Permission accounting in separation logic

Bornat, Richard; Calcagno, Cristiano; O’Hearn, Peter W.; Parkinson, Matthew

doi:10.1145/1040305.1040327

Cited by 246 publications

(221 citation statements)

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“…Examples of separation algebras include multisets with union and unit ∅, the natural numbers with addition and unit 0, heaps as finite partial functions from locations to values ( [9] and example 2.8), heaps with permissions [9,4], and the combination of heaps and variable stacks enabling us to model programs with variables as local functions ( [9], [17] and example 2.8). These examples all have an intuition of resource, with σ 1 • σ 2 intuitively giving more resource than just σ 1 and σ 2 for σ 1 , σ 2 = u.…”

Section: Definition 21 (Separation Algebra)mentioning

confidence: 99%

“…The unit u H is the function with the empty domain which represents the empty heap and empty stack. Although this approach is limited to disjoint reference to stack variables, this constraint can be lifted by enriching the separation algebra with permissions [4]. However, this added complexity using permissions can be avoided for the discussion in this paper.…”

Section: Lemma 27 Locality Is Preserved Under Sequential Compositiomentioning

confidence: 99%

“…The notion of a small specification has until now been used in an informal sense in local reasoning papers [14,4,7] as specifications that completely specify the behaviour of an update command by only describing the command's behaviour on the part of the resource that it affects. Although these papers present examples of such specifications for specific commands, the notion has so far not received a formal treatment in the general case.…”

Section: Proposition 37 (Big Specification) For Any Local Function mentioning

confidence: 99%

“…A notable exception is the fractional permissions model [4] in which the resource includes 'permissions to access', which can be indefinitely divided. We next investigate the non-well-founded case.…”

Section: Corollary 56 (Small Specification) For Well-founded Separamentioning

confidence: 99%

“…They have applied their reasoning to several memory models, including heaps based on pointer arithmetic [14], heaps with permissions [4], and the combination of heaps with variable stacks which views variables as resource [5,17]. In each case, the basic soundness and completeness results for local Hoare reasoning are essentially the same.…”

Section: Introductionmentioning

confidence: 99%

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Footprints in Local Reasoning

Raza¹,

Gardner²

2009

Logical Methods in Computer Science

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ABSTRACT. Local reasoning about programs exploits the natural local behaviour common in programs by focussing on the footprint -that part of the resource accessed by the program. We address the problem of formally characterising and analysing the notion of footprint for abstract local functions introduced by Calcagno, O'Hearn and Yang. With our definition, we prove that the footprints are the only essential elements required for a complete specification of a local function. We formalise the notion of small specifications in local reasoning and show that, for well-founded resource models, a smallest specification always exists that only includes the footprints. We also present results for the non-well-founded case. Finally, we use this theory of footprints to investigate the conditions under which the footprints correspond to the smallest safe states. We present a new model of RAM in which, unlike the standard model, the footprints of every program correspond to the smallest safe states. We also identify a general condition on the primitive commands of a programming language which guarantees this property for arbitrary models.

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