Work ䷯

Functional Logic • Inquiry and Analogy • 21

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Umpire Fig 1

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Umpire TeX 1

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HTML + LaTeX

UMP 1

\Upsilon : \bigcup_{\ell = 1, 2, 3} ((\mathbb{B}^k \to \mathbb{B})^\ell \to \mathbb{B})

UMP 2

\begin{matrix} \Upsilon_p^r q = \Upsilon (p, q, r) \\[10pt] \Upsilon_p^r : (\mathbb{B}^k \to \mathbb{B}) \to \mathbb{B} \end{matrix}

UMP 3

\begin{matrix} \Upsilon_p (q) = \Upsilon (p, q) = \Upsilon (p, q, \textstyle\prod) \\[10pt] \Upsilon_p = \Upsilon (p, \underline{~~}, \textstyle\prod) : (\mathbb{B}^k \to \mathbb{B}) \to \mathbb{B} \end{matrix}

UMP 4

\begin{matrix} \Upsilon q = \Upsilon (q) = \Upsilon_1 (q) = \Upsilon (1, q, \textstyle\prod) \\[10pt] \Upsilon = \Upsilon (1, \underline{~~}, \textstyle\prod)) : (\mathbb{B}^k\ \to \mathbb{B}) \to \mathbb{B} \end{matrix}