Reasoning about explicit strictness in a lazy language using mixed lazy/strict semantics

Abstract. Many functional programmers are familiar with the concept of enforcing strictness for making applications fit their time and space efficiency requirements. Few functional programmers however, are familiar with the consequences of enforcing strictness for formal reasoning about their programs. This paper attempts to fill the gap between the few and the many. Some typical examples are given of the use and the meaning of explicit strictness. We show how formal reasoning can be made easier by the introduction of auxiliary functions in the program. John Launchbury’s [Lau93] natural lazy semantics for lazy evaluation is extended with an explicit strict let construct. We show that this rule extends the semantics in a natural way. In fact, using our mixed semantics it is possible to express in the language itself the semantical difference between Ω and λx.Ω while in Launchbury’s model these two expressions can only be distinguished from outside the language.