We present local Hoare reasoning about data update, using Context Logic for analysing structured data. We apply our reasoning to tree update, heap update which is analogous to local Hoare reasoning using Separation Logic, and term rewriting.
Views: Compositional Reasoning for Concurrent Programs
"... Compositional abstractions underly many reasoning principles for concurrent programs: the concurrent environment is abstracted in order to reason about a thread in isolation; and these abstractions are composed to reason about a program consisting of many threads. For instance, separation logic uses ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Compositional abstractions underly many reasoning principles for concurrent programs: the concurrent environment is abstracted in order to reason about a thread in isolation; and these abstractions are composed to reason about a program consisting of many threads. For instance, separation logic uses formulae that describe part of the state, abstracting the rest; when two threads use disjoint state, their specifications can be composed with the separating conjunction. Type systems abstract the state to the types of variables; threads may be composed when they agree on the types of shared variables. In this paper, we present the “Concurrent Views Framework”, a metatheory of concurrent reasoning principles. The theory is parameterised by an abstraction of state with a notion of composition, which we call views. The metatheory is remarkably simple, but highly applicable: the relyguarantee method, concurrent separation logic, concurrent abstract predicates, type systems for recursive references and for unique pointers, and even an adaptation of the OwickiGries method can all be seen as instances of the Concurrent Views Framework. Moreover, our metatheory proves each of these systems is sound without requiring induction on the operational semantics.
From IF to BI A Tale of Dependence and Separation
"... Abstract. We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges ’ semantics can be seen as a special case of a general construction, which provides a context for a useful ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges ’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle. 1.