Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra

The starting point of this paper is a new, purely functional, simple and efficient data structure combining a search tree and a priority queue, which we call a priority search tree. The salient feature of priority search trees is that they offer a decrease-key operation, something that is missing from other simple, purely functional priority queue implementations. As two applications of this data structure we verify purely functional, simple and efficient implementations of Prim\u27s and Dijkstra\u27s algorithms. This constitutes the first verification of an executable and even efficient version of Prim\u27s algorithm

How functional programming mattered

In 1989 when functional programming was still considered a niche topic, Hughes wrote a visionary paper arguing convincingly ‘why functional programming matters’. More than two decades have passed. Has functional programming really mattered? Our answer is a resounding ‘Yes!’. Functional programming is now at the forefront of a new generation of programming technologies, and enjoying increasing popularity and influence. In this paper, we review the impact of functional programming, focusing on how it has changed the way we may construct programs, the way we may verify programs, and fundamentally the way we may think about programs

The generation of concurrent code for declarative languages

PhD ThesisThis thesis presents an approach to the implementation of declarative languages on a simple, general purpose concurrent architecture. The safe exploitation of the available concurrency is managed by relatively sophisticated code generation techniques to transform programs into an intermediate concurrent machine code. Compilation techniques are discussed for 1'-HYBRID, a strongly typed applicative language, and for 'c-HYBRID, a concurrent, nondeterministic logic language. An approach is presented for 1'- HYBRID whereby the style of programming influences the concurrency utilised when a program executes. Code transformation techniques are presented which generalise tail-recursion optimisation, allowing many recursive functions to be modelled by perpetual processes. A scheme is also presented to allow parallelism to be increased by the use of local declarations, and constrained by the use of special forms of identity function. In order to preserve determinism in the language, a novel fault handling mechanism is used, whereby exceptions generated at run-time are treated as a special class of values within the language. A description is given of ,C-HYBRID, a dialect of the nondeterministic logic language Concurrent Prolog. The language is embedded within the applicative language 1'-HYBRID, yielding a combined applicative and logic programming language. Various cross-calling techniques are described, including the use of applicative scoping rules to allow local logical assertions. A description is given of a polymorphic typechecking algorithm for logic programs, which allows different instances of clauses to unify objects of different types. The concept of a method is derived to allow unification Information to be passed as an implicit argument to clauses which require it. In addition, the typechecking algorithm permits higher-order objects such as functions to be passed within arguments to clauses. Using Concurrent Prolog's model of concurrency, techniques are described which permit compilation of 'c-HYBRID programs to abstract machine code derived from that used for the applicative language. The use of methods allows polymorphic logic programs to execute without the need for run-time type information in data structures.The Science and Engineering Research Council

A methodology for producing reliable software, volume 1

An investigation into the areas having an impact on producing reliable software including automated verification tools, software modeling, testing techniques, structured programming, and management techniques is presented. This final report contains the results of this investigation, analysis of each technique, and the definition of a methodology for producing reliable software

Executable Refinement Types

This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type systems in general. Particular contributions include: (1) Type soundness and a logical relation for extensional equivalence for executable refinement types (though type checking is undecidable); (2) hybrid type checking for executable refinement types, which blends static and dynamic checks in a novel way, in some sense performing better statically than any decidable approximation; (3) a type reconstruction algorithm - reconstruction is decidable even though type checking is not, when suitably redefined to apply to undecidable type systems; (4) a novel use of existential types with dependent types to ensure that the language of logical formulae is closed under type checking (5) a prototype implementation, Sage, of executable refinement types such that all dynamic errors are communicated back to the compiler and are thenceforth static errors.Comment: Ph.D. dissertation. Accepted by the University of California, Santa Cruz, in March 2014. 278 pages (295 including frontmatter

