Innermost strategies are usually used in compiling term rewriting systems (TRSs) since they allow to eciently build result terms in a bottom-up fashion. However, innermost strategies do not always give the shortest normalising derivation. In many cases, using an appropriate laziness annotation on the arguments of function symbols, we evaluate lazy arguments only if it is necessary and hence, get a shorter derivation to normal forms while avoiding non-terminating reductions. We provide in this work a transformation of annotated TRSs, that allows to compute normal forms using an innermost strategy and to extract lazy derivations in the original TRS from normalising derivations in the transformed TRS. We apply our result to improve the eciency of equational reasoning in the Coq proof assistant using ELAN as an external rewriting engine.

In a LOTOS specification there are many types that are build from more basic ones. The operations allowed for types are presented with plenty of examples. 1 Introduction This tutorial intends to cover the gap between normal specifiers and algebricians. The question to answer is what are the abstract data types of LOTOS? LOTOS syntax is used, but not introduced in detail. Readers are referred to the standard [ISO, 88]. This tutorial is dealing with semantics. 1 The author is not a mathematician, nor an algebrician, but a plain computer scientist, with a very pragmatic interest on abstract data types. The presentation will be straightforward, introducing only those theoretical concepts that are strictly required. Many examples will be presented, not big ones, but meaningful ones. The theory of abstract data types is not a single theory, but there are as many as ADT languages. We shall concentrate on ACT ONE, the language used in LOTOS. When there are several choices, they will be brie...