box intersections (or for entire columns or rows by dragging the column- or row-headers). An array of cells is called a sheet or worksheet. It is analogous to an array of variables in a conventional computer program (although certain unchanging values, once entered, could be considered, by the same analogy, constants). In most implementations, many worksheets may be located within a single spreadsheet. A worksheet is simply a subset of the spreadsheet divided for the sake of clarity. Functionally, the spreadsheet operates as a whole and all cells operate as global variables within the spreadsheet (each variable having 'read' access only except its containing cell). A cell may contain a value or a formula, or it may simply be left empty. By convention, formulas usually begin with = sign. Values A value can be entered from the computer keyboard by directly typing into the cell itself. Alternatively, a value can be based on a formula (see below), which might perform a calculation, display the current date or time, or retrieve external data such as a stock quote or a database value. The Spreadsheet Value Rule Computer scientist Alan Kay used the term value rule to summarize a spreadsheet's operation: a cell's value relies solely on the formula the user has typed into the cell. The formula may rely on the value of other cells, but those cells are likewise restricted to user-entered data or formulas. There are no 'side effects' to calculating a formula: the only output is to display the calculated result inside its occupying cell. There is no natural mechanism for permanently modifying the contents of a cell unless the user manually modifies the cell's contents. In the context of programming languages, this yields a limited form of first-order functional programming. Automatic recalculation A standard of spreadsheets since the 1980s, this optional feature eliminates the need to manually request the spreadsheet program to recalculate values (nowadays typically the default option unless specifically 'switched off' for large spreadsheets, usually to improve performance). Some earlier spreadsheets required a manual request to recalculate since the recalculation of large or complex spreadsheets often reduced data entry speed. Many modern spreadsheets still retain this option. Recalculation generally requires that there are no circular dependencies in a spreadsheet. A dependency graph is a graph that has a vertex for each object to be updated, and an edge connecting two objects whenever one of them