4.10 Functions as Relations

Internally, Oz supports only a single kind of procedures which are all relational. The idea is that -ary functions are treated as -ary relations. This can be observed in the Browser:

declare Square = fun{$ X} X*X end 
{Inspect ['Browsing fun{$ X} X*X end yields <P/2>' Square]}  
{Inspect {Square 111}}

When browsing the value of procedure named Square a string is displayed meaning that the value of Square is relational procedure with 2 arguments rather than a functional procedure with a single argument. The additional argument is used for the output.

Note also that the expression {Square 111} denotes a value, wheres {Browse 111} has none. The reason is that Browse denotes a relational procedure which in contrast to a functional procedure does not return a output value.

As said already, the output behaviour of a functional procedure can be simulated by a relational procedure which raises a side effect on a logic variable (see section unification). In fact, Oz supports functional procedure through relational procedures. A functional procedure with arguments is translated into a relational procedure with arguments, where the last arguments serves as an output argument. For instance, the functional procedure  fun{Square X} X*X end  and its application  Y={Square 3}  are translated as follows:

fun{Square X} X*X end  ==>  proc{Square X Out} Out=X*X end  
 declare Y={Square 3}  ==>  declare Y in {Square 3 Y}

The translation introduces a free logic variable Y that is passed as an additional argument to the application {Square 3 Y}. The application is then executed; once it finishes it computation, it binds the logical variable Y to the functional result 9. The result is thus passed by a side effect on a logic variables.