Position and interval notation

[h-2]

There are typically two notations:

1. 0-based numbers and half-open intervals [beg, end)
2. 1-based numbers and closed intervals [beg, end]

Some formats use 1., others use 2.

We would like to use 1. everywhere, but this means that when reading a SAM or VCF record, the reported .pos() will different from the position in the plaintext file and the position shown by samtools / bcftools. That's why I initially proposed to use whatever the common formats use, even if this is inconsistent within the library.

However, with the introduction of bio::genome_region and subregion reading, this becomes more difficult. The algorithm to compute an overlap, for example, needs to know whether the interval is half-open or closed. It's possible to add a template parameter to genome_region that differentiates between half-open and closed, but this adds complexity 😒

I see three solutions:

1. Use 0-based, half-open intervals everywhere. Consistent, but means we deviate from samtools/bcftools and the specification of the most well-known formats.
2. Use 1-based, closed intervals everywhere. I have a bad gut feeling about this, but maybe I need to overcome that? It seems to be what most biologists expect.
3. Use whatever the spec / popular tooling suggests. Add a template parameter to genome_region. Document everywhere which notation is used.