Pointing to Algebraic structures is not an argument since it is fundamental to mathematics and hence to programming in any language. What do you think a Type/ADT is? Why do you think user-defined types exist in any language? It is a given, the only difference is the strict pov taken by functional languages vs. imperative (procedural/OO) languages. There is a reason i pointed to the example of linking the derived type's contracts (i.e. properties) with the base type's because that would have made the isomorphism between two algebraic structures clearer (which you didn't seem to understand). Repeating some slogan is not knowledge. You have to go beyond the immediate notation/syntax in any language to the abstract concept it is trying to express. That is the heart of mathematics and programming.

Since you brought up algebraic structures, C++ can express it directly using template syntax and relationships between them using parametric polymorphism non-OO style. Not only that, but because in C++ genericity is unconstrained, we actually can use OO inheritance for a type hierarchy and then using it to get constrained genericity. This flexibility is quite powerful and you get full type checking.

To understand all this (and apply the concepts in any other language) see the books by Alexander Stepanov viz. From Mathematics to Generic Programming and Elements of Programming.