A question on function reduction, abstract syntax, and involving lambda calculus, I don't know where to begin:

Recalling the abstract syntax, AS P epsilon Program C epsilon Command E epsilon Expression B epsilon Boolean - Expression I epsilon Identifier N epsilon N P_::= main(argc, argv) {C} C_::=C1,C2| if B{C} | while(B) {C} | I=E | diverge E_:: = I | N| E1+E2 B_::,= E1= =E2| !B And the semantic algebra SA, Truth Values, Domain: t epsilon Bool = B Operations, true, false, Bool; not, Bool rightarrow Bool Natural Numbers Domain, t epsilon Nat = N Operations, zero, one,...,Nat Equals, Nat x Nat Plus, Nat x Nat rightarrow Nat Identifiers Domain, i epsilon Id = Identifier Store Domain, s epsilon Store = (Id rightarrow Nat Operations,... And the Valuation Function V, weierp: Program rightarrow Nat rightarrow Nat bottom lambda n.lets = (update[[arg c]n newstore]) in let s_1 = C[[C]]s in (access[[x]])s_1 C: Command rightarrow Store rightarrow Store bottom c[[C_1;C_2]s = lambda s.c[[E_2]]s(c[[E_1]s C[[ifB{C}] = lambda s. if B [[B]] s rightarrow (c[[C]] s)s C[[while (B){C}] = (C [[divergene]]) C [[diverge]] = lambdas. epsilon: Expression rightarrow Store rightarrow Nat bottom E [[E_1 + E_2] = lambda s. E [[E_2]] s plus E [[E_2]] s E[[I]] = lambda s. access [[I]] s E[[N]]= lambda s.N'[[N]] B: Boolean - Expression rightarrow Store rightarrow Bool bottom B [[E_1 + E_2]] = lambda s. E [[E_1] s equal E [[E_2]] s B [[!E]] = lambda s.not E[[E]] s N: Numeral Nat rightarrow Nat bottom N [[N]] = natural number for N add a less than relational operator to this syntax using the semantic algebra Add the changes necessary to support the less than operator '