Recursion may be parametric in another sense, namely that the argument is used in the evaluation phase. This issue itself divides into two parts, depending on whether the argument is used in parsed or unparsed form. Again, formulate and prove the parametric General Recursion Theorem directly without using cartesian closure. A unary recursion problem is one which makes at most one recursive call at each level, but where the argument may be used again after the return from the nested call. Suppose that this factors through another monoid M , which is called an accumulator .
General recursion extends primitive recursion by use of the search or minimalisation operator m .
Express the unification algorithm in the style of Sections 6.3 - 6. 4 . Show that the unifier is the quotient by the parsing congruence, and that the congruence is the kernel of the unifier, cf Section 5.6 . Allow infinitely many equations, and infinite arities. Investigate the non-determinacy in the unification algorithm. By considering the orders of elements of its Sylow subgroups, show that there is no simple group of order 105.