arith2.scala

    tryGrammar(
      "subtract",
      MacroPEGParser.parse(
       """
      |S = ReadRight("") !.;
      |// the number of occurence of '1 represents a natural number.
      |// a-b=c
      |// Essentially, this checks a=b+c.
      |ReadRight(Right)
      |  = &("1"* "-" Right "1") ReadRight(Right "1")
      |  / &("1"* "-" Right "=") ReadDiff(Right, "");
      |
      |ReadDiff(Right, Diff)
      |  = &("1"* "-" Right "=" Diff "1") ReadDiff(Right, Diff "1")
      |  / &("1"* "-" Right "=" Diff !.) Check(Right, Diff);
      |
      |Check(Right, Diff)
      |  = Right Diff "-" Right "=" Diff;
      """.stripMargin),
       "11-1=1", "1-1=", "111-11=1", // should match
       "111-1=1",  "111-1=111", "1-11=" // should not match
    )

    tryGrammar(
       "exponent",
      MacroPEGParser.parse(
       """
      |S = ReadLeft("", "") !.;
      |// the number of occurence of '1 represents a natural number.
      |// |Seq| is the length of a sequence Seq.
      |// ^ is exponent operator
      |// ReadLeft("", "") checks input is a correct expression a^b=c.
      |
      |// Read a.
      |// LeftAsOnes is a sequence of "1" where |LeftAsOnes| = |a|.
      |// LeftAsDots is a sequence of . where |LeftAsDots| = |a|.
      |ReadLeft(LeftAsOnes, LeftAsDots)
      |  = &(LeftAsOnes "1") ReadLeft(LeftAsOnes "1", LeftAsDots .)
      |  / &(LeftAsOnes "^") ComputePadding(LeftAsOnes, LeftAsDots, "");
      |
      |// Compute Padding which is a sequene of .
      |// where |Padding| + |LeftAsDots| = |Input|
      |ComputePadding(LeftAsOnes, LeftAsDots, Padding)
      |  = &(Padding LeftAsDots .) ComputePadding(LeftAsOnes, LeftAsDots, Padding .)
      |  / &(Padding LeftAsDots !.) ReadRight(LeftAsOnes, Padding, "", "1");
      |
      |// Read b.
      |// Exp = a^Right.
      |ReadRight(Left, Padding, Right, Exp)
      |  = &(Left "^" Right "1") Multiply(Left, Padding, Right "1", Exp, "", "")
      |  / &(Left "^" Right "=") Check(Left, Right, Exp);
      |
      |// Compute Left * OldExp.
      |// This adds OldExp Left times into Exp.
      |// I is a loop counter.
      |Multiply(Left, Padding, Right, OldExp, Exp, I)
      |  = &(Padding I .) Multiply(Left, Padding, Right, OldExp, Exp OldExp, I .)
      |  / &(Padding I !.) ReadRight(Left, Padding, Right, Exp);
      |
      |// Check whole input.
      |Check(Left, Right, Exp)
      |  = Left "^" Right "=" Exp;
      """.stripMargin),
       "11^111=11111111", "11^=1", "1^11=1", "^11=", // should match
       "11^111=1111111",  "11^111=111111111" // should not match
    )