Slide 7.2: The syntactic domains of the calculator language

Slide 7.1: A calculator language
Slide 7.3: The semantic domains of the calculator langauge
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The Syntactic Domains of the Calculator

The syntactic domains, on which the semantic functions act, of the calculator is given below. To simplify the definition of the denotational semantics for the calculator, the syntactic domains considerably reduces the complexity of the notation while still representing all the key sequences allowed by the previous syntax. Since +/- acts in much the same way as the answer keys, it has been included with them in the syntactic domains.


   P: Program            O: Operator        N: Numeral
   S: ExprSequence       A: Answer          D: Digit
   E: Expression

   Program ::= ExprSequence
   ExprSequence ::= Expression | Expression ExprSequence
   Expression ::= Numeral | M^R | Clear | Expression Answer
       | Expression Operator Expression
   Operator ::= + | – | ×
   Answer   ::= M⁺ | = | +/-
   Numeral  ::= Digit | Numeral Digit
   Digit    ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Following the syntactic domains for the calculator language, given the sequence of keystrokes

   10 M⁺ + 6 +/- = × M^R =
 = 10 + –6 = × M^R =
 = 4 × M^R =
 = 4 × 10 = 
 = 40

a parser will construct the syntax tree. Notice that most operations associate to the left because of the way keystrokes are processed from left to right.