By Jean-Raymond Abrial (auth.), Zhiming Liu, Jim Woodcock, Huibiao Zhu (eds.)

This Festschrift quantity, devoted to He Jifeng at the social gathering of his seventieth birthday in September 2013, contains 24 refereed papers by way of top researchers, present and previous colleagues, who congratulated at a celebratory symposium held in Shanghai, China, throughout the tenth overseas Colloquium on Theoretical elements of Computing, ICTAC 2013. The papers hide a large spectrum of topics, from foundational and theoretical issues to courses and structures matters and to functions, comprising formal tools, software program and platforms modeling, semantics, legislation of programming, specification and verification, in addition to logics. He Jifeng is understood for his seminal paintings within the theories of programming and formal equipment for software program engineering. he's really linked to Unifying Theories of Programming (UTP) , the idea of knowledge refinement and the legislation of programming, and the rCOS formal technique for item and part procedure development. His e-book on UTP with Tony Hoare has been extensively learn and by way of a lot of researchers, and it's been utilized in many postgraduate classes. He used to be a senior researcher at Oxford in the course of 1984-1998, after which a senior learn fellow on the United countries collage overseas Institute for software program know-how (UNU-IIST) in Macau in the course of 1998-2005. He has been a professor and at the moment the Dean of the Institute of software program Engineering at East China basic college, Shanghai, China. In 2005, He Jifeng used to be elected as an academician to the chinese language Academy of Sciences. He additionally got an honorary doctorate from the college of York. He received a few prestigious technological know-how and expertise awards, together with a second prize of common technological know-how Award from the kingdom Council of China, a 1st prize of ordinary technology Award from the Ministry of schooling of China, a 1st prize of know-how Innovation from the Ministry of digital undefined, and a bunch awards from Shanghai government.

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Extra info for Theories of Programming and Formal Methods: Essays Dedicated to Jifeng He on the Occasion of His 70th Birthday

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The second properties of fix(H) and FIX(H) is that they are respectively greatest lower and least upper bounds, formally: ∀l · (∀k · H(k) ⊆ k ⇒ l ⊆ k) ⇒ l ⊆ fix(H) Theorem 2 ∀l · (∀k · k ⊆ H(k) ⇒ k ⊆ l) ⇒ FIX(H) ⊆ l The Fixpoint Theorems. The third property is the important Knaster-Tarski theorem. It suppose that the function H is monotonic, that is ∀k1, k2 · k1 ⊆ k2 ⇒ H(k1) ⊆ H(k2) Monotonicity Here are the theorems saying that fix(H) and FIX(H) are fixpoints of H: fix(H) = H(fix(H)) Theorem 3 FIX(H) = H(FIX(H)) Least and Greatest Fixpoints.

It is the objective of our research to solve this problem. Example 1 (Mutation of Programs). Consider the Scala program in Figure 1. The function tritype takes three lengths of a triangle and returns the resulting type of triangle. An example mutation operator could rewrite every equality into a greater-equal operator (== ⇒ >=) . This would produce five mutants, each containing exactly one mutation. For example, in the first mutant (Mutant 1), Line 7 would be replaced by case _ if (a >= b && b == c) => "equilateral".

The basic reason for this is that the discrete data types we use in such early models are clearly implementable on the discrete hardware that we ultimately target them to. The case with continuously varying quantities is subtly different. Usually, we build continuous models to reflect the capabilities of real physical phenomena or real physical equipment. In such cases, the modelling flexibility that we have is severely curtailed, because the physical behaviour that we want to model is normally confined within quite tightly constrained parameters.

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