vec_type2() finds the common type for a pair of vectors, or dies trying.
It forms the foundation of the vctrs type system, along with vec_cast().
This powers type coercion but should not usually be called directly;
instead call vec_ptype().
vec_type2(x, y)# S3 method for logical
vec_type2(x, y)
# S3 method for integer
vec_type2(x, y)
# S3 method for double
vec_type2(x, y)
# S3 method for list
vec_type2(x, y)
# S3 method for character
vec_type2(x, y)
# S3 method for factor
vec_type2(x, y)
# S3 method for ordered
vec_type2(x, y)
# S3 method for Date
vec_type2(x, y)
# S3 method for POSIXt
vec_type2(x, y)
# S3 method for difftime
vec_type2(x, y)
# S3 method for data.frame
vec_type2(x, y)
# S3 method for tbl_df
vec_type2(x, y)
Either vector types; i.e.
vctrs thinks of the vector types as forming a partially ordered set, or poset. Then finding the common type from a set of types is a matter of finding the least-upper-bound; if the least-upper-bound does not exist, there is no common type. This is the case for many pairs of 1d vectors.
The poset of the most important base vectors is shown below:
(where datetime stands for POSIXt, and date for Date)

vec_type2() dispatches on both arguments. This is implemented by having
methods of vec_type2(), e.g. vec_type2.integer() also be S3 generics,
which call e.g. vec_type2.integer.double(). vec_type2.x.y() must
return the same value as vec_type2.y.x(); this is currently not enforced,
only checked in unit tests.
See vignette("s3-vector") on how to extend to your own S3
vector classes.