We show that Hilbert type proof systems for classical firstorder logic can be reduced to if-then-else equational logic without losing any substantial efficiency: i.e., for any such proof system H, there exist constants k1, k2 > 0 such that for any proof ψ with size ` in H, there exists a corresponding proof ψ̄ in the if-then-else equational proof system, denoted ITE, with size less than or equal...

We give a notation and a logical calculus for the description and deductive manipulation of dynamic networks of communicating components. We represent such nets by hierarchical systems of recursive equations for streams. We give logical rules that describe the communication within a net and the dynamic creation of components, channels and rearrangement of the net structure. Such net transformat...

We show that certain fixpoint expressions used to describe finite Kripke polynomial coalgebras can be seen as coalgebraic modal fixpoint formulae. Both the synthesis of a coalgebra from its expression and the ability to check behavioural equivalence follow from the same tableau construction. There is an associated complete equational logic, analogous to Kleene algebra, which may now be seen as ...

The application of ideas from universal algebra to computer science has long been a major theme of Joseph Goguen’s research, perhaps even the major theme. One strand of this work concerns algebraic datatypes. Recently there has been some interest in what one may call algebraic computation types. As we will show, these are also given by equational theories, if one only understands the notion of ...

Many formal systems, particularly in computer science, may be expressed through equations modulated by assertions regarding the ‘freshness of names’. It is the presence of binding operators that make such structure non-trivial. Clouston and Pitts’s Nominal Equational Logic presented a formalism for this style of reasoning in which support for name binding was implicit. This paper extends this l...

In 1975 I started a small project to explore the consequences of implementing equational programs with no semantic compromises. Latest results include a compiler that executes exactly the logical consequences of an equa-tional program, with run-time speed comparable to compiled Franz LISP. This paper surveys the development of the project, through theoretical foundations , algorithm development...

Uniication in the presence of an equational theory is an important problem in theorem-proving and in the integration of functional and logic programming languages. This paper presents an improvement of the proposed lazy uniication methods by incorporating simpliication into the uniication process. Since simpliication is a deterministic computation process, more eecient uniication algorithms can...

We introduce a necessary and sufficient condition for the ω-extensionality rule of higherorder equational logic to be conservative over first-order many-sorted equational logic for ground first-order equations. This gives a precise condition under which computation in the higher-order initial model by term rewriting is possible. The condition is then generalised to characterise a normal form fo...