Decidable logics combining heap structures and data

Madhusudan, P., Parlato, Gennaro and Qiu, Xiaokang (2011) Decidable logics combining heap structures and data At POPL '11. Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, United States. 26 - 28 Jan 2011. , pp. 611-622. (doi:10.1145/1925844.1926455).


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We define a new logic, STRAND, that allows reasoning with heap-manipulating programs using deductive verification and SMT solvers. STRAND logic (“STRucture ANd Data” logic) formulas express constraints involving heap structures and the data they contain; they are defined over a class of pointer-structures R defined using MSO-defined relations over trees, and are of the form ?x?y.?(x, y), where ? is a monadic second-order logic (MSO) formula with additional quantification that combines structural constraints as well as data-constraints, but where the data-constraints are only allowed to refer to x and y. The salient aspects of the logic are: (a) the logic is powerful, allowing existential and universal quantification over the nodes, and complex combinations of data and structural constraints; (b) checking Hoare-triples for linear blocks of statements with pre-conditions and post-conditions expressed as Boolean combinations of existential and universal STRAND formulas reduces to satisfiability of a STRAND formula; (c) there are powerful decidable fragments of STRAND, one semantically defined and one syntactically defined, where the decision procedure works by combining the theory of MSO over trees and the quantifier-free theory of the underlying data-logic. We demonstrate the effectiveness and practicality of the logic by checking verification conditions generated in proving properties of several heap-manipulating programs, using a tool that combines an MSO decision procedure over trees (MONA) with an SMT solver for integer constraints (Z3).

Item Type: Conference or Workshop Item (Paper)
Digital Object Identifier (DOI): doi:10.1145/1925844.1926455
Venue - Dates: POPL '11. Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, United States, 2011-01-26 - 2011-01-28
Keywords: heap analysis, smt solvers, monadic second-order logic, combining decision procedures, automata, decidability
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Organisations: Electronic & Software Systems
ePrint ID: 272448
Date :
Date Event
Date Deposited: 13 Jun 2011 12:51
Last Modified: 17 Apr 2017 17:44
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