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Curious OCaml

From logic rules to programming constructs

What logical connectives do you know?

$\top$	$\bot$	$\wedge$	$\vee$	$\rightarrow$
		$a \wedge b$	$a \vee b$	$a \rightarrow b$
truth	falsehood	conjunction	disjunction	implication
"trivial"	"impossible"	$a$ and $b$	$a$ or $b$	$a$ gives $b$
	shouldn't get	got both	got at least one	given $a$, we get $b$

How can we define them? Think in terms of derivation trees:

$$ \frac{ \frac{\frac{,}{\text{a premise}} ; \frac{,}{\text{another premise}}}{\frac{,}{\text{some fact}}} ; \frac{\frac{,}{\text{a premise}} ; \frac{,}{\text{another premise}}}{\frac{,}{\text{another fact}}}} {\text{final conclusion}} $$

To define the connectives, we provide rules for using them: for example, a rule $\frac{a ; b}{c}$ matches parts of the tree that have two premises, represented by variables $a$ and $b$, and have any conclusion, represented by variable $c$.

Rules for Logical Connectives

Introduction rules say how to produce a connective. Elimination rules say how to use it. Text in parentheses is comments. Letters are variables: stand for anything.

Try to use only the connective you define in its definition.

TODO