HsSymMath
=========

Interactive mathematical languages written in haskell

## Logic.hs ##

Formal logic parser 

### Command line ###

Currently the command line will take a logical expression as an argument and print out its corresponding truth table.

```
$ ./Logic
Enter Command
> TruthTable: a&b+c->~a&b
'a'   'b'   'c'   | (((a&b)+c)->(~a&b))
True  True  True  | False
True  True  False | False
True  False True  | False
True  False False | True 
False True  True  | True 
False True  False | True 
False False True  | False
False False False | True 

Enter Command
> ToNand: a&b->c 
(((((a|b)|(a|b))|((a|b)|(a|b)))|(((a|b)|(a|b))|((a|b)|(a|b))))|(c|c))

Enter Command
> ToNor: a&b->c
(((((a/a)/(b/b))/((a/a)/(b/b)))/c)/((((a/a)/(b/b))/((a/a)/(b/b)))/c))
```

### Code ###

```haskell
> And (Atom 'a') (Not (Atom 'b'))
(a&~b)

> truthTable $ And (Atom 'a') (Not (Atom 'b'))
'a'   'b'   | (a&~b)
True  True  | False
True  False | True 
False True  | False
False False | False

> toNand $ And (Atom 'a') (Not (Atom 'b'))
((a|(b|b))|(a|(b|b)))

> toNor $ And (Atom 'a') (Not (Atom 'b'))
((a/a)/((b/b)/(b/b)))

> let exp = And (Atom 'a') (Not (Atom 'b'))
> exp == toNand exp
True
> exp == toNor exp
True
> exp == toNor (toNand exp)
True
```