[Haskell-cafe] In what language...?

Richard O'Keefe ok at cs.otago.ac.nz
Tue Oct 26 19:21:45 EDT 2010

On 27/10/2010, at 8:43 AM, Andrew Coppin wrote:

> Already I'm feeling slightly lost. (What does the arrow denote? What's are "the usual logcal connectives"?)

You mentioned Information Science, so there's a good chance you know something
about Visual Basic, where they are called
"connective" in this sense means something like "operator".

>> Predicates are usually interpreted as properties; we might write
>> "P(x)" or "Px" to indicate that object x has the property P.
> Right. So a proposition is a statement which may or may not be true, while a predicate is some property that an object may or may not possess?

A predicate is simply any function returning truth values.
> is a (binary) predicate. (> 0) is a (unary) predicate.

> Right... so its domain is simply *everything* that is discrete? From graph theory to cellular automina to finite fields to difference equations to number theory?

Here's the table of contents of a typical 1st year discrete mathematics book,
selected and edited:
	- algorithms on integers
	- sets
	- functions
	- relations
	- sequences
	- propositional logic
	- predicate calculus
	- proof
	- induction and well-ordering
	- recursion
	- analysis of algorithms
	- graphs
	- trees
	- spanning trees
	- combinatorics
	- binomial and multinomial theorem
	- groups
	- posets and lattices
	- Boolean algebras
	- finite fields
	- natural deduction
	- correctness of algorithms

Graph theory is in.  Cellular automata could be but usually aren't.
Difference equations are out.  Number theory would probably be out
except maybe in a 2nd or 3rd year course leading to cryptography.


> That would seem to cover approximately 50% of all of mathematics. (The other 50% being the continuous mathematics, presumably...)
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