Several types of types in programming languages

Types are an important part of any modern programming language, but we often forget that the concept of type we understand nowadays is not the same it was perceived in the sixties. Moreover, we conflate the concept of "type" in programming languages with the concept of the same name in mathematical logic, an identification that is only the result of the convergence of two different paths, which started apart with different aims. The paper will present several remarks (some historical, some of more conceptual character) on the subject, as a basis for a further investigation. The thesis we will argue is that there are three different characters at play in programming languages, all of them now called types: the technical concept used in language design to guide implementation; the general abstraction mechanism used as a modelling tool; the classifying tool inherited from mathematical logic. We will suggest three possible dates ad quem for their presence in the programming language literature, suggesting that the emergence of the concept of type in computer science is relatively independent from the logical tradition, until the Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC

Data structures for algebraic manipulation

Imperial Users onl

A decidable class of verification conditions for programs with higher order store

Recent years have seen a surge in techniques and tools for automatic and semi-automatic static checking of imperative heap-manipulating programs. At the heart of such tools are algorithms for automatic logical reasoning, using heap description formalisms such as separation logic. In this paper we work towards extending these static checking techniques to languages with procedures as first class citizens. To do this, we first identify a class of entailment problems which arise naturally as verification conditions during the static checking of higher order heap-manipulating programs. We then present a decision procedure for this class and prove its correctness. Entailments in our class combine simple symbolic heaps, which are descriptions of the heap using a subset of separation logic, with (limited use of) nested Hoare triples to specify properties of higher order procedures

10351 Abstracts Collection -- Modelling, Controlling and Reasoning About State

From 29 August 2010 to 3 September 2010, the Dagstuhl Seminar 10351 ``Modelling, Controlling and Reasoning About State \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. Links to extended abstracts or full papers are provided, if available