The co-invariant generator: An aid in deriving loop bodies

Given a loop invariant,I, and an assignment,α, which decreases the variant, we define a constructive function, cg, called the co-invariant generator, which has the property thatIΛ cg (α, I) ⇒ wp (α, I), where wp (α, I) is the weakest precondition forα to establish I. Several results about the co-invariant generator are proved, important special cases are considered, and a non-trivial example of its use in deriving the body of a loop is given. We also define a function which performs a related constructive action on terms formed from binary operations. The coinvariant generator makes a useful contribution to formalising and automating a key step in program derivation.