On 11-01-17 01:55 PM, David Sankel wrote:

I've recently had the opportunity to explain in prose what denotational semantics are to a person unfamiliar with it. I was trying to get across the concept of distilling the essence out of some problem domain. I wasn't able to get the idea across so I'm looking for some simple ways to explain it.

Does anyone know of a way to explain what's the meaning and objective of "distilling the essence" without introducing more jargon. One thing that comes to mind is how Newton's equations for gravity were a distillation of the essence of the way things fall.

(I'm afraid Newton's equations introduced more jargon too.) A denotational semantics maps programs to math things. The mapping has to be by structural recursion over program syntax. Why math: it's the universal modelling language. Why do we model programs by a math model: to explain and predict. Why structural recursion over syntax: to be compositional, the same reason we stay close to CFGs for syntax: you can build bottom-up and analyze top-down. It also happens that the math things are given a partial order to help answer "what to do with loop constructs and/or cyclic definitions". A moment of trying to re-invent denotational semantics reveals that this is the only hard part, and so learning denotational semantics typically takes 90% of the time on this part.

On Mon, Jan 17, 2011 at 12:55 PM, David Sankel wrote:

Hello All,

I've recently had the opportunity to explain in prose what denotational semantics are to a person unfamiliar with it. I was trying to get across the concept of distilling the essence out of some problem domain. I wasn't able to get the idea across so I'm looking for some simple ways to explain it.

Does anyone know of a way to explain what's the meaning and objective of "distilling the essence" without introducing more jargon. One thing that comes to mind is how Newton's equations for gravity were a distillation of the essence of the way things fall.

A stick figure as an iconic image of a person serves as a symbol of "person"; i.e. it denotes person. It works because of the parts and their arrangement. Ditto for mathematical expressions: the whole is equal to the sum of its parts (and the way they are arranged.) The individual parts (e.g. the symbol '3') are not iconic, but the way the whole system works corresponds exactly with the way we imagine mathematical objects work. Google around for "correspondence theory of truth" and you might find some useful material. It might be useful to introduce Platonism (see wikipedia.) Also try boiling it down to compositionality, substitutability, and equality. It might also help to draw a contrast with what is not denotational. Denotational semantics depends essentially on the fiction of univocality, namely that every symbol has one delimited meaning: it means what it means, and nothing else. But in fact univocality is not possible even in theory; you cannot circumscribe the the proliferation of meanings. A simple example: 2+3 denotes (the same thing as) 5; it may also be taken to denote a computation that yields 5. But it does not denote the energy consumed in carrying out that computation. A horribly inefficient algorithm may have the same denotation as a very efficient one. Another way of putting it is that denotation is about extensionality to the exclusion of intensional meanings. Going beyond extensionality is where Category Theory enters the picture. HTH -Gregg Reynolds