We move the basic notions of pointed types into init.pointed, to avoid cycles in the import graph. Also adds pointed versions of pi and sigma, with corresponding notation
more about pointed truncated types, including pointed sets.
also increase the priority of some basic instances that nat/num/pos_num/trunc_index have 0, 1 and + (in both libraries)
also move the notation + for sum into the namespace sum, to (sometimes) avoid overloading with add
@avigad and @fpvandoorn, I changed the metaclasses names. They
were not uniform:
- The plural was used in some cases (e.g., [coercions]).
- In other cases a cryptic name was used (e.g., [brs]).
Now, I tried to use the attribute name as the metaclass name whenever
possible. For example, we write
definition foo [coercion] ...
definition bla [forward] ...
and
open [coercion] nat
open [forward] nat
It is easier to remember and is uniform.
This also involves:
- adding definitions about logic and natural numbers existing in the standard library to init
- porting the current algebraic hierarchy
remove funext class,
remove a couple of sorry's,
add characterization of equality in trunctypes,
use Jeremy's format for headers everywhere in the HoTT library,
continue working on Yoneda embedding
also add more definitions in types.pi, types.path, algebra.precategory
the (pre)category library still needs cleanup
authors of this commit: @avigad, @javra, @fpvandoorn
