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| ===Step 1=== | | ===Step 1=== |
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− | <pre>
| + | Consider the following problem requirements: |
− | Given a syntactic specification (or paraphrastic definition):
| + | |
| + | One is given a syntactic specification of the following form: |
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− | x = xI
| + | {| align="center" cellpadding="8" width="90%" |
| + | | <math>x = x \operatorname{I}</math> |
| + | |} |
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− | where "x = x..." is the definiens,
| + | In effect, this specification amounts to a so-called ''paraphrastic definition'' of the operator <math>\operatorname{I},</math> one in which the syntactic frame <math>^{\backprime\backprime} x = x \ldots ^{\prime\prime}</math> may be regarded as the defining context, or ''definiens'', and <math>\operatorname{I}</math> is regarded as the object to be defined, or ''definiendum''. |
− | or defining context, and "I" is | |
− | the definiendum, | |
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− | Find a pure interpretant for I, that is, an equivalent term
| + | One is asked to find a ''pure interpretant'' for <math>\operatorname{I},</math> that is, an equivalent term in <math>\langle \operatorname{K}, \operatorname{S} \rangle,</math> the ''combinatory algebra'' generated by <math>\operatorname{K}</math> and <math>\operatorname{S},</math> that does as <math>\operatorname{I}</math> does. |
− | in <<K, S>>, the combinatory algebra generated by K and S, | |
− | that does as I does. | |
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| + | <pre> |
| Observe: | | Observe: |
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