Between functions and relations in calculating programs

This thesis is about the calculational approach to programming, in which one derives programs from specifications. One such calculational paradigm is Ruby, the relational calculus developed by Jones and Sheeran for describing and designing circuits. We identify two shortcomings with derivations made using Ruby. The first is that the notion of a program being an implementation of a specification has never been made precise. The second is to do with types. Fundamental to the use of type information in deriving programs is the idea of having types as special kinds of programs. In Ruby, types are partial equivalence relations (pers). Unfortunately, manipulating some formulae involving types has proved difficult within Ruby. In particular, the preconditions of the ‘induction’ laws that are much used within program derivation often work out to be assertions about types; such assertions have typically been verified either by informal arguments or by using predicate calculus, rather than by applying algebraic laws from Ruby. In this thesis we address both of the shortcomings noted above. We define what it means for a Ruby program to be an implementation, by introducing the notion of a causal relation, and the network denoted by a Ruby program. A relation is causal if it is functional in some structural way, but not necessarily from domain to range; a network captures the connectivity between the primitive relations in a program. Moreover, we present an interpreter for Ruby programs that are implementations. Our technique for verifying an assertion about types is to first express it using operators that give the best left and right types for a relation, and then verify this assertion by using algebraic properties of these operators

Between functions and relations in calculating programs

This thesis is about the calculational approach to programming, in which one derives programs from specifications. One such calculational paradigm is Ruby, the relational calculus developed by Jones and Sheeran for describing and designing circuits. We identify two shortcomings with derivations made using Ruby. The first is that the notion of a program being an implementation of a specification has never been made precise. The second is to do with types. Fundamental to the use of type information in deriving programs is the idea of having types as special kinds of programs. In Ruby, types are partial equivalence relations (pers). Unfortunately, manipulating some formulae involving types has proved difficult within Ruby. In particular, the preconditions of the ‘induction’ laws that are much used within program derivation often work out to be assertions about types; such assertions have typically been verified either by informal arguments or by using predicate calculus, rather than by applying algebraic laws from Ruby. In this thesis we address both of the shortcomings noted above. We define what it means for a Ruby program to be an implementation, by introducing the notion of a causal relation, and the network denoted by a Ruby program. A relation is causal if it is functional in some structural way, but not necessarily from domain to range; a network captures the connectivity between the primitive relations in a program. Moreover, we present an interpreter for Ruby programs that are implementations. Our technique for verifying an assertion about types is to first express it using operators that give the best left and right types for a relation, and then verify this assertion by using algebraic properties of these operators

A Language-Independent Static Checking System for Coding Conventions

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.Despite decades of research aiming to ameliorate the difficulties of creating software, programming still remains an error-prone task. Much work in Computer Science deals with the problem of specification, or writing the right program, rather than the complementary problem of implementation, or writing the program right. However, many desirable software properties (such as portability) are obtained via adherence to coding standards, and therefore fall outside the remit of formal specification and automatic verification. Moreover, code inspections and manual detection of standards violations are time consuming. To address these issues, this thesis describes Exstatic, a novel framework for the static detection of coding standards violations. Unlike many other static checkers Exstatic can be used to examine code in a variety of languages, including program code, in-line documentation, markup languages and so on. This means that checkable coding standards adhered to by a particular project or institution can be handled by a single tool. Consequently, a major challenge in the design of Exstatic has been to invent a way of representing code from a variety of source languages. Therefore, this thesis describes ICODE, which is an intermediate language suitable for representing code from a number of different programming paradigms. To substantiate the claim that ICODE is a universal intermediate language, a proof strategy has been developed: for a number of different programming paradigms (imperative, declarative, etc.), a proof is constructed to show that semantics-preserving translation exists from an exemplar language (such as IMP or PCF) to ICODE. The usefulness of Exstatic has been demonstrated by the implementation of a number of static analysers for different languages. This includes a checker for technical documentation written in Javadoc which validates documents against the Sun Microsystems (now Oracle) Coding Conventions and a checker for HTML pages against a site-specifc standard. A third system is targeted at a variant of the Python language, written by the author, called python-csp, based on Hoare's Communicating Sequential Processes

Review of catalytic systems and thermodynamics for the Guerbet condensation reaction and challenges for biomass valorization

The Guerbet condensation reaction is an alcohol coupling reaction that has been known for more than a century. Because of the increasing availability of bio-based alcohol feedstock, this reaction is of growing importance and interest in terms of value chains of renewable chemical and biofuel production. Due to the specific branching pattern of the alcohol products, the Guerbet reaction has many interesting applications. In comparison to their linear isomers, branched-chain Guerbet alcohols have extremely low melting points and excellent fluidity. This review provides thermodynamic insights and unravels the various mechanistic steps involved. A comprehensive overview of the homogeneous, heterogeneous and combined homogeneous and heterogeneous catalytic systems described in published reports and patents is also given. Technological considerations, challenges and perspectives for the Guerbet chemistry are discussed