/**
 * A transformation from boolean expressions to the
 * lambda calculus.
 * 
 * @author Jacob Andersen
 */

let
  lambda = "lambda.l"
in let
  logic = "logic.l"
in let
  extendedLogic =
    {
      Exp.not   :  "!" Exp ;
      Exp.or    :  Exp "|" Exp ;
      Exp.and   :  Exp "&" Exp ;
    }
in
  idx(logic \ extendedLogic) +  
    (|
      extendedLogic -> (logic \ extendedLogic)

      [ Exp -> Exp ]
      
      Exp.not   =  '$1 ? #f : #t' ;
      Exp.or    =  '$1 ? #t : $2' ;
      Exp.and   =  '$1 ? $2 : #f' ;
    |)

  |

    (|
      (logic \ extendedLogic) -> lambda 

      [ Exp -> Exp ]
      
      Exp.true  =  '\xy.x' ;
      Exp.false =  '\xy.y' ;
      Exp.xor   =  '(\xy.(x(y(\xy.y)(\xy.x))y)) ($1) ($2)' ;
      Exp.if    =  '($1) ($2) ($3)' ;
      Exp.paren =  '($1)' ;
    |)