A general construction for abstract interpretation of higher-order automatic differentiation

Relational Abstract Interpretation of Higher Order Functional Programs (extended abstract)

Most applications of the abstract interpretation framework[2] have been for analyzing functional programs use functions on abstract values to approximate functions, thus assuming that functions may be called at all arguments. When the abstract domain is finite, this approach can easily be generalized to higher order functional languages as shown for example by [1]. In practice this leads to com...

Automatic Construction of Hoare Proofs from Abstract Interpretation Results

Interpretation Results Sunae Seo, Hongseok Yang, and Kwangkeun Yi 1 Department of Computer Science, Korea Advanced Institute of Science and Technology [email protected] 2 MICROS Research Center, Korea Advanced Institute of Science and Technology [email protected] 3 School of Computer Science and Engineering, Seoul National University [email protected] Abstract. By combining program lo...

A Higher - Order Interpretation

Higher Order Abstract Interpretation with Flow-Effect Types

This paper describes a novel flow-effect type system that combines concepts of type constraint systems and type effect systems, to achieve a flow-sensitive abstract interpretation of programs with higher-order functions. We prove that a decidable, safe closure algorithm exists. Deriving a decidable type closure algorithm in the presence of higher-order recursive functions is the main technical ...

Automatic Verification by Abstract Interpretation

We discuss the use of abstract interpretation in the context of automatic program veri cation requiring precise abstractions. We compare entirely manual versus user-guided abstractions ranging from program-speci c abstractions including predicate abstraction to the systematic design of abstract domains and iteration strategies. 1 Abstract Interpretation Theory Abstract interpretation theory [1,...