Slide 7.5: The semantic functions of the calculator language
Slide 7.7: A sample calculation
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The Semantic Functions (Cont.)

The denotational semantics for this calculator has a semantic function for each of the syntactic domains.

The Semantic Function meaning
It calls perform on a sequence of one or more expressions that makes up a program, giving perform an initial state (0, nop, 0, 0) as its argument. An expression sequence is evaluated one expression at a time by composing executions of the evaluate function. Finally, meaning returns the display value given as a result of evaluating the last expression in the sequence.

The Semantic Function evaluate
It produces a function in State → State as its result when applied to an expression.

The Semantic Functions compute and calculate
They give meaning to operators and “totaling” keys. For example, + computes the pending operation with the accumulator and display, updating the accumulator and display but leaving the display unchanged. Moreover, plus becomes the new pending operation. In contrast, = places the computed value into the display with nop signaling that there is no longer a pending operation. Observe that MR and +/- act only on the display.

Compund Keystrokes
Compound keystrokes are handled as compositions, eliminating the need to give the argument tuple. The semantic equation, given here as a composition, 
   evaluate[[E A]] = calculate[[A]] º evaluate[[E]]
is equivalent to writing 
    evaluate[[E A]](a, op, d, m)
  = calculate[[A]]( evaluate[[E]](a, op, d, m) )