Conclusions
When comparing λ68 to other type systems with definitions, we find an important difference. In λ68, the correspondence between types of definiendum and definiens differs from the similar correspondence in the systems in [137] and [14].
The reason why λ68 differs from other theories in this respect has been discussed in Section 7b3: The definition system in AUTOMATH allows parameters to occur in the definiens, and there is no parameter mechanism in PTSs. In Chapters 9 and 10, we extend PTSs with a parameter mechanism. This extension has A-68 as a subsystem. Moreover, we show that a parameter mechanism has also other advantages.
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(2005). Pure Type Systems with definitions. In: A Modern Perspective on Type Theory. Applied Logic Series, vol 29. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2335-9_9
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DOI: https://doi.org/10.1007/1-4020-2335-9_9
Publisher Name: Springer, Dordrecht
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