Typed Lambda Calculi and Applications

Volume 664 of the series Lecture Notes in Computer Science pp 361-375


A logic for parametric polymorphism

  • Gordon PlotkinAffiliated withDepartment of Computer Science, University of Edinburgh
  • , Martín AbadiAffiliated withSystems Research Center, Digital Equipment Corporation


In this paper we introduce a logic for parametric polymorphism. Just as LCF is a logic for the simply-typed λ-calculus with recursion and arithmetic, our logic is a logic for System F. The logic permits the formal presentation and use of relational parametricity. Parametricity yields-for example-encodings of initial algebras, final co-algebras and abstract datatypes, with corresponding proof principles of induction, co-induction and simulation.