We introduce an equationally definable counterpart of the notion of combinatory model. The new notion, called an algebraic combinatory model, is weaker than that of a lambda algebra but is strong enough to interpret lambda calculus. The class of algebraic combinatory models admits finite axiomatisation with seven closed equations, and it can be characterised as the retracts of combinatory models. Lambda algebras are then characterised as algebraic combinatory models which are stable, and there is a canonical construction of a lambda algebra from an algebraic combinatory model. This passage to a lambda algebra also manifests itself in our construction of a cartesian closed category with a reflexive object from an algebraic combinatory model. The resulting axiomatisation of lambda algebras with the seven equations and stability corresponds to that of Selinger [J. Funct. Programming, 12(6), 549-566, 2002], which would clarify the origin and the role of each axiom in his axiomatisation.
翻译：我们引入了一种可等式分解的组合模型概念对应方。 这个新概念叫做代数组合模型,比羊羔代数模型弱,但强到足以解释羊羔缩微积分。 代数组合模型的等级承认有7个封闭方程式的有限分解, 并可以被定性为复式模型的反射。 Lambda代数随后被定性为稳定的代数组合模型, 并且从一个代数组合模型中形成了羊驼代数的粗体构造。 羊驼代数的通过也体现在我们构筑一个带有7个闭合方程式的反射物体的漫画类中。 由此形成的羊驼代数和7个方程式的反射度与Selinger[J. Funct. prographic, 12(6), 549-566, 2002], 这可以澄清每个xima的起源和作用。
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