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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''.

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 \underline{~~~} \, ^{\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''.

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.

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.