Primitive recursive function: Difference between revisions

Revision as of 11:30, 20 May 2004

Revision as of 12:23, 30 May 2004

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:In order to fit this into a strict primitive recursive definition, we define:

::add(0,''x'')=''P''₀₁¹(''x'')

::add(S(''n''),''x'')=''S''(''P''₀₁³(add(''n'',''x''),''n'',''x''))

:Note that ''P''₀¹ is simply the [[identity function]]; its inclusion is required by the definition of the primitive recursion operator above; it plays the role of ''h''. The composition of ''S'' and ''P''₀³, which is primitive recursive, plays the role of ''g''.