Changes

===Step 1===

===Step 1===

Given a syntactic specification (or paraphrastic definition):

 

One is given a syntactic specification of the following form:

  x = xI

| <math>x = x \operatorname{I}</math>

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,

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.

Observe:

Observe: