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N), and if the function to be integrated is given as fct{n,x), where χ is the array ^[1], ^ [ 2 ] , . x [ n ] y then such a program looks as follows: real procedure g{n,fctylbyUb,ordyk) ; value k,n ; integer n^ord, k ; array IbyUb ; real procedure fit ; begin o w n real array ^ [ 1 : w] ; real procedure f{v) ; real ν ; if k=n then begin χ[ή] : = v ; f:=fitM end else begin x[k] : = v ; f' = gin/ctylbyUb,ordyk+l) end ; g: = rombergintegr(filb[k],ub[k],ord) endg However, this construction is rather intricate and its feasibility for publication may be seriously doubted for two reasons.

T h e whole paragraph is equivalent t o ; ' There are two possibilities, b e c a u s e . . I have not thought of any others'. And, alas, this narrowness of outlook is not confined to Thüring: in a book by Prof. E. Billeter, published in 1961, we find t h i s ' Reciprocity L a w ' quoted with full approval. I n 1961 the University Mathematical Laboratory Technical Memorandum No. 61/5, 'Some proposals for improving the efficiency of A L G O L 6 0 ' , was published, written by nobody less than C.

INCREASING I. INTRODUCTION Unfortunately recursive procedures have been advertised by examples such as real procedure fact{n) ; value η ; integer η ; fact: = i f n = 0 t h e n 1 elsenxfact{n—I) ; or real procedure homer 1{α^Η^ζ^η) ; value η,^,Α; ; real ζ ; integer k^n ; array a ; hornerl: = i f t h e n a[n] else{zxhornerl{a,k+l,z,n)+a[k]) True, these examples look quite elegant and may serve to exemplify recursive procedures, but if a computing process can just as well be described by a simple induction loop, then transforming it into a recursive procedure is sheer extravagance and might well discredit the concept of recursivity altogether.

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