The spreadsheet has become a very popular tool in recent years. A modern commercial package provides many thousands of features – we shall be less ambitious. In essence, a simple two-dimensional spreadsheet is based on the concept of a matrix of cells, typically identified by a letter–digit pair (such as E7) in which the letter specifies a row and the digit a column. Part (or all) of this matrix is displayed on the terminal screen – one cell is taken as the active cell and is usually highlighted in some way (for example, in inverse video). Input to a spreadsheet is then provided in the form of expressions typed by the user, interleaved with commands that can reselect the position of the active cell. Each time an expression is typed, its formula is associated with the active cell and its value is displayed in the correct position. Changing the contents of one cell may affect the values of other cells. In a very simple spreadsheet implementation, each time one cell is assigned a new expression the values of all the other cells are recomputed and redisplayed. For this exercise assume that the expressions are confined to integer expressions of the sort discussed exhaustively in this text. The operands may be integer literals or the designators of cells. No attempt need be made to handle string or character values. A simple session with such a spreadsheet might be described as follows.

It is possible to develop such a system using Coco/R in a number of ways, but it is suggested that you proceed as follows.

 (a) Derive a context-free grammar that will describe the form of a session with the spreadsheet like that exemplified above.

 (b) Enhance your grammar to provide the necessary attributes and actions to enable a complete system to be generated that will read and process a file of input, and compute and display the spreadsheet updating the display each time new expressions become associated with cells.

n Arrange that the spreadsheet starts with the values of each cell set to zero and with no expressions associated with any cell. n No facilities for editing an expression need be provided – if a cell’s expression is to be altered it must be typed afresh. Hint: The most intriguing part of this exercise is deciding on a way to store an expression so that it can be evaluated again when needed. It is suggested that you associate a simple auxiliary data structure with each cell of the spreadsheet. Each element of this structure can store an operation or operand for a simple interpreter.