Logic interpreter.

WeberLogic

Logic interpreter and parsing library

Install

cabal update
cabal install WeberLogic

Interpreter

$ ./WeberLogic
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))

Library

The library contains two modules.

1. WeberLogic.Parser
2. WeberLogic.Actions

WeberLogic.Parser

The WeberLogic.Parser provides functions which read stings and return an abstract syntax tree (AST). The AST in implement with a data type called LogicExp and Letter.

• Data Types

  • LogicExp - A recursively defined data type which implements as abstract syntax tree. It provides the following type constructors which function as nodes in the AST: Not, And, Or, Implies, Iff, Nand, and Nor. The Predicate type constructor functions as the AST leaves.

  > import WeberLogic.Parser
  > Predicate 'A' [(Variable 'x', Name 'a')]
  > Not (Predicate 'A' [(Variable 'x', Name 'a')])
  > And (Predicate 'A' [(Variable 'x', Name 'a')]) (Predicate 'B' [])
  

  • Letter - This Data Constructor provies two Type constructors Variable and Name. They are used in the construction of Predicate which requires a list of type Letter

  > import WeberLogic.Parser
  > Predicate 'A' [(Variable 'x', Name 'a')]
  

• Functions

  • parseExp

  > import WeberLogic.Parser
  > a = parseExp "Axa"
  > b = parseExp "~Axa"
  > c = parseExp "Axa&B"
  

  • parseArg

  > import WeberLogic.Parser
  > a = parseExp "|- Axa"
  > b = parseExp "~Axa, B |- Cax"
  > c = parseExp "Axa&B, B, C |- Ax->By"
  

WeberLogic.Actions

The WeberLogic.Actions modules provides functions which manipulate the LogicExp AST.

> import WeberLogic.Parser
> import WeberLogic.Actions

> mapM_ putStrLn $ truthTableStr $ readExp "A&B"
'a'   'b'   | (a&~b)
True  True  | False
True  False | True 
False True  | False
False False | False

> toNand $ readExp "A&~B" 
((a|(b|b))|(a|(b|b)))

> toNor $ readExp "A&~B" 
((a/a)/((b/b)/(b/b)))