Interpretation of State-Transformed Strongest Postcondition Elements

Determine how to interpret the elements of the lawful monad obtained by applying the state monad transformer to the base strongest-postcondition monad as stateful strongest postconditions.

Background

The paper distinguishes between the expected stateful strongest-postcondition carrier, which accepts a precondition over initial states, and the carrier produced by the ordinary state monad transformer, which first takes an initial state and then a separate proposition. Although the resulting structure is a lawful monad, its elements do not directly have the intended stateful strongest-postcondition interpretation. The authors address this mismatch later by generalizing strongest-postcondition monads to arrows and applying state arrow transformers, but the quoted passage explicitly identifies the interpretation problem before that construction.