An Equational Logical Framework for Type Theories

06/02/2021

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by   Robert Harper, et al.

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A wide range of intuitionistic type theories may be presented as equational theories within a logical framework. This method was formulated by Per Martin-Löf in the mid-1980's and further developed by Uemura, who used it to prove an initiality result for a class of models. Herein is presented a logical framework for type theories that includes an extensional equality type so that a type theory may be given by a signature of constants. The framework is illustrated by a number of examples of type-theoretic concepts, including identity and equality types, and a hierarchy of universes.