I'm studying programming languages (more specifically type systems) and came across a concept I couldn't quite wrap my head around: soundness and completeness.
I'm taking a class, and according to my instructor:
Soundness is an analyzer's ability to prove the absence of errors. If a program is accepted by an analyzer, then the program is guaranteed to be safe.
On the other hand, completeness is an analyzer's ability to prove the presence of errors. If a program is rejected, then that program has errors.
An example that I thought of is: If an analyzer is designed to accept all programs, does this mean the analyzer's system is sound but incomplete? I'm not quite sure if my reasoning is correct.
I've taken a look at other answers on this community:
Is there a relationship between “sound and complete” in logic and “type safety” in PLs? and
Example of Soundness & Completeness of Inference
but still am not quite sure how the logical concepts apply to type systems of programming languages.
Would anyone be kind enough to explain the differences?
Thank you.
