# Alignment of rows in a diagram

For example, in the following diagram I want to allow the rows as in the picture below (i.e, so that m in the bottom row aligns with the top of the fraction it is adjacent to, and so that the top row aligns in the way in the picture)? How can I do this?

\documentclass[11pt]{beamer}
\usepackage{pgfpages,amsmath,amssymb,mathtools,color, graphicx, amsfonts, braket}
\usepackage{subfig}
$\begin{matrix} \begin{pmatrix} \begin{matrix} \begin{array}{c|c} \multicolumn{2}{c}{\Diamond \alpha} \end{array} \\[3ex]\text{exp} \\[1ex] m \end{matrix} \end{pmatrix}^{\uparrow} = \kern15pt& \begin{matrix} \begin{array}{c|c} \multicolumn{2}{c}{\cfrac{\ \Diamond \beta\ }{\ \alpha\ }} \end{array} & & \begin{array}{c|c} \multicolumn{2}{c}{\cfrac{\ \Diamond \beta\ }{\ \alpha\ }} \end{array} \\[3ex] \text{exp} & = & \text{exp}\\[1ex] m^{\uparrow} &\kern15pt& \cfrac{\ \operatorname{m \bigstar \lambda v. [\;]}\ }{\ v\ } \end{matrix} \end{matrix}$