We review the concept of logical relations and how they interact with structural induction; furthermore we give examples of their use, and of particular interest is the combination with the PER-idea (partial equivalence relations). This is then generalized to Kripke-logical relations; the major application is to show that in combination with the PER-idea this solves the problem of establishing a substitution property in a manner conducive to structural induction. Finally we introduce the concept of Kripke-layered predicates; this allows a modular definition of predicates and supports a methodology of “proofs in stages” where each stage focuses on only one aspect and thus is more manageable. All of these techniques have been tested and refined in “realistic applications” that have been documented elsewhere.
Keywordslogical relations partial equivalence relations Kripke-logical relations layered predicates Kripke-layered predicates substitution properties well-structured proofs denotational semantics correctness of code generation proof principles
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