## <-> beta-reduction \leftrightarrow^{*}_{\beta} \leftrightarrow \beta

### Seeing It as a Relationship: <-> beta-reduction

on January 29, 2010 - 2:36pm

Last week I got a question that asks me to show that the following statement about Y combinator (http://en.wikipedia.org/wiki/Fixed_point_combinator#Y_combinator) in LaTeX is correct:

Y z \leftrightarrow^{*}_{\beta} z (Y z)

where \leftrightarrow{\beta} = \rightarrow{\beta} \bigcup \leftarrow{\beta}