Dec 31, 2016

There's two reasons pseudocode is used in most cases:

1. Private exploration as you said.

2. Publication of algorithms in a form most will understand and be able to duplicate.

There's an example of 2 on the front page right now:

https://arxiv.org/abs/1610.08129

In the PDF, they describe their algorithms in pseudo-code that combines the common, BASIC/ALGOL-like text with some common notation (i.e. division) from math. I immediately understood the algorithms enough to implement them myself in about any language without soneone telling me what the notation meant. A common effect of published pseudocode since it's intended to be widely understood.

This new notation Id have to think about and practice with. Just using it in a paper with the label pseudocode would cause confusion. It's less intuitive in a world of widely-deployed, ALGOL-like notations. Maybe it has benefits worth sacrificing the wide usability but person switching it better be OK with that.