Formula Definition

A definition of an object is expressed as a mathematical expression. A variable is called a formula variable if its value is defined in terms of other variables, e.g:

v == phi(v1, v2, ..., vn)

where v is the name of the formula variable, and phi represents an expression with the variables v₁, v₂, ... , v_n involved. The variables v₁, v₂, ... , v_n are called the source variables of this definition since the value of v is computed from their values. Hence the formula variable v, can also be called the target variable. EDEN supports the concept of definition. A formula definition has the form:

v is phi(v1, v2, ..., vn)

The keyword ``is'' defines a formula variable v whose value is computed from the values of source variables v₁, v₂, ..., v_n and the expression on the right hand side, denoted by phi , is the formula of the variable $v$ . In other words, a formula describes how the value of a variable is computed from other data. These formulae are permanently valid (unless they are re-defined). That is, no matter what the values of source variables are, the value of variable $v$ is always equal to phi(v1,
v2, ..., vn) . Thus a formula gives an abstract definition of a variable rather than the explicit value of it. This is the major difference between formula definitions and assignment statements. For example, after executing the assignment

v == phi(v1, v2, ..., vn)

v is equal to only after the expression phi is evaluated and before any of the values of the source variables is altered.

Unlike the assignment statement, the formula definition, itself, is not an executable statement. When and how the formula expression defined in the definition is managed by the system. However, the values of the formula variables are guaranteed to be up-to-date when the variables are examined.

Notice that a definition does not imply the inverse definitions (where these exist); for example, the definition (2-1) does not imply

vi is phi(i)^-1(v, v1, v2, ..., vi, vi+1, ..., vn) where 1<=i<=n

A definition can be a representation of a real relationship among objects; for instance, ``a lamp is placed (somewhere) on a table'' can be formulated as:

lamp_position is table_position + something

If the table is re-positioned the lamp will also be moved because the definition has specified the position of the lamp in terms of the position of the table, the system can automatically keep track of these definitions and re-calculate lamp_position whenever table_position has been changed. But if the lamp_position is then redefined to

lamp_position is desk_position + something

we mean to put the lamp on the desk instead of the table. The table remains at the same position because it is not defined in terms of the lamp. Note that the new definition of lamp_position overwrites the previous definition. Hence the lamp can be moved independently by redefining its definition.