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Denotational Semantics: A Methodology for Language Development

Denotational Semantics: A Methodology for Language Development. David Schmidt, Kansas State University.

I don't recall seeing this book mentioned on LtU before. The entire book is online and seems quite detailed and understandable. Each chapter ends with exercises for the reader and suggested readings.

Thanks, Henry!

By Ehud Lamm at 2004-11-26 21:25 | Semantics | other blogs | 8098 reads

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Is "error" a natural number?

The ease with which the author extends rational numbers with "bottom" (Chapter 2) and natural numbers with "error" (Chapter 3) makes me a bit uneasy...

I understand that it makes arities shorter (as domain already contains a special value, there is no need to lift it), but somehow I don't feel this justifies calling "error" a natural number.

I intend to finish the paper nevertheless, as it looks quite interesting (I was ever curious what kind of beasts domains are).

PS: the underlined lambda (2.3) looks remarkably like Maybe monad's bind...

By Andris Birkmanis at Sun, 2004-11-28 20:13 | login or register to post comments

Another way to look at it

The ease with which the author extends rational numbers with "bottom" (Chapter 2) and natural numbers with "error" (Chapter 3) makes me a bit uneasy...

If it makes you more comfortable, think of them as different mathematical structures that have all of the order structure of the naturals ( or positive rationals ) with an added element that is by definition less than all the other elements.

It would probably be better, though, to get over the idea that the naturals or rationals are special in some way: they are "just" mathematical structures with certain very useful properties. ;-)

By Marc Hamann at Sun, 2004-11-28 20:56 | login or register to post comments