52 research outputs found
Higher-order Program Verification as Satisfiability Modulo Theories with Algebraic Data-types
We report on work in progress on automatic procedures for proving properties
of programs written in higher-order functional languages. Our approach encodes
higher-order programs directly as first-order SMT problems over Horn clauses.
It is straight-forward to reduce Hoare-style verification of first-order
programs into satisfiability of Horn clauses. The presence of closures offers
several challenges: relatively complete proof systems have to account for
closures; and in practice, the effectiveness of search procedures depend on
encoding strategies and capabilities of underlying solvers. We here use
algebraic data-types to encode closures and rely on solvers that support
algebraic data-types. The viability of the approach is examined using examples
from the literature on higher-order program verification
CTL+FO Verification as Constraint Solving
Expressing program correctness often requires relating program data
throughout (different branches of) an execution. Such properties can be
represented using CTL+FO, a logic that allows mixing temporal and first-order
quantification. Verifying that a program satisfies a CTL+FO property is a
challenging problem that requires both temporal and data reasoning. Temporal
quantifiers require discovery of invariants and ranking functions, while
first-order quantifiers demand instantiation techniques. In this paper, we
present a constraint-based method for proving CTL+FO properties automatically.
Our method makes the interplay between the temporal and first-order
quantification explicit in a constraint encoding that combines recursion and
existential quantification. By integrating this constraint encoding with an
off-the-shelf solver we obtain an automatic verifier for CTL+FO
Termination Analysis by Learning Terminating Programs
We present a novel approach to termination analysis. In a first step, the
analysis uses a program as a black-box which exhibits only a finite set of
sample traces. Each sample trace is infinite but can be represented by a finite
lasso. The analysis can "learn" a program from a termination proof for the
lasso, a program that is terminating by construction. In a second step, the
analysis checks that the set of sample traces is representative in a sense that
we can make formal. An experimental evaluation indicates that the approach is a
potentially useful addition to the portfolio of existing approaches to
termination analysis
Automatic Abstraction in SMT-Based Unbounded Software Model Checking
Software model checkers based on under-approximations and SMT solvers are
very successful at verifying safety (i.e. reachability) properties. They
combine two key ideas -- (a) "concreteness": a counterexample in an
under-approximation is a counterexample in the original program as well, and
(b) "generalization": a proof of safety of an under-approximation, produced by
an SMT solver, are generalizable to proofs of safety of the original program.
In this paper, we present a combination of "automatic abstraction" with the
under-approximation-driven framework. We explore two iterative approaches for
obtaining and refining abstractions -- "proof based" and "counterexample based"
-- and show how they can be combined into a unified algorithm. To the best of
our knowledge, this is the first application of Proof-Based Abstraction,
primarily used to verify hardware, to Software Verification. We have
implemented a prototype of the framework using Z3, and evaluate it on many
benchmarks from the Software Verification Competition. We show experimentally
that our combination is quite effective on hard instances.Comment: Extended version of a paper in the proceedings of CAV 201
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