From categorical combinators to lambda-sygma-calculi, a quest for confluence
Abstract
The l-calculus is known to be the theoretical base of functional programming languages. But, the substitution, which describes the parameters' passage, belongs only to the meta-language and this is a major drawback when dealing with compilation. Therefore, extensions of l-calculus, able to manipulate explicity substitutions and still confluent, are required. The categorical combinatory logic, introduced in 1983, and the ls-calculi, presented in 1988 and 1989, are responses to this question. We give here a survey of these theories, explaining their evolution from a confluence point of view. This report does not contain new results and remains rather informal, avoiding too technical details.