Tool Support for Proof Engineering

Mulhern, Anne; Fischer, Charles N.; Liblit, Ben

doi:10.1016/j.entcs.2006.09.023

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…To assess the efficacy of our formal model, the proof facility of Coq is used to carry out proof of correctness of gate-level combinational circuits and reason about Boolean algebra. Among other numerous advantages (Section 2) of computer-aided verification using interactive theorem prover are the following: (a) all the formal definitions and proofs can be defined in the computer, and (b) the correctness of the proofs can be automatically checked by the computer [34].…”

Section: Solution Overview In Order To Formally Reason Aboutmentioning

confidence: 99%

Formal Verification of Hardware Components in Critical Systems

Khan

Kamran

Naqvi

et al. 2020

Wireless Communications and Mobile Computing

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Hardware components, such as memory and arithmetic units, are integral part of every computer-controlled system, for example, Unmanned Aerial Vehicles (UAVs). The fundamental requirement of these hardware components is that they must behave as desired; otherwise, the whole system built upon them may fail. To determine whether or not a component is behaving adequately, the desired behaviour of the component is often specified in the Boolean algebra. Boolean algebra is one of the most widely used mathematical tools to analyse hardware components represented at gate level using Boolean functions. To ensure reliable computer-controlled system design, simulation and testing methods are commonly used to detect faults; however, such methods do not ensure absence of faults. In critical systems’ design, such as UAVs, the simulation-based techniques are often augmented with mathematical tools and techniques to prove stronger properties, for example, absence of faults, in the early stages of the system design. In this paper, we define a lightweight mathematical framework in computer-based theorem prover Coq for describing and reasoning about Boolean algebra and hardware components (logic circuits) modelled as Boolean functions. To demonstrate the usefulness of the framework, we (1) define and prove the correctness of principle of duality mechanically using a computer tool and all basic theorems of Boolean algebra, (2) formally define the algebraic manipulation (step-by-step procedure of proving functional equivalence of functions) used in Boolean function simplification, and (3) verify functional correctness and reliability properties of two hardware components. The major advantage of using mechanical theorem provers is that the correctness of all definitions and proofs can be checked mechanically using the type checker and proof checker facilities of the proof assistant Coq.

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Section: Solution Overview In Order To Formally Reason Aboutmentioning

confidence: 99%

Formal Verification of Hardware Components in Critical Systems

Khan

Kamran

Naqvi

et al. 2020

Wireless Communications and Mobile Computing

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“…The word "edit-time" is a wordplay on the terms "compile time" and "run time", and it means that we run the tactics when we are still writing our program in the editor. The area of bringing IDE features to proof assistants is not new [9,36,44,55], but it has been focusing on their usefulness as proof tools, not necessarily how they can help mainstream programmers. In contrast, we take tactics from proof assistants and see how they can help type-driven developers.…”

Section: Introductionmentioning

confidence: 99%

Edit-Time Tactics in Idris

Korkut¹

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Metaprogramming allows users to write programs that write programs. In dependently-typed languages such as Idris, recent work on elaborator reflection [17] paved the way for new applications of metaprogramming by showing that a tacticbased proof language can be substituted with a monadic interface that exposes the internal elaborator. The goal of our work is to use elaborator reflection to write editor interaction actions in Idris. Currently in Idris modes of editors such as Emacs, users can perform actions like type-checking holes, case-splitting, and lemma extraction. Implementations of all of these Idris editor actions are hard-coded in the compiler, and they are written in Haskell. Our work will allow us to rewrite them in Idris as metaprograms and to move them into an Idris library, instead of having them embedded into the compiler. 4.1. New constructors for the new Elab primitives, and function definitions based on them. 4.2. The relationship between reflection, reification, quotation, unquotation, elaboration and delaboration. 4.3. The function to reflect Haskell terms of the type SExp to the internal representations of Idris terms of the Idris type SExp. 4.4. The function to reify the internal representations of Idris terms of the Idris type SExp to Haskell terms of the type SExp. 4.5. The runElabAction function in the compiler, how Elab action terms are run under the hood. viii 4.6. Adding cases for Prim__FromEditor and Prim__ToEditor in runTacTm in the compiler. 4.7. The function elabEditAt that runs editor actions in the compiler. 4.8. The function collectTypes to dissect a type signature to its components. 5.1. Implementation of the edit-time tactic for "add clause". 5.2. Example function to run addClause on. 5.3. Result of running addClause on the example function. 5.4. Definitions of Context and Sequent for Hezarfen. 5.5. The "Either implies" case in Hezarfen 5.6. Rudimentary implementation of reduce in Hezarfen. 6.1. Definition of hole_command in Lean. ix CHAPTER 1 Especially as dependent types gradually sneak into mainstream languages, like they already have to Haskell [26] and Scala [3], we predict that TDD will only get more popular. 2 Propositions and types are distinct in these systems.

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Tool Support for Proof Engineering

Cited by 2 publications

References 20 publications

Formal Verification of Hardware Components in Critical Systems

Formal Verification of Hardware Components in Critical Systems

Edit-Time Tactics in Idris

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