Comments on: “Elements of Programming” Chapter 3 Preview

By: learner

learner — Wed, 21 Jul 2010 21:53:21 +0000

Hi friends…is this thread still alive ? I am interesting a lot !!

By: Sean Parent

Sean Parent — Fri, 30 Apr 2010 23:23:51 +0000

Yes – And I agree that it could be made more clear in the book. Perhaps with stronger wording when the term partial is introduced on page 17 and add an exercise in chapter 3 to relate the definition space of an op to associativity. This could also been done in chapter 2 – much of the code in that chapter is carefully written to stay within the definition space of the operations.

By: Piotr Jachowicz

Piotr Jachowicz — Wed, 28 Apr 2010 06:32:59 +0000

If I get you correctly, you've said that my example is invalid because operator+(INT_MAX, INT_MAX) is not valid expression because arguments are not in definition space?

It is good point, but IMHO it should be explicit stated in the book.

By: Sean Parent

Sean Parent — Tue, 27 Apr 2010 22:51:16 +0000

operator+ on int is a partial function. The book doesn’t track the definition space through all of the operations, instead it assumes we are dealing with partial models and we say that operator+ is associative in those cases where it is defined and push the requirement back as a precondition to operator+. This is called out back on page 17 (and the example of + on int is used) and discussed a bit more on page 70. Early drafts of the book where littered with checks for the definition space, but they add little since we are dealing with partial operations so often. Partiality is only called out explicitly in a few cases. Much of the discussion back in chapter 2 is about carefully managing the precondition that the operands must stay within the definition space of the function.

By: Piotr Jachowicz

Piotr Jachowicz — Tue, 27 Apr 2010 22:01:35 +0000

seems to me not associative on int because there exists a,b,c of type int such that . For example = INT_MAX, = INT_MAX, = INT_MIN

By: Mark Ruzon

Mark Ruzon — Mon, 26 Apr 2010 21:36:13 +0000

That should say “op is associative on integers.” The + sign was munged, sorry.

By: Mark Ruzon

Mark Ruzon — Mon, 26 Apr 2010 21:35:15 +0000

is associative on integers. It is partially associative on char. The definition of associativity in Ch. 3 implicitly refers to abstract entities and not concrete types.

By: Piotr Jachowicz

Piotr Jachowicz — Tue, 20 Apr 2010 06:30:49 +0000

Let us consider concrete example. Let op(a,b) = a + b, Domain(op) = char. Let a = -127, b = 127, c = 127. All a,b and c belong to Domain(op). But op(op(a,b),c) != op(a, op(b,c)) because right side of this equation makes no sense.

Does it mean that op is not an associative operation?

By: Mark Ruzon

Mark Ruzon — Mon, 19 Apr 2010 22:24:51 +0000

I think you mean "It can happen that op(a,b) belongs to the definition space of op, but op(b,c) does not". If op is associative, then by definition op(a,op(b,c)) = op(op(a,b),c).

But to me the point is that a definition space is more of a practical concept necessary in computer science because int != Integer, whereas associativity is a mathematical property on a operation on abstract entities.

By: Piotr Jachowicz

Piotr Jachowicz — Sun, 18 Apr 2010 20:10:43 +0000

Ok, so if all a,b,c belong to Domain(op), then op(a, op(b,c)) and op(op(a,b), c) makes sense in terms that argument types matches Domain(op).

What about definition space? It can happen that (a, op(b,c)) belongs to definitions space of op, but (op(a,b), c) does not.

I don't understand why partially_associative definition cares about definition space, but associative do not? Is there a guarantee that op in associative is total?