Abstract
We study context free closed families of languages, that is families L verifying the equation CF o L = L where CF denotes the family of context free languages and o is the substitution operation. Call a family L a context free AFL if it is both context free closed and a rational cone. The families CF and RE (of recursively enumerable languages) have this property. We show that the class of context free AFL's is properly contained into that of full AFL's. Moreover the context free AFL generated by a family L, is given by the formula L Δ = CF o LΓ where LΓ denotes the rational cone generated by L. Using this result we establish the remarkable inclusion (L o M)Δ ⊃ LΔ o MΔ holding for all families L and M as well as the equality LΔ = CF o LΓ LΓ being the full AFL generated by L.
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