Set recursion and Πhalf-logic

Partiality and Recursion in Higher-Order Logic

We present an illative system Is of classical higher-order logic with subtyping and basic inductive types. The system Is allows for direct definitions of partial and general recursive functions, and provides means for handling functions whose termination has not been proven. We give examples of how properties of some recursive functions may be established in our system. In a technical appendix ...

Logic and proof method of recursion

1 What makes a useful calculus? 7 1.0 The r^ ole of proofs and calculi in program development : 9 1.1 Choice of the proof 5 Conclusion 133 xii CONTENTS Chapter 0 Introduction Today there is general agreement that program development is important and diicult. Much research has been done and still is done, in order to make program development reliable and manageable. The main ingredients of progr...

Testing Hennessy-Milner Logic with Recursion

This study o ers a characterization of the collection of properties expressible in Hennessy-Milner Logic (HML) with recursion that can be tested using nite LTSs. In addition to actions used to probe the behaviour of the tested system, the LTSs that we use as tests will be able to perform a distinguished action nok to signal their dissatisfaction during the interaction with the tested process. A...

Set Constraints and Logic

Set constraints are inclusion relations between expressions denoting sets of ground terms over a ranked alphabet. They are the main ingredient in set-In this paper we describe a constraint logic programming language clp(sc) over set constraints in the style of Jaaar and Lassez 17]. The language subsumes ordinary logic programs over an Herbrand domain. We give an eecient uniication algorithm and...

Logic and Set Theory