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Everybody says that Valuation is a truth value assignment to all variables in the formula.

  1. How do you call the valuation when some (neither single yet nor all) variables are assigned a value?

  2. Truth value implies that variables are binary. How do you call the multivalued case?

  3. I know that Haskel uses the term "partial application". If "partial application" is supplied with optimization, they call it "partial evaluation". I am not sure whether boolean valuation falls into the application or evaluation or second category?

ps, Dec 2013

  1. Is it right that single variable assignment is called Restrict operation? I read Restrict(Function F, variable v, constant k) is defined as "Shannon cofactor of $F$ w.r.t. $v=k$" in Berkly lectures.
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  • $\begingroup$ "Truth value" does not imply that variables are binary. It implies that variables take on truth values. Whether there are ust two truth values is then determined by presence of excluded middle. $\endgroup$ – Andrej Bauer Jan 16 '14 at 7:36
  • $\begingroup$ I am asking how do you call f(4). $\endgroup$ – Val Jan 16 '14 at 8:54
  • $\begingroup$ An application (of $f$ to $4$). The result of $f(4)$ is a value. $\endgroup$ – Andrej Bauer Jan 16 '14 at 9:11
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Here's what I'd use:

  1. partial valuation

  2. value

  3. "partial evaluation" means something different; for instance, if you have the expression (3+x)*y and you learn that x=5, transforming it to 8*y would be an instance of partial evaluation. Partial evaluation is a technique; it is not a special kind of a valuation.

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  • $\begingroup$ How partial evaluation is different? Is it because not all arguments are assigned or because values are not limited to binary? $\endgroup$ – Val Oct 15 '13 at 16:43
  • $\begingroup$ @Val, see revised answer. $\endgroup$ – D.W. Oct 15 '13 at 16:55
  • $\begingroup$ Do you mean that evaluation necessarily implies constant propagation whereas valuation is strictly not? Does partial application refer to partial evaluation, partial valuation, special case of those or something absolutely different? By case in second point I asked how is assignment of some, may be all, but not necessary all non-binary variables is called. $\endgroup$ – Val Oct 15 '13 at 17:17
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    $\begingroup$ @Val, this site isn't great for back-and-forths and lots of discussion; it is meant for getting an answer to a single, well-scoped question. To make sure that answers to your question are useful to you, it's important to do some research on your own so you know what question to ask. At this point, I recommend that you go spend some time reading about partial evaluation, specialization, and related topics... then if you still have a confusion, come back and ask a separate, focused question based upon what you've learned and what you want to know. $\endgroup$ – D.W. Oct 15 '13 at 17:23
  • $\begingroup$ I asked not just how the general values are called (the values) but rather how the valuation of general values is called and I do not think that asking you to clarify the meaning of your words can be a loss of focus. Your reaction tells that you should not be answering in the first place. It is actually my question: why nobody can circumscribe what the actual meaning of valuation? $\endgroup$ – Val Apr 19 '14 at 21:38

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