In spite of decades of work, the practical impact of programming language semantics (denotational semantics) has been limited. Our thesis is that a major contributing factor to this lack of practical impact is the declarative notation used for expressing the semantics, namely, the lambda-calculus. We propose to use Horn Logic (and eventually Constraint Logic) instead of the lambda-calculus to express denotational semantics. This simple change leads to many practical applications, most notably to automatic program verification and automatic generation of compilers from semantic specifications. These Horn Logic denotations and their applications are discussed at length in this paper.