Changes

===Step 1===

===Step 1===

Find a "pure interpretant" for T, that is, an equivalent term

 

doing the job of T which is constructed purely in terms of the

Find a ''pure interpretant'' for <math>\operatorname{T},</math> that is, an equivalent term doing the job of <math>\operatorname{T}</math> which is constructed purely in terms of the

primitive combinators K and S.

primitive combinators <math>\operatorname{K}</math> and <math>\operatorname{S}.</math>

This will constitute an operational algorithm for T, though

Doing this yields an operational algorithm for <math>\operatorname{T},</math> understood as a sequence of manipulations on formal identifiers, or on symbols taken as objects in their own rights.

still operating at the level of abstract syntax, understood

as a sequence of manipulations on formal identifiers, or on

symbols taken as objects in themselves.

  x(y(zT)) = y(xz)

| <math>\begin{matrix}x(y(z\operatorname{T})) & = & y(xz)\end{matrix}</math>

Observe that y(xz) matches (xy)(xz) on the right,

Observe that y(xz) matches (xy)(xz) on the right,

and that we can express y as x(yK), consequently:

and that we can express y as x(yK), consequently: