Function and Constructor Declarations

In mathematics, we sometimes define functions that takes some inputs and returns some output. Penrose allows us to define functions that behave similarly:

function function_name (argument_list) -> output_type

where

• function_name declares the name of the function, which can be referred to by the Substance and Style schemas;
• argument_list is a list of the types of inputs that this function accepts, similar to the argument list in predicate declarations; and
• output_type represents the type of the output of the function. When we assign the result of the function to an object in the Substance and Style schema, the output of the function must match the type of the assigned object (either the types are exactly the same, or the output type is a subtype of the assigned object type).

For example, in the linear-algebra domain, we can define

type Vector
function addVector (Vector v1, Vector v2) -> Vector

Constructors in Penrose are functionally equivalent to functions, with the same declaration syntax, except for the first word:

constructor constructor_name (argument_list) -> output_type

Optionally, where the constructor name is the same as the output type, constructors may omit the output type:

constructor constructor_name (argument_list)