LAMBDALG: Higher order algebraic specification language
Typed functional languages like ML or Haskel do not allow algebraic definitions of abtract data types and operators although they may employ a very rich machinery for defining polymorphic recursive functions of a higher type. On the other hand, equational languages like OBJ allow arbitrary (first order) algebraic definitions, but they do not have the full-power of parametricity given by ML polylmorphism nor functional definitions of higher types. Under these circumstances it is very attractive to combined these two different kinds of languages to host both features. Then the unified language would allow easy definitions of quite complex objects in a simple declarative style. LAMBDALG is a specification language which hosts both these features. The computation model (operational semantics) of LAMBDALG is based on the combined system of polymorphic typed lambda calculus and the first order and restricted higher order term rewriting in [Jouannaud-Okada 91]. As a high-level specification language, LAMBDALG integrates the OBJ3 style module based algebraic specification language [Goguen-Winkler 88] and the ML style polymorphic typed functional language [Harper et al. 86]. Algebraic definition of abstract data types and context-sensitive definitions of operators can be directly executed, in contrast to the traditional ML-style languages or their extensions (eg. [Mitchell et al. 90]).
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