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, 14:54, 24 March 2009
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| We are asked to find an explication of <math>\operatorname{P}</math> in terms of primitive combinators. | | We are asked to find an explication of <math>\operatorname{P}</math> in terms of primitive combinators. |
| | | |
− | <pre>
| |
| Proceed as follows: | | Proceed as follows: |
| | | |
− | (xy)z = (xy)(x(zK)) = x(y((zK)S))
| + | {| align="center" cellpadding="8" width="90%" |
− | | + | | |
− | (zK)S = (zK)(z(SK)) = z(K((SK)S))
| + | <math>\begin{array}{ccccc} |
− | | + | (xy)z |
− | =>
| + | & = & |
− | | + | (xy)(x(z\operatorname{K})) |
− | x(y(zP)) = (xy)z = x(y(z(K((SK)S))))
| + | & = & |
− | | + | x(y((z\operatorname{K})\operatorname{S})) |
− | =>
| + | \\[8pt] |
− | | + | (z\operatorname{K})\operatorname{S} |
− | P = (K((SK)S))
| + | & = & |
− | </pre> | + | (z\operatorname{K})(z(\operatorname{S}\operatorname{K})) |
| + | & = & |
| + | z(\operatorname{K}((\operatorname{S}\operatorname{K})\operatorname{S})) |
| + | \\[6pt] |
| + | & & \Downarrow |
| + | \\[8pt] |
| + | x(y(z\operatorname{P})) |
| + | & = & |
| + | (xy)z |
| + | & = & |
| + | x(y(z(\operatorname{K}((\operatorname{S}\operatorname{K})\operatorname{S})))) |
| + | \\[8pt] |
| + | & & \Downarrow |
| + | \\[8pt] |
| + | \operatorname{P} |
| + | & = & |
| + | (\operatorname{K}((\operatorname{S}\operatorname{K})\operatorname{S})) |
| + | \end{array}</math> |
| + | |} |
| | | |
| ===Step 2=== | | ===Step 2=== |