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Stratified Type Theory: A Type Theory with Stratified Typing Judgements and Floating Function Types
Stratified Type Theory (StraTT) is a type theory that stratifies typing judgements rather than universes, and includes a separate nondependent function type with a floating domain to overcome the limitations of strict stratification.
Primitive Recursive Dependent Type Theory: A Formal System for Capturing Primitive Recursive Functions
Restricting the elimination principle of the natural numbers type in Martin-Löf Type Theory to a universe of types not containing Π-types ensures that all definable functions are primitive recursive, extending the concept of primitive recursiveness to general types.
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