Type theory in a type theory with quotient inductive typesTools Kaposi, Ambrus (2017) Type theory in a type theory with quotient inductive types. PhD thesis, University of Nottingham.
AbstractType theory (with dependent types) was introduced by Per MartinLöf with the intention of providing a foundation for constructive mathematics. A part of constructive mathematics is type theory itself, hence we should be able to say what type theory is using the formal language of type theory. In addition, metatheoretic properties of type theory such as normalisation should be provable in type theory.
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