Non-failure Analysis (contd.)

• Ideally we would like to have a decision procedure to determine whether a test covers the type of a set of variables.

• Unfortunately this problem is undecidable.

• In the last period we developed a simple and efficient polynomial time algorithm which is successful in a significant number of cases.

• In this period we have identified classes of covering problems which are decidable and provided special algorithms for them.

• Decidable problems are:
  • unification/dis-unification tests, and tuple-distributive regular types, which are specified by regular term grammars in which each type symbol has exactly one defining type rule and each type rule is deterministic, and
  • linear arithmetic tests, and variables of integer or real type.
• (Intuitively) a call will not fail if:
  • The type of its input is covered by the test of the corresponding procedure.
  • Each literal in the clauses defining the procedure (recursively) will not fail.