When I study the Bohm tree defined in The Lambda Calculus: Its Syntax and Semantics, H.P. Barendregt, Elseviser,$\cap\Phi$ or $\cup_i(M_i)$ always occurs. But I'm confused about the union and the intersection operation of Bohm trees. For example, $A=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, x>\}$ and $B=\{<<>, \lambda x.x>, <<0>, x>, <<1>, x>, <<0,0>, x>\}$; $A=\{<<>, \lambda xy.x>, <<0>, \bot>, <<1>, x>\}$ and $B=\{<<>, \lambda x.x>, <<0>, y>, <<1>, \bot>\}$; $A=\{<<>, \lambda xy.x>, <<0>, \bot>, <<1>, x>\}$ and $B=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, y>\}$; $A=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, \bot>\}$ and $B=\{<<>, \lambda x.x>, <<0>, \bot>, <<1>, \bot>, <<2>, \bot>\}$. What's the results after doing union or intersection $A$ and $B$?
Asked
Active
Viewed 54 times
1
-
I think the union or intersection operation only works on the case when two trees are consistent. So operation on the last two cases is meaningless. – Lily Oct 22 '14 at 02:22