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An Elimination Theorem for Regular Behaviours with Integration
 LNCS 715
, 1993
"... This chapter deals with an extension of the process algebra ACP with rational time and integration. We determine a proper subdomain of the regular processes for which an elimination theorem holds, namely, for each pair of processes p0 ; p1 in this class there is a process q in this class such that p ..."
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This chapter deals with an extension of the process algebra ACP with rational time and integration. We determine a proper subdomain of the regular processes for which an elimination theorem holds, namely, for each pair of processes p0 ; p1 in this class there is a process q in this class such that p0kp1 and q are bisimilar. Some simple examples show that if this subdomain is enlarged, then the elimination result is lost. The subdomain is equivalent to the model of timed automata from Alur and Dill. 1 Introduction In recent years, process algebras such as CCS, CSP and ACP, have been extended with constructs that mean to describe some notion of either discrete or dense time. This chapter is based on the approach of Baeten and Bergstra [3], which extends ACP with real time. They introduced the notion of integration, which expresses the possibility that an action occurs somewhere within a time interval. The construct R v2V p executes the process p, where the behaviour of p may depend on...
Alphastructural recursion and induction (Extended Abstract)
 THEOREM PROVING IN HIGHER ORDER LOGICS, 18TH INTERNATIONAL CONFERENCE, TPHOLS 2005, OXFORD UK, AUGUST 2005, PROCEEDINGS, VOLUME 3603 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... There is growing evidence for the usefulness of name permutations when dealing with syntax involving names and namebinding. In particular they facilitate an attractively simple formalisation of common, but often technically incorrect uses of structural recursion and induction for abstract syntax tr ..."
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There is growing evidence for the usefulness of name permutations when dealing with syntax involving names and namebinding. In particular they facilitate an attractively simple formalisation of common, but often technically incorrect uses of structural recursion and induction for abstract syntax trees modulo αequivalence. At the heart of this formalisation is the notion of finitely supported mathematical objects. This paper explains the idea in as concrete a way as possible and gives a new derivation within higherorder logic of principles of αstructural recursion and induction for αequivalence classes from the ordinary versions of these principles for abstract syntax trees.
Tracing Lazy Functional Languages
 In Proceedings of Computing: The Australasian Theory Symposium
, 1996
"... We argue that Ariola and Felleisen's and Maraist, Odersky and Wadler's callbyneed lambda calculus forms a suitable formal basis for tracing evaluation in lazy functional languages. Keywords Functional programming, tracing, callbyneed, lambda calculus, lazy evaluation. 1 Tracing function ..."
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We argue that Ariola and Felleisen's and Maraist, Odersky and Wadler's callbyneed lambda calculus forms a suitable formal basis for tracing evaluation in lazy functional languages. Keywords Functional programming, tracing, callbyneed, lambda calculus, lazy evaluation. 1 Tracing functional languages One major advantage of pure, and especially lazy, functional languages over more conventional imperative languages is in not having to directly and completely specify the order of execution of a program. Leaving execution order unspecified allows the compiler or interpreter to perform transformations on the code, changing the order of execution and perhaps even executing parts of the program in parallel. However, when it comes to debugging a program, this feature turns into a disadvantage. In a more conventional language, one can `trace' execution by inserting write statements in interesting places in order to monitor what is happening. More sophisticated tracing systems provide stepb...
External and internal syntax of the λcalculus
 In: Buchberger, Ida, Kutsia (Eds.), Proc. of the AustrianJapanese Workshop on Symbolic Computation in Software Science, SCSS 2008. No. 08–08 in RISCLinz Report Series
"... There is growing interest in the study of the syntactic structure of expressions equipped with a variable binding mechanism. The importance of this study can be justified for various reasons, e.g. educational, scientific and engineering reasons. This study is educationally important since in logic a ..."
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There is growing interest in the study of the syntactic structure of expressions equipped with a variable binding mechanism. The importance of this study can be justified for various reasons, e.g. educational, scientific and engineering reasons. This study is educationally important since in logic and computer science, we cannot avoid teaching the
Coding binding and substitution explicitly in isabelle
 University of Cambridge Computer Laboratory
, 1995
"... Logical frameworks provide powerful methods of encoding objectlogical binding and substitution using metalogical λabstraction and application. However, there are some cases in which these methods are not general enough: in such cases objectlogical binding and substitution must be explicitly code ..."
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Logical frameworks provide powerful methods of encoding objectlogical binding and substitution using metalogical λabstraction and application. However, there are some cases in which these methods are not general enough: in such cases objectlogical binding and substitution must be explicitly coded. McKinna and Pollack [MP93] give a novel formalization of binding, where they use it principally to prove metatheorems of Type Theory. We analyse the practical use of McKinnaPollack binding in Isabelle objectlogics, and illustrate its use with a simple example logic. 1
Unique Fixpoint Induction for ValuePassing Processes (Extended Abstract)
 In Proceedings 12th IEEE Symposium on Logic in Computer Science (LICS'97
, 1997
"... We investigate the use of unique fixpoint induction as a proof method for valuepassing process languages with recursion. An intuitive generalisation of unique fixpoint induction based on loop invariants for symbolic graphs yields strong completeness results; we give an axiomatic characterisation of ..."
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We investigate the use of unique fixpoint induction as a proof method for valuepassing process languages with recursion. An intuitive generalisation of unique fixpoint induction based on loop invariants for symbolic graphs yields strong completeness results; we give an axiomatic characterisation of both late and early observational congruence for a class of fully parameterised processes. This new, generalised, rule is shown to be derivable from existing formulations of unique fixpoint induction for valuepassing calculi, thereby providing original completeness results. An example of the use of this new rule is presented in detail.
Type Theory with FirstOrder Data Types and SizeChange Termination
, 2004
"... We prove normalization for a dependently typed lambdacalculus extended with firstorder data types and computation schemata for firstorder sizechange terminating recursive functions. Sizechange termination, introduced by C.S. Lee, N.D. Jones and A.M. BenAmram, can be seen as a generalized form ..."
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We prove normalization for a dependently typed lambdacalculus extended with firstorder data types and computation schemata for firstorder sizechange terminating recursive functions. Sizechange termination, introduced by C.S. Lee, N.D. Jones and A.M. BenAmram, can be seen as a generalized form of structural induction, which allows inductive computations and proofs to be defined in a straightforward manner. The language can be used as a proof system—an extension of MartinLöf’s Logical Framework.
A Canonical Locally Named Representation of Binding
 JOURNAL OF AUTOMATED REASONING
"... This paper is about completely formal representation of languages with binding. We have previously written about a representation following an approach going back to Frege, based on firstorder syntax using distinct syntactic classes for locally bound variables vs. global or free variables. The pres ..."
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This paper is about completely formal representation of languages with binding. We have previously written about a representation following an approach going back to Frege, based on firstorder syntax using distinct syntactic classes for locally bound variables vs. global or free variables. The present paper differs from our previous work by being more abstract. Whereas we previously gave a particular concrete function for canonically choosing the names of binders, here we characterize abstractly the properties required of such a choice function to guarantee canonical representation, and focus on the metatheory of the representation, proving that it is in substitution preserving isomorphism with the nominal Isabelle representation of pure lambda terms. This metatheory is formalized in Isabelle/HOL. The final section outlines a formalization in Matita of a challenging language with multiple binding and simultaneous substitution. The Isabelle and Matita proof files are available online.