Signature checking

If all STELF had were the features we’ve introduced so far, it would still be a useful tool: we can represent a large variety of complex types and do searches and logic programming over them. But where STELF really shines is in its signature checks. Having created a STELF signature—which, as we’ve seen, we can interpret as a labeled logic program—we can then ask STELF to check certain properties of that signature. In particular, as we will see shortly, we can designate the arguments of a type family as inputs and outputs, and then ask

• whether this designation is consistent with the reading of the signature as a logic program, that is, whether the outputs of the constructor will be ground (involve no logic variables) if the inputs are all ground (a mode check),
• whether the constructor will produce at most one combination of outputs for any given combination of ground inputs (a uniqueness check),
• whether the logic program will always terminate if it is given ground inputs (a termination check), or
• whether the constructor will always produce at least one combination of ground outputs for any possible combination of ground inputs (a totality check). The totality check subsumes termination, but it has a couple of additional elements: input coverage and output coverage. Input coverage involves checking whether there are enough clauses for the constructor to match any possible combination of inputs; we then say that all possible inputs are covered. Output coverage involves checking that certain assumptions made about the form of outputs from “subroutine” calls are justified. Let’s now take a look at these checks in more detail and see some examples.