arith.hopeg

# '1'を並べた数で自然数を表すとする。
# a+b=c$をチェックする。
Plus = Plus0();
Plus0(Left)
  = &(Left "+") Plus1(Left, )
  / &(Left "1") Plus0(Left "1");

Plus1(Left, Right)
  = &(Left "+" Right "=") Plus2(Left, Right)
  / &(Left "+" Right "1") Plus1(Left, Right "1");

Plus2(Left, Right)
  = Left "+" Right "=" Left Right "$";

# a*b=c$をチェックする。
Mul = Mul0();
Mul0(Left)
  = &(Left "*") Mul1(Left, , )
  / &(Left "1") Mul0(Left "1");

Mul1(Left, Right, Prod)
  = &(Left "*" Right "=") Mul2(Left, Right, Prod)
  / &(Left "*" Right "1") Mul1(Left, Right "1", Prod Left);

Mul2(Left, Right, Prod)
  = Left "*" Right "=" Prod "$";


# a-b=c$をチェックする。
Minus = Minus0()
Minus0(Right)
  = &(.* "-" Right "=") Minus1(Right, )
  / &(.* "-" Right "1") Minus0(Right "1");

Minus1(Right, Diff)
  = &(.* "-" Right "=" Diff "$") Minus2(Right, Diff)
  / &(.* "-" Right "=" Diff "1") Minus1(Right, Diff "1");

Minus2(Right, Diff)
  = Right Diff "-" Right "=" Diff "$";

# a/b=cも同様にチェックできるはず。


# おまけ
# 終端記号をt1, t2, ..., tnとする。また、入力の末尾には特殊な記号$があるものとする。

# 入力を消費せずに、入力にのみマッチするパターンで継続を呼ぶ
ReadAll(C) = ReadAll0(, C)
ReadAll0(I, C)
  = &(I "$") C(I "$")
  / &(I "t1") ReadAll(I "t1", C)
  / &(I "t2") ReadAll(I "t2", C)
  ...
  / &(I "tn") ReadAll(I "tn", C);