Contravariant families in simplicial HoTT supply proof-relevant expansion, yielding directed Boolean canonicity and a binary parametricity model over reduction-aware syntax.
An Equational Logical Framework for Type Theories
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
A wide range of intuitionistic type theories may be presented as equational theories within a logical framework. This method was formulated by Per Martin-L\"{o}f in the mid-1980's and further developed by Uemura, who used it to prove an initiality result for a class of models. Herein is presented a logical framework for type theories that includes an extensional equality type so that a type theory may be given by a signature of constants. The framework is illustrated by a number of examples of type-theoretic concepts, including identity and equality types, and a hierarchy of universes.
fields
cs.LO 1years
2026 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Directed proof-relevant logical relations in simplicial HoTT
Contravariant families in simplicial HoTT supply proof-relevant expansion, yielding directed Boolean canonicity and a binary parametricity model over reduction-aware syntax.