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    • last data update: 2011/10/15, 18:36

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    title: Existential Type

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    Website code analysis

    one word phrases repeated minimum three times

    two word phrases repeated minimum three times

    three word phrases repeated minimum three times

    B tags

    U tags

    I tags

    images

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    latex.php?latex=x%3AA.B&bg=ffffff&fg=333333&s=0\displaystyle{{\Gamma\vdash \beta:N\simeq P:A\quad \Gamma\vdash \alpha:M\simeq N:A}\over{\Gamma\vdash\beta\circ\alpha:M\simeq P:A}}
    latex.php?latex=%5Cdisplaystyle%7B%5CGamma%5Cvdash+%5Ctextit%7Bid%7D%3A%3AM%5Csimeq+M%3AA%7D&bg=ffffff&fg=333333&s=0\gamma\circ(\beta\circ\alpha)\equiv (\gamma\circ\beta)\circ\alpha::M\simeq N:A
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    latex.php?latex=%5Cdisplaystyle+%5CGamma%5Cvdash+A%5Cequiv+B&bg=ffffff&fg=333333&s=01\leq i\leq n
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    latex.php?latex=x_1%3AA_1%2C%5Cdots%2Cx_%7Bi-1%7D%3AA_%7Bi-1%7D%5Cvdash+A_i%5C%2C%5Cmathsf%7Btype%7D&bg=ffffff&fg=333333&s=0\textit{Nat}
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    latex.php?latex=%5Cvdash+n%3A%5Ctextit%7BNat%7D&bg=ffffff&fg=333333&s=0\displaystyle \vdash \textit{Set}\,\textsf{type}
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    latex.php?latex=%5Cdisplaystyle+%5Cvdash+%5Ctextit%7BSet%7D%5C%2C%5Ctextsf%7Btype%7D&bg=ffffff&fg=333333&s=0\displaystyle \vdash \textit{Elt}(\textit{nat})\equiv\textit{Nat}
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    latex.php?latex=%5Ctextit%7BElt%7D&bg=ffffff&fg=333333&s=0\textit{Elt}(\textit{nat}\times\textit{nat})
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    latex.php?latex=%5Ctextit%7BElt%7D%28%5Ctextit%7Bnat%7D%5Ctimes%5Ctextit%7Bnat%7D%29&bg=ffffff&fg=333333&s=0\displaystyle \Gamma\vdash \alpha :: M\simeq N : A
    latex.php?latex=%5Ctextit%7BElt%7D%28%5Ctextit%7B2%7D%5Cto%5Ctextit%7Bnat%7D%29&bg=ffffff&fg=333333&s=0\displaystyle{{\Gamma,x:A\vdash B\,\textsf{type}\quad \Gamma\vdash \alpha :: M\simeq N:A \quad \Gamma\vdash P:B[M/x]}\over {\Gamma\vdash \textit{map}\{x:A.B\}[\alpha](P):B[N/x]}}.
    latex.php?latex=%5Ctextit%7B2%7D&bg=ffffff&fg=333333&s=0\displaystyle{ {\begin{array}{c} \Gamma,x:\textit{Elt}(a)\vdash f(x):\textit{Elt}(b) \\ \Gamma,x:\textit{Elt}(b)\vdash g(x):\textit{Elt}(a) \\ \Gamma,x:\textit{Elt}(a)\vdash g(f(x))\equiv x:\textit{Elt}(a) \\ \Gamma,x:\textit{Elt}(b)\vdash f(g(x))\equiv x:\textit{Elt}(b) \end{array}} \over {\Gamma\vdash\textit{iso}(f,g)::a\simeq b:\textit{Set}}}
    latex.php?latex=%5Cdisplaystyle+%5CGamma%5Cvdash+%5Calpha+%3A%3A+M%5Csimeq+N+%3A+A&bg=ffffff&fg=333333&s=0\displaystyle{ {\Gamma\vdash M:\textit{Elt}(a)}\over {\Gamma\vdash \textit{map}\{\textit{Elt}\}[\textit{iso}(f,g)](M)\equiv f(M) : \textit{Elt}(b)}}
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    latex.php?latex=g&bg=ffffff&fg=333333&s=0\textit{map}\{x:A.B\}
    latex.php?latex=a&bg=ffffff&fg=333333&s=0\displaystyle{{\Gamma\vdash M : A \qquad \Gamma,x:A \vdash N:B}\over{\Gamma\vdash [M/x]N:B}}
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