# Theory ILL_predlog

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theory ILL_predlog
imports ILL
uses [ILL_predlog.ML]
begin

    (* $Id: ILL_predlog.thy,v 1.3 2005/09/18 13:20:10 wenzelm Exp $ *)

    theory ILL_predlog
    imports ILL
    begin

    typedecl plf

    consts
      "&"   :: "[plf,plf] => plf"   (infixr 35)
      "|"   :: "[plf,plf] => plf"   (infixr 35)
      ">"   :: "[plf,plf] => plf"   (infixr 35)
      "="   :: "[plf,plf] => plf"   (infixr 35)
      "@NG" :: "plf => plf"   ("- _ " [50] 55)
      ff    :: "plf"

      PL    :: "plf => o"      ("[* / _ / *]" [] 100)

    translations

      "[* A & B *]" == "[*A*] && [*B*]"
      "[* A | B *]" == "![*A*] ++ ![*B*]"
      "[* - A *]"   == "[*A > ff*]"
      "[* ff *]"    == "0"
      "[* A = B *]" => "[* (A > B) & (B > A) *]"

      "[* A > B *]" == "![*A*] -o [*B*]"

    (* another translations for linear implication:
      "[* A > B *]" == "!([*A*] -o [*B*])" *)

    end