Programming in Standard ML by Robert Harper

By Robert Harper

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In chapter 2 we said that a typing assertion has the form exp : typ, and that an evaluation assertion has the form exp ⇓ val. While two-place typing and evaluation assertions are sufficient for closed expressions (those without variables), we must extend these relations to account for open expressions (those with variables). Each must be equipped with an environment recording information about type constructors and variables introduced by declarations. 2 We may think of typenv as a sequence of specifications of one of the following two forms: 1.

0} invokes this function with the indicated x and y values. Functions with multiple results may be thought of as functions yielding tuples (or records). 3 Multiple Arguments and Multiple Results 49 fun dist2 (x:real, y:real):real*real = (sqrt (x*x+y*y), abs(x-y)) Notice that the result type is a pair, which may be thought of as two results. These examples illustrate a pleasing regularity in the design of ML. Rather than introduce ad hoc notions such as multiple arguments, multiple results, or keyword parameters, we make use of the general mechanisms of tuples, records, and pattern matching.

Each must be equipped with an environment recording information about type constructors and variables introduced by declarations. 2 We may think of typenv as a sequence of specifications of one of the following two forms: 1. type typvar = typ 2. val var : typ Note that the second form does not include the binding for var, only its type! Evaluation assertions are generalized to have the form valenv exp ⇓ val where valenv is a value environment that records the bindings of the variables that may occur in exp.

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