On Sat, Dec 24, 2011 at 2:31 AM, Albert Y. C. Lai
1. a function f is strict if f ⊥ = ⊥ 2. ⊥ represents any computation which does not terminate, i.e. an exception or an infinite loop 3. "strict" describes the denotational semantics
All three of these statements are true. The only potentially controversial one is 2, but any term that the operational semantics would identify as simple non-termination (which is invariably what they're talking about when they say 2; not some partially defined term) will be given denotation ⊥.
B. Actually there are more, but apparently two is already enough to cause all kinds of incoherent statements. If I draw your attention to algebraic semantics, will you start saying "it is too lazy, need to make it more idempotent"?
Yes, there are more than two. And they don't exist in completely separate vacuums from one another. Denotational and operational properties are sometimes (often?) correlated. And algebraic semantics is often the sweet spot for reasoning about the structure of the operational or denotational semantics of your code, without bringing in all the irrelevant details from the latter two. I can make a denotational semantics for System F where each term is denoted by its normal form (an operational concept). I think it's good to be clear on all these specifics, and people could do with a better recognition of the difference between (non-)strict and (lazy)eager (hint: you can have an eager, non-strict language). But it isn't necessarily a problem that people speak in terms of more than one at once. The different kinds of semantics aren't in conflict with one another. The main problem would be that such casual mixing prevents newcomers from learning the distinctions by osmosis. -- Dan