  We introduce the notion of reflexivity for combinatory algebras. Reflexivity
can be thought of as an equational counterpart of the Meyer-Scott axiom of
combinatory models, which indeed allows us to characterise an equationally
definable counterpart of combinatory models. This new structure, called
strongly reflexive combinatory algebra, admits a finite axiomatisation with
seven closed equations, and the structure is shown to be exactly the retract of
combinatory models. Lambda algebras can be characterised as strongly reflexive
combinatory algebras which are stable. Moreover, there is a canonical
construction of a lambda algebra from a strongly reflexive combinatory algebra.
The resulting axiomatisation of lambda algebras by the seven axioms for strong
reflexivity together with those for stability is shown to correspond to the
axiomatisation of lambda algebras due to Selinger [J.Funct.Programming, 12(6),
549--566, 2002].
