Slide 7.3: The semantic domains of the calculator language Slide 7.5: The semantic functions of the calculator language Home

The Semantic Domains of the Calculator (Cont.)

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Calculator arithmetic will be modeled by several auxiliary functions that carry out the three basic binary operations and an “identity” operation for the case when no operator is pending. Although the meaning of a calculator program will be the final integer value shown on the display, the behavior of the calculator in response to individual keystrokes and partial results will be studied too. This meaning depends on the following semantic domains:

Domains     v: Integer = { ..., -2, -1, 0, 1, 2, ...}     s: State = Integer × Operation × Integer × Integer Operations     +: Integer × Integer → Integer     –: Integer × Integer → Integer     *: Integer × Integer → Integer     nop: Integer × Integer → Integer     where nop( a, d ) = d

• The Operations domain can be compared to an enumerated type in Pascal. These four values act as flags inside the calculator by saving the last operator keystroke.


• Integer represents the abstract collection of mathematical integers.


• State takes values that are quadruples embodying the internal accumulator, the pending operation, the display, and the memory. The following table shows which entries change the various values in the State tuple:

State Tuple Value Tokens that May Alter the Value Accumulator Clear, +, –, and × Operator Flag Clear, +, –, ×, =, and M+ Display Clear, numeral, =, M+, MR, and +/- Memory Clear and M+

To Divide use / Symbol