Mechanizing Abstract Interpretation
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It is important when developing software to verify the absence of undesirable
behavior such as crashes, bugs and security vulnerabilities. Some settings
require high assurance in verification results, e.g., for embedded software in
automobiles or airplanes. To achieve high assurance in these verification
results, formal methods are used to automatically construct or check proofs of
their correctness. However, achieving high assurance for program analysis
results is challenging, and current methods are ill suited for both complex
critical domains and mainstream use.
To verify the correctness of software we consider program analyzers---automated
tools which detect software defects---and to achieve high assurance in
verification results we consider mechanized verification---a rigorous process
for establishing the correctness of program analyzers via computer-checked
The key challenges to designing verified program analyzers are: (1) achieving
an analyzer design for a given programming language and correctness property;
(2) achieving an implementation for the design; and (3) achieving a mechanized
verification that the implementation is correct w.r.t. the design. The state of
the art in (1) and (2) is to use abstract interpretation: a guiding
mathematical framework for systematically constructing analyzers directly from
programming language semantics. However, achieving (3) in the presence of
abstract interpretation has remained an open problem since the late 1990's.
Furthermore, even the state-of-the art which achieves (3) in the absence of
abstract interpretation suffers from the inability to be reused in the presence
of new analyzer designs or programming language features.
First, we solve the open problem which has prevented the combination of
abstract interpretation (and in particular, calculational abstract
interpretation) with mechanized verification, which advances the state of the
art in designing, implementing, and verifying analyzers for critical software.
We do this through a new mathematical framework Constructive Galois Connections
which supports synthesizing specifications for program analyzers, calculating
implementations from these induced specifications, and is amenable to
Finally, we introduce reusable components for implementing analyzers for a wide
range of designs and semantics. We do this though two new frameworks Galois
Transformers and Definitional Abstract Interpreters. These frameworks tightly
couple analyzer design decisions, implementation fragments, and verification
properties into compositional components which are (target)
programming-language independent and amenable to mechanized verification.
Variations in the analysis design are then recovered by simply re-assembling
the combination of components. Using this framework, sophisticated program
analyzers can be assembled by non-experts, and the result are guaranteed to be
verified by construction.