Easily solving dynamic programming problems in Haskell by memoization of hylomorphisms

Dynamic programming is a well-known algorithmic technique that solves problems by a combination of dividing a problem into subproblems and using memoization to avoid an exponential growth of the costs. We show how to implement dynamic programming in Haskell using a variation of hylomorphisms that includes memoization. Our implementation uses polymorphism so the same function can return the best score or the solution to the problem based on the type of the returned value.     

An old new notation for elementary probability theory

The Eindhoven approach to quantifier notation is 40 years old. We extend it by adding “distribution comprehensions” systematically to its repertoire; we believe the resulting notation for elementary probability theory is new.After a step-by-step explanation of the proposed notational innovations, with small examples, we give as our exemplary case study the probabilistic reasoning associated with a quantitative noninterference semantics based on Hidden Markov Models of computation. Although that example was the motivation for this work, we believe the proposal here will be more generally applicable: and so we also revisit a number of popular puzzles, to illustrate the notation's wider utility.Finally, we review the connection between comprehension notations and (category-theoretic) monads, and show how the Haskell approach to monad comprehensions applies to the distribution comprehensions we have introduced.     

面向访问验证保护级的安全VMM形式化原型系统设计和实现

操作系统是计算机软件系统的基础,具有控制逻辑复杂、安全性和可靠性要求高等特点。在国内外高等级安全操作系统的规范和标准中,都提出了对内核进行形式化规范和验证的要求。近年来国内相关研究机构相继开发了满足GB 17859-1999“强制访问控制级”和“结构化保护级”的安全操作系统原型,但对更高级别的安全操作系统的研发尚属空白。在“面向访问验证保护级安全操作系统”课题的研究中,设计并实现了一个基于Haskell的安全VMM原型系统—CASVisor.CASVisor严格定义了系统的形式化规范,可用于指导高性能的C程序的实现,并为形式化的分析和验证打下基础,同时CASVisor具备模拟功能,以便实施基于快速原型的开发方法。     

Verifying Haskell programs by combining testing, model checking and interactive theorem proving

We propose a program verification method that combines random testing, model checking and interactive theorem proving. Testing and model checking are used for debugging programs and specifications before a costly interactive proof attempt. During proof development, testing and model checking quickly eliminate false conjectures and generate counterexamples which help to correct them. With an interactive theorem prover we also ensure the correctness of the reduction of a top level problem to subproblems that can be tested or proved. We demonstrate the method using our random testing tool and binary decision diagrams-based (BDDs) tautology checker, which are added to the Agda/Alfa interactive proof assistant for dependent type theory. In particular we apply our techniques to the verification of Haskell programs. The first example verifies the BDD checker itself by testing its components. The second uses the tautology checker to verify bitonic sort together with a proof that the reduction of the problem to the checked form is correct.     

Functional programming languages for verification tools: a comparison of Standard ML and Haskell

We compare Haskell with Standard ML as programming languages for verification tools based on our experience developing the verification platform Truth in Haskell and the Edinburgh Concurrency Workbench (CWB) in Standard ML. We review not only technical language features but also the worlds of the languages, for example, the availability of compilers, tools, and libraries. We also discuss the merits and difficulties of comparing programming languages in this wide sense and support our view that Truth and the CWB are similar enough to justify the conclusions drawn in this paper.     

Programmed Strategies for Program Verification

Plover is an automated property-verifier for Haskell programs that has been under development for the past three years as a component of the Programatica project. In Programatica, predicate definitions and property assertions written in P-logic, a programming logic for Haskell, can be embedded in the text of a Haskell program module. Properties refine the type system of Haskell but cannot be verified by type-checking alone; a more powerful logical verifier is needed.Plover codes the proof rules of P-logic, and additionally, embeds strategies and decision procedures for their application and discharge. It integrates a reduction system that implements a rewriting semantics for Haskell terms with a congruence-closure algorithm that supports reasoning with equality. It employs strategies such as structure splitting and case analysis to explore alternative valuations of expressions of type Bool or other finite data types, but these strategies can lead to exponential growth of terms and must be employed cautiously.Plover itself is written in Stratego, which has proven to be a powerful language tool for implementating a verifier. We discuss the design and implementation of some strategies that enable Plover to comprehend Haskell and verify many valid property assertions.     

Extending a functional programming system for embedded applications

Functional languages do not usually mesh well with embedded applications because of the need for special I/O device-handling. By introducing a process model to a language, however, it becomes possible to express register-level device operations and interrupts in a modular manner. This paper describes such a model, its implementation by extension to the Gofer programming system, and examples of its use. Performance results indicate that even this prototype interpretive system is adequate for small applications. The major gain of using a functional language is the ease with which abstraction can be layered over low-level detail, improving both the readability of code and its tractability.