<blockquote style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;" class="gmail_quote">... so I
don't think it makes sense to consider (>) a part of Bool's semantics, no?</blockquote><div><br>A denotational semantic definition for a type (more traditionally, a syntactic category) have two parts: a semantic domain and a collection of *compositional* definitions for the building blocks of that type. ("Compositional" in that a construct is defined strictly in terms of the meanings of its components.) I think you're talking about the latter, while my complexity claim is about the former: What semantic model can we have for Bool, i.e. what is [[Bool]]? The model I'd like in a lazy functional language is the domain containing exactly three elements: true, false, and bottom (with the usual information ordering).<br>
<br>Whatever the domain corresponding to Bool is, the denotation of every (well-formed) Bool expression is an element of that domain.<br><br>The question I'm asking is this: Assuming compositional semantics, can [[Bool]] be this simple & customary three-value domain in the presence of an implementation-dependent [[Int]] (given that Int expressions can play a non-trivial role in Bool expressions)?<br>
<br>(Now you might say that Bool is just a data type definition. If so, then rephrase the question in terms of simple data type definitions.)<br><br> - Conal<br></div><br><div class="gmail_quote">On Mon, Mar 23, 2009 at 7:54 AM, Jake McArthur <span dir="ltr"><<a href="mailto:jake@pikewerks.com">jake@pikewerks.com</a>></span> wrote:<br>
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Conal Elliott wrote:<br>
| Consider<br>
| big :: Int<br>
| big = 2147483647<br>
| dodgy :: Bool<br>
| dodgy = big + 1 > big<br>
| oops :: ()<br>
| oops = if dodgy then () else undefined<br>
|<br>
| Assuming compositional semantics, the meaning of oops depends on the<br>
| meaning of dodgy, which depends on the meaning of big+1, which is<br>
| implementation-dependent. So a semantic domain for Bool and even ()<br>
| would have to include the machine-dependence of Int, so that oops could<br>
| mean a function from MachineInfo that returns () sometimes and bottom<br>
| sometimes. If the denotations (semantic domains) for Bool and () didn't<br>
| include this complexity, they wouldn't be rich enough to capture the<br>
| machine-dependence of dodgy and oops.<br>
<br></div>
Since Bool's constructors are exported, we can define (>) anywhere, so I<br>
don't think it makes sense to consider (>) a part of Bool's semantics, no?<br>
<br>
- - Jake McArthur<br>
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