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Exercise 12 - Chapter 4
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 \(\Phi\).
$$ \textbf{Bool}\text{-profunctor } \Phi : X \nrightarrow Y $$
Comments
$$ \begin{array}{c | c c c c c} \Phi & a & b & c & d & e \\ \hline N & true & false & true & false & true \\ E & true & true & true & true & true \\ W & true & false & true & false & true \\ S & true & true & true & true & true \end{array} $$
\[ \begin{array}{c | c c c c c} \Phi & a & b & c & d & e \\\\ \hline N & true & false & true & false & true \\\\ E & true & true & true & true & true \\\\ W & true & false & true & false & true \\\\ S & true & true & true & true & true \end{array} \]