The model for the defined operation identifies the name of the operation, its valence, and whether or not an explicit result may be returned. Valence is the number of explicit arguments or operands, either 0, 1 or 2; whence the operation is termed NILADIC, MONADIC or DYADIC respectively. Only a defined function may be niladic. There is no relationship between the valence of a defined operator, and the valence of the derived function which it produces. Defined functions and derived functions produced by defined operators may be ambivalent, i.e. may be executed monadically with one argument, or dyadically with two. An ambivalent operation is identified in its model by enclosing the left argument in braces.
The value of a result-returning function or derived function may be suppressed in execution if not explicitly used or assigned by enclosing the result in its model within braces. Such a suppressed result is termed SHY.
The tables below show all possible models for defined functions and operators respectively.
| Result | Niladic | Monadic | Dyadic | Ambivalent |
|---|---|---|---|---|
| None | f | f Y | X f Y | {X} f Y |
| Explicit | R←f | R←f Y | R←X f Y | R←{X} f Y |
| Suppressed | {R}←f | {R}←f Y | {R}←X f Y | {R}←{X} f Y |
Note: the right argument Y and/or the result R may be represented by a single name, or as a blank-delimited list of names surrounded by parentheses. For further details, see Namelists.
| Result | Monadic | Dyadic | Ambivalent |
| None | (A op)Y | X(A op)Y | {X}(A op)Y |
| Explicit | R←(A op)Y | R←X(A op)Y | R←{X}(A op)Y |
| Suppressed | {R}←(A op)Y | {R}←X(A op)Y | {R}←{X}(A op)Y |
| Result | Monadic | Dyadic | Ambivalent |
| None | (A op B)Y | X(A op B)Y | {X}(A op B)Y |
| Explicit | R←(A op B)Y | R←X(A op B)Y | R←{X}(A op B)Y |
| Suppressed | {R}←(A op B)Y | {R}←X(A op B)Y | {R}←{X}(A op B)Y |