Introducing Type Properties

In type theory, we can express many practical ideas by attributing some additional data to expressions we operate on during compilation. For instance, some substructural type theories augment variables' typing judgments with the information of their usage. That is, they allow one to explicitly state how many times - 0, 1, or many - a variable can be used. This solves the problem of resource usage control and allows us to treat variables as resources. What's more, it often happens that this attributed information is interpreted (used) during the same compilation and erased before we run a program. A case in the point is that in the same substructural type theories, their type checkers use these 0, 1, or many, to ensure that all variables are used as many times as these attributions say them to be. Yet, there wasn't any programming language concept whose concern would be to allow a programmer to express these attributions in the language itself. That is, to let the programmer express which data the one wants to attribute to what expressions and, most importantly, the meaning of the attributed data in their program. As it turned out, the presence of such a concept allows us to express many practical ideas in the language itself. For instance, with appropriate means for assigning the meaning of these attributions, this concept would allow one to express linear types as functionality in a separate program module, without the need to refine the whole type system to add them. In this paper, we present such a concept - we propose type properties. It allows a programmer to express these attributions while fulfilling the requirement of being fully on the static level. That is, it allows one to express how to interpret these attributions during compilation and erases them before a program is passed to the runtime.