Tom, Reflecting a bit more, there are other places in mathematics where similar ideas arise. Consider a series like:
1 + 1/2 + 1/4 + 1/8 + ... mathematicians will often wish to treat these infinite sums as if they were lists. One thing to do with a list is to *pop* the head from the list and return just the tail. Multiplying the list by 1/2 does exactly this: 1/2 (1 + 1/2 + 1/4 + 1/8 + ...) 1/2 + 1/4 + 1/8 + ... Now I have *just* the same list but without the head. Manipulations like this one are more-or-less part of the machinery for working with a series. Another classic example are the pair of functions *div* and *mod.* The first of these acts like division but only gives back the integer part (quotient), thus div 4 25 is 6. *mod* on the other hand is a function which returns the remainder, 1 here. Now given a number like 273427893045 in base 10, we can use *mod 10* to pop the 5 off the end of the number as-if-it-were a list and div 10 to return the rest of the number as-if-it-were a list. Examples like these are ubiquitous in mathematics and are in part what makes the whole project seem like black magic or index twiddling. Really, they are perhaps just conveniences that arise via analogies between one domain of mathematics and another. The Iverson bracket is similarly one such device, connecting logic (Bool) to number (Int). Jon
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