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As in Ada, suppose that each expression must have a unique type, but that from a subexpression, by itself, all we can deduce is a set of possible types. That is, the application of function E1 to argument E2, represented by E ! E₁ ( E₂ ), has the associated rule

Describe an SDD that determines a unique type for each subexpression by using an attribute type to synthesize a set of possible types bottom-up, and, once the unique type of the overall expression is determined, proceeds top-down to determine attribute unique for the type of each subexpression.

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