Formalizing a strong normalization proof for Moggi's computational metalanguage: a case study in Isabelle/HOL-nominal

Abstract

Lindley and Stark have given an elegant proof of strong normalization for various lambda calculi whose type systems preclude a direct inductive definition of Girard-Tait style logical relations, such as the simply typed lambda calculus with sum types or Moggi's calculus with monadic computation types. The key construction in their proof is a notion of relational TT-lifting, which is expressed with the help of stacks of evaluation contexts. We describe a formalization of Lindley and Stark's strong normalization proof for Moggi's computational metalanguage in Isabelle/HOL, using the nominal package.