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Five axioms of alphaconversion
 Ninth international Conference on Theorem Proving in Higher Order Logics TPHOL
, 1996
"... Abstract. We present five axioms of namecarrying lambdaterms identified up to alphaconversion—that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambdaabstraction. Other constants represent a function Fv that returns the set of free variab ..."
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Abstract. We present five axioms of namecarrying lambdaterms identified up to alphaconversion—that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambdaabstraction. Other constants represent a function Fv that returns the set of free variables in a term and a function that substitutes a term for a variable free in another term. Our axioms are (1) equations relating Fv and each constructor, (2) equations relating substitution and each constructor, (3) alphaconversion itself, (4) unique existence of functions on lambdaterms defined by structural iteration, and (5) construction of lambdaabstractions given certain functions from variables to terms. By building a model from de Bruijn’s nameless lambdaterms, we show that our five axioms are a conservative extension of HOL. Theorems provable from the axioms include distinctness, injectivity and an exhaustion principle for the constructors, principles of structural induction and primitive recursion on lambdaterms, Hindley and Seldin’s substitution lemmas and
Modular Verification Of Function Block Based Industrial Control Systems
, 1999
"... : IEC 611313, the worldwide standard for industrial control programming, is increasingly being used in safetyrelated control applications. Control loops are built from components taken from domainspecific function block libraries. Code inspection and testing are the two predominant quality as ..."
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: IEC 611313, the worldwide standard for industrial control programming, is increasingly being used in safetyrelated control applications. Control loops are built from components taken from domainspecific function block libraries. Code inspection and testing are the two predominant quality assurance techniques. For highly dependable control applications, however, these techniques are not sufficient, in general. This paper suggests to augment testing with compositional, theoremprover supported verification. The approach is based on a representation of IEC 611313 function blocks in higherorder logic. The verification task is separated into the a priori verification of library components and a separate proof of individual application programs. Keywords: Safetycritical control systems, dependable software, PLC programming, IEC 611313, modular verification, higher order logic theorem proving. 1. INTRODUCTION Programmable logic controllers (PLCs) form a growing market of...