Editing Bunched logic (section)

{{short description|Branch of logic}}
'''Bunched logic'''<ref name=OP99>{{cite journal|last1=O'Hearn|first1=Peter|last2=Pym|first2=David|title=The Logic of Bunched Implications|journal=[[Bulletin of Symbolic Logic]]|date=1999|volume=5|issue=2|pages=215–244|doi=10.2307/421090|url=http://www.cs.ucl.ac.uk/staff/p.ohearn/papers/BI.pdf|jstor=421090|citeseerx=10.1.1.27.4742|s2cid=2948552 }}</ref> is a variety of [[substructural logic]] proposed by [[Peter O'Hearn]] and [[David Pym]]. Bunched logic provides primitives for reasoning about ''resource composition'', which aid in the compositional analysis of computer and other systems. It has [[category-theoretic]] and truth-functional semantics, which can be understood in terms of an abstract concept of resource, and a proof theory in which the contexts Γ in an [[Logical consequence|entailment]] judgement Γ ⊢ A are tree-like structures (bunches) rather than [[sequence (mathematics)|list]]s or ([[multiset|multi]])[[set (mathematics)|set]]s as in most [[proof calculi]]. Bunched logic has an associated [[type theory]], and its first application was in providing a way to control the [[aliasing (computing)|aliasing]] and other forms of interference in [[imperative program]]s.<ref name=OHearn02>{{cite journal|last1=O'Hearn|first1=Peter|title=On Bunched Typing|journal=[[Journal of Functional Programming]]|date=2003|volume=13|issue=4|pages=747–796|doi=10.1017/S0956796802004495|url=http://www0.cs.ucl.ac.uk/staff/p.ohearn/papers/BunchedTyping.pdf}}</ref>
The logic has seen further applications in [[program verification]], where it is the basis of the assertion language of [[separation logic]],<ref name=IO01>{{cite journal|last1=Ishtiaq|first1=Samin|last2=O'Hearn|first2=Peter|title=BI as an assertion language for mutable data structures|journal=POPL|date=2001|volume=28th|issue=3|pages=14–26|doi=10.1145/373243.375719|url=http://www0.cs.ucl.ac.uk/staff/p.ohearn/papers/bi-assertion-lan.pdf|citeseerx=10.1.1.11.4925}}</ref> and in [[systems modelling]], where it provides a way to decompose the resources used by components of a system.<ref name="PymTofts2" /><ref name=":0" /><ref name=":1" />