Calculational design of a regular model checker by abstract interpretation

Cousot, Patrick

doi:10.1016/j.tcs.2021.01.037

Cited by 3 publications

(3 citation statements)

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“…A , which uses two monotone maps α : P A → A and γ : A → P A to map between the two domains, so that the following relation is preserved a ⊆ γ(a ) ⇐⇒ α(a) a . The existence of a Galois connection formalises the way in which an abstract property describes a set of concrete values, provides a notion of "best approximation" and even suggests a design methodology for deriving program analysers in a systematic way by composing the semantic function with an abstraction function α [9,18] We are interested in abstract interpretation in which abstract domains are defined as compositional interpretations of types, where the semantics of a type is composed of the types it contains. E.g., the semantics of A * B is composed of the semantics of A and B.…”

Section: Abstract Interpretation and Galois Connectionsmentioning

confidence: 99%

“…The core of our implementation depends on a modular interface of semantic operations (SemanticOps), which our language interpretation 8 relies on. It relies on a field [[_]]t to provide an interpretation of our syntax of types into concrete and abstract domains 9 . The rest of the semantic operations are specified in a strongly typed fashion with regards to that implementation, which ensures that we can modularly exchange the domains for a particular type t. We parameterize over m to allow possible general monadic computations in the computation rule for sums, E-case, since it contains function arguments.…”

Section: A Proofsmentioning

confidence: 99%

“…In Language.Rec and Language.Semantics modules 9. In Domains.Concrete and Domains.Abstract modules respectively.…”

mentioning

confidence: 99%

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Galois Connections for Recursive Types

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From Lambda Calculus to Cybersecurity Through Program Analysis

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Building a static analyser for a real language involves modeling of large domains capturing the many available data types. To scale domain design and support efficient development of project-specific analyzers, it is desirable to be able to build, extend, and change abstractions in a systematic and modular fashion. We present a framework for modular design of abstract domains for recursive types and higher-order functions, based on the theory of solving recursive domain equations. We show how to relate computable abstract domains to our framework, and illustrate the potential of the construction by modularizing a monolithic domain for regular tree grammars. A prototype implementation in the dependently typed functional language Agda shows how the theoretical solution can be used in practice to construct static analysers. Authors ordered alphabetically type Fml = Atom ( int ) | Neg ( Fml ) | And ( Fml , Fml ) | Or ( Fml , Fml ) nnf ( f : Fml ) = case f of | Atom ( i ) -> Atom ( i ) | Neg ( Atom ( i )) -> Neg ( Atom ( i )) | Neg ( Neg ( f )) -> nnf f | Neg ( And ( f1 , f2 )) -> Or ( nnf ( Neg f1 ) , nnf ( Neg f2 )) | Neg ( Or ( f1 , f2 )) -> And ( nnf ( Neg f1 ) , nnf ( Neg f2 )) | Or ( f1 , f2 ) -> Or ( nnf f1 , nnf f2 ) | And ( f1 , f2 ) -> And ( nnf f1 , nnf f2 ) bool = unit+unit x0 : A0, . . . , xn : An ex xi : Ai Γ ex n : int Γ ex tt : unit Γ ex e1 : int Γ ex e2 : int Γ ex e1 e2 : int ( ∈ {+, −, ×}) Γ ex e1 : int Γ ex e2 : int Γ ex e1 ≤ e2 : bool Γ ex e1 : A1 Γ ex e2 : A2 Γ ex (e1, e2

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Section: Abstract Interpretation and Galois Connectionsmentioning

confidence: 99%

Section: A Proofsmentioning

confidence: 99%