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November 4, 2012 16:17
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Lambda Calculus in LaTeX
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| \begin{eqnarray*} | |
| && (\lambda xyz.xyz)(\lambda x.xx)(\lambda x.x)x \\ | |
| & \to_\beta & (\lambda yz.xyz)[x := \lambda x.xx](\lambda x.x)x \\ | |
| & \equiv & (\lambda yz.(\lambda x.xx)yz)(\lambda x.x)x \\ | |
| & \to_\beta & (\lambda yz.(xx)[ x := y]z)(\lambda x.x)x \\ | |
| & \equiv & (\lambda yz.yyz)(\lambda x.x)x \\ | |
| & \to_\beta & (\lambda z.yy)[ y := \lambda x.x ]x \\ | |
| & \equiv & (\lambda z.(\lambda x.x)(\lambda x.x)z)x \\ | |
| & \to_\beta & (\lambda z.x[x := \lambda x.x]z)x \\ | |
| & \equiv & (\lambda z.(\lambda x.x)z)x \\ | |
| & \to_\beta & (\lambda z.x[x := z])x \\ | |
| & \equiv & (\lambda z.z)x \\ | |
| & \to_\beta & z[z := x] \\ | |
| & \equiv & x | |
| \end{eqnarray*} |
Since the original image is down:
pdfTeX 3.14159265-2.6-1.40.16 (TeX Live 2015)
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Priduces:
Taken with scrot in evince.