There is basically one computational operation, called beta-reduction.
(v.E1) E2
->
E1 [E2/v]
This means that the left hand expression is reduced to the right hand expression, which is E1 with E2 substituted for all free occurrences of v in E1.
example:
(v.v c) (
x.x a)
=
((v.(v c)) (
x.(x a)))
->
(v c)[x.(x a)/v]
= (x.(x a) c)
-> (x a)[c/x]
= (c a)
We can define
->* to be the transitive closure of
->