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...t of this section is to 41prove that there is a correspondence between the maximal traces of agents and the sequences of actions performed by agents according to a labelled transition semantics. See =-=[8]-=- for an introduction to process algebra. For a much more complex example done in HOL, see [7]. The syntax of agents is defined as follows: A ::= Nil (does nothing) | Pre label A (action prefixing) | S...

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...---------------------------------------------------- % ], "^EVAL (while B C) s1 s3" ];; 22The rules given here are just the standard rules for the operational semantics of while-programs (see [4] or =-=[9]-=-). The HOL theorems that are automatically generated as a result of the above definition of EVAL are the following theorems stating the rules rules = [⊢ ∀s. EVAL skip s s; ⊢ ∀V E s. EVAL(V := E)s(λv. ...

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...duction relation ---> on terms of combinatory logic and prove that it has the Church-Rosser property as formulated above. The proof presented here follows the same lines as the proof by Tait given in =-=[5]-=-. 4.1 The syntax of terms The syntax of terms in combinatory logic can be represented in the HOL logic by a recursive type cl, defined in the usual way using the recursive types package discussed in s...

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... s1" % ---------------------------------------------------- % ], "^EVAL (while B C) s1 s3" ];; 22The rules given here are just the standard rules for the operational semantics of while-programs (see =-=[4]-=- or [9]). The HOL theorems that are automatically generated as a result of the above definition of EVAL are the following theorems stating the rules rules = [⊢ ∀s. EVAL skip s s; ⊢ ∀V E s. EVAL(V := E...

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...ot admitted by the primitive rules of definition of the HOL logic. But certain recursive type definitions and function definitions are supported in the system by derived inference rules written in ML =-=[6, 10]-=-. The details of the primitive definitions that underlie these rules are hidden from the user, and their ML implementations are highly optimized. So these derived principles of definition may simply b...

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... the rules is also closed under the rules. Hence the intersection of the class of all relations closed under the rules is also closed under the rules and is, moreover, the smallest such relation. See =-=[1]-=- for more details about the theory of inductive definitions. 1.1 Rule induction For every inductively defined relation there is an associated induction principle which holds by virtue of its definitio...

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...e predicate calculus. 3.4 Proving the soundness of Floyd-Hoare rules Our final example in this section is a proof of soundness for the Floyd-Hoare rules of partial correctness for while-programs (see =-=[3]-=-). We are interested in correctness specifications of the form {P } C {Q}, where C is a command and P and Q are conditions on the values of the program variables in C. We will represent such a correct...

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... This is an inductive form of argument; if the property P holds in the ‘base cases’, corresponding to rules R1 and R2, and if P is preserved 1 The term ‘rule induction’ was coined by Glynn Winskel in =-=[11]-=-. 6by the rule R3 (the ‘step case’ of the induction), then every pair in R ∗ has the property P . A similar induction principle holds for every relation inductively defined by a set of rules. In addi...

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... agents and the sequences of actions performed by agents according to a labelled transition semantics. See [8] for an introduction to process algebra. For a much more complex example done in HOL, see =-=[7]-=-. The syntax of agents is defined as follows: A ::= Nil (does nothing) | Pre label A (action prefixing) | Sum A1 A2 (nondeterministic choice) | Prod A1 A2 (parallel composition) where label is the typ...