Using left joins instead of inner joins as an optimization

Hi All!

I'm currently writing a view that joins many tables and I was wondering
how PostgreSQL optimizes
projections on such a view. In particular I was wondering if it is a
correct and valid optimization
technique to use left joins when they are equivalent to an inner join.

I have created a minimal example. Suppose we have two tables:

> create table a(a_id int primary key generated always as identity, a_data
text);
> create table b(b_id int primary key generated always as identity, a_id
int not null references a(a_id), b_data text);

Then the query
> explain select b_id from b natural left join a;
results in a `Seq Scan on b`. Whereas the query
> explain select b_id from b natural join a;
results in a join with sequential scans on both a and b.

I believe because b.a_id is not null and references a.a_id a left and an
inner join are exactly equivalent.

My questions are:
- Am I wrong that in such a situation a left and inner join are equivalent?
- Why does PostgreSQL not automatically optimize this?
- Is it a bad idea to use left joins to optimize this even if semantically
an inner join would be correct?

Thank you for your help!