Acta Informatica

, Volume 37, Issue 8, pp 541–561 | Cite as

A theory of bunches

  • Joseph M. Morris
  • Alexander Bunkenburg
Original articles


A bunch is a simple data structure, similar in many respects to a set. However, bunches differ from sets in that the data is not packaged up or encapsulated, and in particular in that a bunch consisting of one element is the same as that element. Bunches are attractive for handling nondeterminacy and underspecification, by which is meant that for any particular input to the program or specification, the associated output is not fully determined. The acceptable outputs for any given input can be described by a bunch. This approach nicely generalises traditional single-output programs and specifications. We present a formal theory of bunches. It includes an axiomatisations of boolean and function types whose behaviour is well-known to be complicated by the presence of nondeterminacy. The axiomatisation of the booleans preserves most of the laws of classical predicate calculus. The axiomatisation of functions accommodates higher-order functions in all their generality, while avoiding the dangers of inconsistency when functions and nondeterminacy intermix. Our theory is presented as a Hilbert-style system of axioms and inference rules for a small specification language. We prove consistency.


Data Structure Formal Theory Inference Rule Function Type Specification Language 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Joseph M. Morris
    • 1
  • Alexander Bunkenburg
    • 2
  1. 1.School of Computer Applications, Dublin City University, Dublin, Ireland (e-mail: IE
  2. 2.Department of Computing Science, University of Glasgow, Glasgow G12 8RZ, United Kingdom GB

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