No exceptions?

This little puzzle is prompted by my distaste for exceptions. In a language such as TTM Algebra, I wonder if they can be avoided in theory.   By 'avoided' I mean in the sense of avoiding direct language support for them - an implementation might prefer to give ways to detect them outside of specific language syntax. (Whether one wants to avoid exceptions is a different question than whether one can avoid them.) To put it another way, once we have whatever superstructure is needed to give us domains and relations, can operational results be

1. Syntax exceptions - An expression "x join y" might be a valid syntax but one such as "x y" might not. An implementation could stipulate that the reason it's not is because it is not an element of the domain for expressions in the chosen language given a particular syntax. If we have a way to test membership of such a domain, the syntax error could be indicated by the value "false" given by a boolean function. (One such way might be for all statements in a language to be treated as propositions of a relation that describes some program unit.)
2. Semantic exceptions - "x join y" might be valid syntax but "x" might be undefined, eg., there is no relation named "x".

However, the interpretation of a language could be defined such that the mention of "x" without any collateral description stands for a relation with no attributes. According to Hugh Darwen, there are (only) two such relations, aka DEE and DUM and each must have a value (since each is a relation). Although their values are hard to write down, he does say (eg., at http://www.dbdebunk.com/page/page/1043196.htm) that DEE has one tuple.

Within the TTM logical framework (and others), the Closed World Assumption is a convention that says an unmentioned fact is false, ie., if the extension of a relation has no tuples, there are no propositions that satisfy that relation's predicate. This seems to me to provide a way around the non-determinism of "x join y" in isolation. Is it reasonable for a language (again, in theory) to interpret the lack of an extension for "x" as standing for DUM?

There could be operational exceptions such as "out of memory" but before   examining them, I'd appreciate comments on the above, especially as to whether I'm not applying the CWA correctly.

p Received on Thu Jun 29 2006 - 11:56:58 CDT