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Bound and free variables

An occurrence of v inside E is said to be bound if it occurs in v.E, and is free otherwise.

examples:

v occurs free in v(x y v)
v occurs bound in v.v(x y v)
v occurs both bound and free in v(x (v.y v) y)

We say v is free in E if there is at least one free occurrence of v in E.

fv(x) = {x}
fv(E1 E2) = fv(E1) 1#1 fv(E2)
fv(x.E) = fv(E) - {x}.

E is said to be closed iff fv(E) = {}.
example: z.(x.z x)(y.y z) is closed.

Expressions equal up to renaming are called equivalent.



Alan Bond
1998-10-12