I'll omit generalizations and make this overly concrete as I think it will be easier to understand what I'm looking for here.
An implementable example is a small example of a programming library that uses the core ideas of of the library. Its purpose is to make the interface very explicit, so that someone can say "if I didn't have this library, how would I make the example actually work?" and then go implement their solution and see it work. This has been incredibly valuable for me in understanding the tools I use, what they are capable of, what decisions they make and why, and what their limitations are. Ideally it only takes a couple of hours to implement, and it provides a very deep intuition for how that tool works and why.
Examples:
- Learn how web servers work by writing one. This was where I started: a web app that can be run by a real web server: https://github.com/JoshCheek/chicago_ruby_build_a_server/blob/97e7f2b77f98ad02a3e5e33f46a4a070392bf164/app.rb
- Sinatra, a minimalistic Ruby web server: https://github.com/JoshCheek/fake-sinatra-2/blob/147a912f648b9eedbd2ce7236c1cb5da75a5465c/spec/fake_sinatra_spec.rb#L32-L44
- An example Rakefile (Ruby's most common build tool), invocations and expected output are listed in the readme, https://github.com/JoshCheek/Minirake/blob/5034e7f8335bdf2923c1a5c1abaadd80f8aac502/Minirakefile
- ERB (embedded Ruby): https://gist.github.com/JoshCheek/2b30b052560337522f94#file-procedural_oo_parser-rb-L40-L56
- A Ruby interpreter: https://github.com/JoshCheek/book_club_interpreter/blob/f650146318b2ddcc5742d9bba064042130c34f6b/examples/print_username.rb
- Use a web client that doesn't exist, then go figure out what it takes to make it pass: https://github.com/JoshCheek/example_client/blob/599fcdae7e4463646483e926ae648635c00d3506/spec/client_spec.rb#L6-L17
- A JavaScript interpreter https://github.com/JoshCheek/interpreter-for-scna/blob/fcbd602cde0527a58dd819b83ee4d6347cd549c3/examples/word_count.js
- Here is a context sensitive bit of code that I parsed. The expectation here is maybe too general, it's an example because I already understood what success looked like when I made it. https://github.com/JoshCheek/ruby_slippers_for_the_cobblers_children/tree/6a4794de5763370bcdc044f9add2116883e6970d/interpreter/defs/experiments/success-indentation-based-interactive-debugging#grammar
Thre's a lot more, but hard to remember where they are, and they're not necessarily packaged up to be easy to show off as an example.