On Dec 29, 2007 11:14 AM, Cristian Baboi
In The Implementation of Functional Programming Languages by S.P. Jones, section 2.5.3, page 32 it is written:
Eval [[*]] a b = a x b Eval [[*]] _|_ b = _|_ Eval [[*]] a _|_ = _|_
but in section 2.5.2 it is said that _|_ is an element of the value domain. What business does it have on the left side of the '=' ?
I don't know the book you're talking about, but I suspect that this is not a definition of a function in a language, but rather the denotational semantics for a function. Just as mathematics is allowed to categorize all turing machines into two categories (those that halt and those that do not), even though to actually do this is impossible, so too can mathematics talk about what a function returns when given _|_, even though it is impossible in general to know when you actually do have _|_ or you're just waiting for a value. However, if you saw something like this: Eval [[*]] a b = a x b Eval [[*]] _|_ b = b Eval [[*]] a _|_ = a Then you would have cause for alarm, since this is not a monotone function (am I using that term correctly?). Luke