A theory of typed coercions and its applications

Reviewer: William M. Waite

The report on ALGOL 68 [1] introduced the term "coercion" to describe an implicit change of mode. For example, if x is an ALGOL 68 integer variable, then it has mode "ref integer." In the expression x +1, however, the operator requires operands of mode integer. Rather than requiring the programmer to explicitly change the mode of x , the language definition implies a mode change on the basis of context. In effect, the compiler is allowed to insert an operation not specified by the programmer. For many situations, the concept of implicit operations inserted by a processor is useful. This paper provides a theory that covers a wide variety of such applications, and explores the tradeoff between expressiveness and ambiguity, which are inherent to these applications. Although the paper is clearly written and includes relevant examples to illustrate the concepts, readers must be familiar with lambda calculus and the notations used for grammars and type-checking rules. The theory is stated in terms of rewriting systems for the simply typed lambda calculus that is based on sets of coercion generation and coercion insertion rules. For each system, Swamy, Hicks, and Bierman indicate the conditions under which the rewriting will be unambiguous. Overload resolution provides a simple example that has both ambiguous and unambiguous solutions, with the ambiguous solution offering certain practical advantages. Although there is a general mechanism for solving the ambiguity in this case, it lies beyond the scope of the paper. Despite such limitations, thoughtful compiler writers will find much to mull over in this paper. Online Computing Reviews Service