One can attempt to solve the problem of establishing the correctness of some software w.r.t. a formal speciication at the semantical level. For this purpose, the semantics of an algebraic speciication should be the class of all algebras which correspond to the correct realizations of the speciication. We approach this goal by deening an observational satisfaction relation which is less restrict...

The de nition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to de ne an equality relation in ML. However, the standard de nition is incomplete in the sense that there are interesting and useful types which are not inferred to be equality types but for which an equality relation can be de ned in ML in a unif...

We consider algebraic speciications with observational features. Axioms as well as observations are formulae of full (Many-Sorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of this semantics for software speciication and the relationship with behavioural equivalence of alge...

In this paper we present a category equivalent to that of tense Nelson algebras. The objects in new are pairs consisting an IKt-algebra and Boolean IKt-congruence the morphisms special kind IKt-homomorphisms. This categorical equivalence permits understanding algebras terms better–known IKt-algebras.

We introduce an intersection typing system for combinatory logic, such that a term of combinatory logic is typeable ii it is sn. We then prove the soundness and completeness for the class of partial com-binatory algebras. Let F be the class of non-empty lters which consist of types. Then F is an extensional non-total partial combinatory algebra. Furthermore, it validates the strongest consisten...

To establish the correctness of some software w.r.t. its formal speciication is widely recognized as a diicult task. A rst simpliication is obtained when the semantics of an algebraic speciication is deened as the class of all algebras which correspond to the correct realizations of the speciication. A software is then declared correct if it corresponds to some algebra of this class. We approac...

Hirsch and Hodkinson proved, for 3 ≤ m < ω and any k < ω, that the class SNrmCAm+k+1 is strictly contained in SNrmCAm+k and if k ≥ 1 then the former class cannot be defined by any finite set of first order formulas, within the latter class. We generalise this result to the following algebras of m-ary relations for which the neat reduct operator Nrm is meaningful: polyadic algebras with or witho...