Modern eyes on λ-calculus presents detail on the three level signature as applied to formalism implicitly appearing in classic work like Schönfinkel's Bausteine (1924), Curry's functionality (1934) and Church's simple types (1940). "Fuzzy λ-calculus" can be easily developed. Modern type theory, including Martin-Löf's Type theory (MLTT) and Homotopy Type Theory (HoTT), ignores the use of levels of signature, and also allows for incompleteness in the use of a "universe". This basically falls down on a restricted understanding of the semantics of Church's 'ι' (iota), and on a informal notion related to Church's 'ο' (omicron). Modern type theory departs from Church's 1940 work and also from Grothendieck's view on universes.

PhD thesis work on Generalized General Logics provide background and powerful tools for a broader view of lative logic as generalizing the logical frameworks by Goguen and Burstall on 'institutions' (1984) and by Meseguer on 'entailment systems' (1987).