Consider a restrictive clause of this form:

By program state here we mean the aggregate of values assumed by all variables involved. Because this clause constrains the states assumable by the program, it is called a state constraint, or a constraint for short, and is denoted by /\C.

State constraints are designed to be inserted into a program to create another program. For instance, given a program of the form of Program 2.1, a new program can be created, as shown in Program 2.2.

Program 2.1

S1; S2.

Program 2.2

S1; /\C; S2.

Program 2.2 is said to be created from Program 2.1 by constraining the program states to C prior to execution of S2. Intuitively, 2.2 is a subprogram of 2.1 because its definition is that of 2.1 restricted to C. Within that restriction, 2.2 performs the same computation as 2.1.

A state constraint is a semantic modifier. The meaning of a program modified by a state constraint can be formally defined in terms of Dijkstra's (1976) weakest precondition as follows. Let S be a programming construct and C be a predicate, then for any postcondition R,

Axiom 2.3

wp(/\C;S, R) ≡ C ⋀ wp(S, R).

Of course a constraint can also be inserted after a program.