Abstract
Paterson introduced the notions of semantic restrictions on the class of restricted classes of schemas might have and also be realistic models of what "good" or "efficient" programs. With the introduce two new classes of schemas: Freedom and liberality as schemas. He felt that such solvable decision problems, would generally be considered latter viewpoint in mind, we the reachable schemas and the semi free schemas. A schema is reachable if every statement in the schema is executed under some interpretation. A schema is semi free if every test in the schema is necessary in the sense that each exit of the test is taken under some interpretation. We discuss various decision problems for these classes, and translatability between these classes and other semantically restricted schema classes. We also mention the implications of these results for questions of program optimization and verification.