Standard model semantics for DSL, a data type specification language

We discuss a data type specification language DSL(∑) which is obtained from the first order language L(∑) for a given signature ∑ by augmenting it with schemes. A specification is a pair (∑, IF) with IF a finite set of axioms in DSL(∑). As semantics of such specifications we propose: standard model semantics, SMS. We investigate DSL/SMS as a specification mechanism for data types and compare it with both first order and algebraic specifications. A concise theory of parametrized data types is developed in this context