&gt; <i>Types are by definition associated to terms in a language.</i><p>This is true, within a particular paradigm, which isn&#x27;t the be-all and end-all of what &quot;type&quot; means in computer science.<p>All kinds of things are type. For instance, &quot;JPEG file&quot; or &quot;alphanumeric character&quot; are both type terms.<p>You don&#x27;t get to dictate to everyone one narrow definition of a term that has an obviously broad applicability in numerous contexts.<p>If we are discussing Common Lisp, and you want to get properly pedantic about what &quot;type&quot; means, the way you can do that is to look up its definition in the ANSI CL glossary, which says:<p>&quot;type n. 1. a set of objects, usually with common structure, behavior, or purpose.&quot;<p>Or you can use it in a broader way which is compatible with this concept.<p>If you insist that it means something else which is not compatible with the glossary definition, and you still want to talk about Lisp, then I&#x27;m afraid it&#x27;s not productive; you are more interested in engaging in a conflict about word semantics: which &quot;camp&quot; gets to &quot;own&quot; the ideologically precious word, such as &quot;type&quot;.<p>Usually how we can resolve that conflict is to split our vocabulary into different words. You can have &quot;type&quot;, I don&#x27;t need it; I will call it this other thing that the CL glossary refers to &quot;genus&quot;. Now type can be the property of a syntactic term in a program, and genus refers to sets of objects which have something in common.<p>I&#x27;m mostly interested in genus systems, and type systems in their context (agreement between the type of a program term, and the genus of the run-time thing it operates on).