PostgreSQL boolean comparison

Question

Is there a difference in the following comparisons

#1

where x = true

#2

where x is true

#3

where x = '1'

#4

where x

Answer 1

1. This is exactly the same as

   WHERE x
   

   It is TRUE, FALSE or NULL exactly when x is.

2. This is the same as the first case, except when x is NULL, in which case it will be FALSE. So it is the same as

   WHERE coalesce(x, FALSE)
   

3. This happens to be the same as the first case, since '1' is interpreted as TRUE. See the documentation:

   The datatype input function for type boolean accepts these string representations for the “true” state:

   true
yes
on
1

My preferred way is the simplest:

WHERE x