Decidable logics combining heap structures and data

P. Madhusudan, Gennaro Parlato, Xiaokang Qiu

Research output: Contribution to journalArticlepeer-review


We define a new logic, STRAND, that allows reasoning with heapmanipulating 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 Ex→Ay→φ(x→, y→), where φ 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 preconditions 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).

Original languageEnglish (US)
Pages (from-to)611-622
Number of pages12
JournalACM SIGPLAN Notices
Issue number1
StatePublished - Jan 2011


  • Automata
  • Combining decision procedures
  • Decidability
  • Heap analysis
  • Monadic second-order logic
  • SMT solvers

ASJC Scopus subject areas

  • General Computer Science


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