A treatment of languages with stages of evaluation

Abstract

The notion of languages that inherently have multiple stages of evaluation is introduced. Typically, evaluation is done in stages so that evaluation in some one stage is able to be done very efficiently, even at the expense of prior stages of evaluation. A key novel feature in such languages is that constructs may have appropriate times of meaning as well as appropriate meanings. While it is possible to give semantics to such languages without regard to times of meaning, it is shown that certain semantic related concepts, such as translation, cannot be adequately described without reference to times of evaluation. The major contribution provided here to the study of complex languages with multiple stages of evaluation is the development of a method of describing such languages so that semantics reflecting various times of evaluation can be derived from the descriptions.