2 posts from November 2008

1. Notion of representation 2. Notion of encoding 3. Requirements to glyphs: equality, recognisability, one might always realise where one ends and another begins 4. Deductive apparatus, mathematical theories 5. Interpretations of mathematical theories, constants 6. Variables, historic excursion into prop calc, difference between variables and constants; quantors; variable substitution and its pitfalls 7. Soundness, completeness, consistency 8. Proof theory 9. Model theory 10. What is Existence 11. What is Truth 12. Art of proof (12 lessons, first two or three are short and may be conducted together)

/* Stop >>= \a -> >>= \b insane! */

instance + (m a) | + a & Monad m
where
 (+) ma mb = ma >>= \a -> mb >>= \b -> return $! a + b

instance - (m a) | - a & Monad m
where
 (-) ma mb = ma >>= \a -> mb >>= \b -> return $! a - b

instance * (m a) | * a & Monad m
where
 (*) ma mb = ma >>= \a -> mb >>= \b -> return $! a * b

instance / (m a) | / a & Monad m
where
 (/) ma mb = ma >>= \a -> mb >>= \b -> return $! a / b

instance mod (m a) | mod a & Monad m
where
 (mod) ma mb = ma >>= \a -> mb >>= \b -> return $! a mod b

instance rem (m a) | rem a & Monad m
where
 (rem) ma mb = ma >>= \a -> mb >>= \b -> return $! a rem b

/* http://hpaste.org/10673 */