Digital & Computing

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Data and processes in computing

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# 3.2 Combining data structures

In Section 2, we introduced the notation SeqOfX for the set of all sequences whose members come from the set X. In Section 2, we looked only at sequences whose members were of one of the primitive forms of data (integers, characters or Booleans). We can have sequences whose members are themselves data with a more complicated form. For example, suppose that Jo is working at the till T1 and is replaced by Jessica. We might represent this handover by the 3-tuple (Jo, T1, Jessica). Now suppose that we want to give all the handovers that occur during a particular day, in the order in which they occur. We could give this information in a sequence. This sequence would come from the set SeqOfX , where X is the Cartesian product Staff × Tills × Staff.

As another example, one might think of a sentence as a sequence of words, where each word is seen as a sequence of characters. If we did this, then the sentence would be regarded as coming from the set SeqOfSeqOfChar. We can use notations introduced earlier to show when we want to see a sentence in this way, and when it is to be regarded as a single string (from SeqOfChar).

## Activity 11

Which of the following is a member of the set SeqOfSeqOfChar?

• (a) [‘W’,‘o’,‘r’,‘d’].

• (b) “This is a sentence.”.

• (c) [“This”,“is”,“a”,“sentence”].

### Discussion

Only (c) is a member of SeqOfSeqOfChar.

• (a) This is a sequence of characters and so a member of SeqOfChar.

• (b) This is a string, so is again a sequence of characters (written in our more compact notation).

• (c) This is a sequence each of whose members is a string. Thus each item in the sequence in (c) comes from SeqOfChar. The sequence itself comes from SeqOfSeqOfChar.

Consider a computer system which has a finite set of error messages, each of which may be displayed to a cashier at the till. Suppose these messages are: “Barcode error”; “Item code not recognised” and “System error 1234”. This set of error messages can be represented thus:

Errors = {“Barcode error”, “Item code not recognised”, “System error 1234”}.

Each of these messages is given as a string, that is, as a sequence of characters. So Errors is a set of sequences of characters.