Oberwolfach HoTT-Coq tutorial   Type theory  natural deduction
metalanguage, practical foundations    1. type formation rule
2. term introduction rule   3. term elimination rule   4.
computation rule   syntax object language   logiccategory
theorytype theory falseinitial objectempty type proofgeneralized
elementprogram cut rule?compositionsubstitution cut
elimination?counitbeta reduction ?uniteta conversion
conjunctionproductproduct type implicationinternal homfunction
type negationinternal hom into initial objectfunction type into
empty type universal quantificationdependent productdependent
product type equivalencepath space objectidentity type
equivalence classquotientquotient type inductioncolimitinductive
type, W-type, M-type higher inductionhigher colimithigher
inductive type setinternal 0-groupoidBishop set/setoid
universeobject classifiertype of types modalityclosure operator
monadmodal type theory, monad (in computer science)  homotopy
levels   At an Oberwolfach workshop in 2011 on homotopy type th