Abstract

We study a typing scheme derived from a semantic situation where a single category possesses several closed structures, corresponding to dierent varieties of function type. In this scheme typing contexts are trees built from two (or more) binary combining operations, or in short, bunches. Bunched typing and its logical counterpart, bunched implications, have arisen in joint work of the author and David Pym. The present paper gives a basic account of the type system, and then focusses on concrete models that illustrate how it may be understood in terms of resource access and sharing. The most

Citations

815	Categories for the Working Mathematician - Lane - 1971
272	Computational interpretations of linear logic - Abramsky - 1993
237	H.: Local Reasoning about Programs that Alter Data Structures - O’Hearn, Reynolds, et al. - 2001
203	A Linear Logical Framework - CERVESATO, PFENNING - 2002
172	The logic of bunched implications - O’Hearn, Pym - 1999
155	The essence of Algol - Reynolds - 1981
148	as an assertion language for mutable data structures - BI - 2001
127	Syntactic Control of Interference - Reynolds - 1978
121	P.: BI as an assertion language for mutable data structures - Ishtiaq, O’Hearn - 2001
101	Intuitionistic reasoning about shared mutable data structure - Reynolds - 2000
98	Display logic - Belnap - 1982
92	What is a Categorical Model of Intuitionistic Linear Logic - Bierman - 1995
92	Relevance logic and entailment - Dunn - 1986
89	On closed categories of functors - Day - 1970
89	The linear abstract machine - Lafont - 1988
88	A mixed linear and non-linear logic: Proofs, terms and models - Benton - 1995
88	The Semantics and Proof Theory of the Logic of Bunched Implications - Pym
79	Dual intuitionistic linear logic - Barber - 1996
79	Formal Category Theory: Adjointness for 2-Categories - Gray - 1974
76	Operating systems principles - Hansen - 1973
68	A term calculus for intuitionistic Linear Logic - Benton, Bierman, et al. - 1993
64	The Craft of Programming - Reynolds - 1981
56	A Spatial Logic for Querying Graphs - Cardelli, Gardner, et al. - 2002
53	J.C.: From Algol to polymorphic linear lambda-calculus - O’Hearn, Reynolds - 2000
46	The Geometry of Concurrency - Goubault - 1995
44	A Category-Theoretic Approach to the Semantics of Programming Languages - Oles - 1982
41	Syntactic control of interference revisited - O’Hearn, Power, et al.
35	Semantics of local variables - O'Hearn, Tennent - 1992
31	Modal Logic for Mobile Ambients - Anytime - 2000
31	Natural deduction for intuitionistic non-commutative linear logic - Polakow, Pfenning - 1999
31	Pomset logic: a non-commutative extension of classical linear logic - Retoré - 1997
30	Polymorphic eect systems - Lucassen, Giord - 1988
30	Relevant logic: A philosophical examination of inference - Read - 1988
29	Anembedding theorem for closed categories - Day - 1974
27	On bunched predicate logic - Pym - 1999
26	Syntactic Control of Interference, Part 2 - Reynolds - 1989
23	A relevant analysis of natural deduction - Ishtiaq, Pym - 1998
23	R.D.: Algol-like Languages (Two volumes - O’Hearn, Tennent - 1997
19	A model for syntactic control of interference - O’Hearn
17	Linear logic and interference control - O’Hearn - 1991
16	Objects, interference and the Yoneda embedding - O’Hearn, Reddy - 1999
12	Linear *-Calculus and Categorical Models Revisited - Benton, Bierman, et al.
11	The semantics of non-interference: a natural approach - O’Hearn - 1990
10	Algebraic categories with few monoidal biclosed structures or none - Foltz, Lair, et al. - 1980
10	Resource interpretations, bunched implications and the ##-calculus, in preparation, preliminary version - O'Hearn
7	29{April 1 - Brookes, Main, et al.
4	A linear logic model of state - Reddy - 1993
3	Type Systems for Polynomial Time Complexity. Habilitation thesis, Darmstadt. Available as Edinburgh report ECS-LFCS-99-406 - Hofmann - 1999
3	Linear continuationpassing - Berdine, O'Hearn, et al. - 2002
2	Possible worlds and resources: The semantics of BI. Submitted - O'Hearn, Pym, et al. - 2000