Titlebook: Concrete Semantics; With Isabelle/HOL Tobias Nipkow,Gerwin Klein Textbook 2014 Springer International Publishing Switzerland 2014 Abstract

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Rolf Golombek,Cathrine Hagem,Michael Hoele main aim of this chapter is to introduce the concepts of commands and their abstract syntax, and to use them to illustrate two styles of defining the semantics of a programming language: big-step and small-step operational semantics. Our first larger theorem about IMP will be the equivalence of th

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Foreign Trade and Renewable Resources language based on a simple stack machine. Stack machines are common lowlevel intermediate languages; the Java Virtual Machine is one example. We then write a compiler from IMP to this language and prove that the compiled program has the same semantics as the source program. The compiler will perfor

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Case Study: IMP Expressionsis book. In this chapter we define their syntax and semantics, write little optimizers for them and show how to compile arithmetic expressions to a simple stack machine. Of course we also prove the correctness of the optimizers and compiler!

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Isar: a Language for Structured Proofsured, not linear. (2) It is readable without its being run because you need to state what you are proving at any given point. Whereas apply-scripts are like assembly language programs, Isar proofs are like structured programs with comments. A typical Isar proof looks like this.

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Denotational Semanticst those rules do not tell us directly what the meaning of a command is. This is what denotational semantics is about: mapping syntactic objects to their denotation or meaning. In fact, we are already familiar with two examples, namely the evaluation of arithmetic and boolean expressions.

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and the practical use of a proof assistant.Represents a for.Part I of this book is a practical introduction to working with the Isabelle proof assistant. It teaches you how to write functional programs and inductive definitions and how to prove properties about them in Isabelle’s structured proof l

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IMP: A Simple Imperative Languagee semantics of a programming language: big-step and small-step operational semantics. Our first larger theorem about IMP will be the equivalence of these two definitions of its semantics. As a smaller concrete example, we will apply our semantics to the concept of program equivalence.