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# Exercise 12 - Chapter 4

edited June 2018

We can express $$\Phi$$ as a matrix where the $$(m, n)^{th}$$ entry is the value of $$\Phi(m, n) \in \mathbb{B}$$ . Fill out the $$\textbf{Bool}$$-matrix:

$$\begin{array}{c | c c c c c} \Phi & a & b & c & d & e \\ \hline N & ? & ? & ? & ? & true \\ E & true & ? & ? & ? & ? \\ W & ? & ? & ? & false & ? \\ S & ? & ? & ? & ? & ? \end{array}$$ We’ll call this the feasibility matrix of $$\Phi$$.

$$\textbf{Bool}\text{-profunctor } \Phi : X \nrightarrow Y$$

$$\begin{array}{c | c c c c c} \Phi & a & b & c & d & e \\ \hline N & true & false & true & false & true \\ E & true & true & true & true & true \\ W & true & false & true & false & true \\ S & true & true & true & true & true \end{array}$$
Comment Source:$\begin{array}{c | c c c c c} \Phi & a & b & c & d & e \\\\ \hline N & true & false & true & false & true \\\\ E & true & true & true & true & true \\\\ W & true & false & true & false & true \\\\ S & true & true & true & true & true \end{array}$