On Sat, Dec 24, 2011 at 2:31 AM, Albert Y. C. Lai <trebla@vex.net> wrote:
> 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

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