We define a theory of type isomorphisms by combining two existing theories. One of these theories, due to Bruce, Di Cosmo, and Longo, covers the isomorphisms that hold in models of simply typed lambda-calculus with pairs and unit. It does not include recursive types. The second theory is a standard theory of equality of recursive types. It does not include the isomorphisms of the first theory. Each theory is individually decidable but proving the combined theory decidable is nontrivial and is not solved in this report. We discuss the practical importance of the combined theory and of possible extensions to it.
By: Joshua Auerbach, Charles Barton, Mukund Raghavachari
Published in: RC21247 in 1998
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