Abstract
Typed homomorphic relations on heterogeneous algebras are generalized to allow relationships between elements in the carrier sets of different types. Such relations are needed for the model theory of incomplete, hierarchical specifications with subtypes. Typed logical relations are generalized similarly. These tools help give a simple model-theoretic account of subtyping among abstract data types as observed by terms of a simply-typed lambda-calculus with subtypes.
Leavens's work was supported in part by the ISU Achievement Foundation, the National Science Foundation under Grants DCR-8510014 and CCR-8716884, the Defense Advanced Research Projects Agency under Contract N00014-83-K-0125, and by a GenRad/AEA Faculty Development Fellowship.
Pigozzi's work was supported in part by the National Science Foundation under Grant DMS-8805870.
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Leavens, G.T., Pigozzi, D. (1992). Typed homomorphic relations extended with subtypes. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_7
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