Motion M0052: Note on my revised text of Nov 4th
P1788
I circulated the Nov 4 revised text for Clause 6 in rather a hurry, and forgot to give any explanation.
(1) The main change is that §6.2 has been renamed from "Mapping to a library" to "Function libraries", and its start (2 paragraphs) replaced by a much improved version (1 paragraph) due to Michel Hack.
(2) I also rewrote the last part of §6.1. Previously I had used the weasel words that the three descriptions of an expression (graph, code list, algebraic) are "essentially equivalent". What is "essentially"? Clearly not that there is a lossless transformation from one form to another, e.g., the code list has extra structure not present in the graph, and the algebraic form has different extra structure.
The point -- an important one -- is that they are *computationally equivalent* in the sense that (assuming they use the same function library as in 6.2) they compute the same numbers or intervals in some order, and the same output. This is an idea familiar in numerical analysis: e.g. it is the sense in which LU factorisation is equivalent to Gaussian elimination.
Also familiar is the idea in the next paragraph: "... using the operations exactly as written". The possibility of *not* doing so is one reason why LU wins over Gauss -- writing LU in "compact" (Crout/Doolittle) form lets one use an accumulated dot product instead of individual multiplies and adds, with different (better) numerical behaviour.
I hope the text expresses these ideas with an appropriate amount of detail.
John Pryce