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.
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.