Up to this point direct implementations of axiomatic or equational specifications have been limited because the implementation mechanisms used are incapable of capturing the full semantics of the specifications. The programming language Unicorn was designed and implemented with the intention of exploring the full potential of programming with equations. Unicorn introduces a new language mechanism, called constraining-unification. When coupled with semantic unification, constraining-unification closely models the semantics of equational specifications thereby allowing for the implementation of a wider class of specifications. Unlike the language mechanisms of rewrite-rule and logic programming, constraining-unification is free of order dependencies. The same results are produced regardless of the order in which the axioms are stated. The use of viewpoints contributes to the flexibility of the Unicorn language. Preconditions for partial operations can be specified without added machinery.