I think this POV is limiting. In my experience, many people who take the &quot;maths model&quot; respect and use the &quot;machine model&quot; quite often as well.<p>The formal term of note here is &quot;denotation&quot; in that &quot;a language may be understood through its denotation&quot; as an abstract machine or as a mathematical object. The best understanding comes from recognizing that many denotations may be valid for a language and that great richness comes from this. To work, the denotations must be in alignment in various ways and when they are it means that you can transport understanding from one denotation to another to the language itself.<p>So I don&#x27;t think there&#x27;s an honest conflict, though I imagine there are programmers and PL experts who either (a) honestly only ever use one denotation or (b) play favorites and this may lead to some clouding of things.