A PM Grammar

A Grammar for a Subset of

Principia Mathematica

By Dennis J. Darland

June 15, 2007

I’ve changed the notation a little, but I think it is equivalent & makes it clearer.

I used Introduction to Automata Theory , Languages and Computation by John E. Hopcroft and Jeffrey D. Ullman. pp 79-80. as my reference on context free grammars.

Grammar = G = {V,T,P,S}

Variables= V= ‘C’,’V’,’F’,’P’,’S’,’A’

Terminals= T= (‘f’,’g’,’z’,’w’,’x’,’{‘,’}’,’(‘,’)’,’ó’,’=’,’!’,’e’,’$’,"’,’p’,’q’,’c’,’d’,’x’,’y’,’~’,’&’)

Start Symbol = S= ‘S’

Productions= P (below)

A => F(V)

A=>V e ( C)

C => P ! z

A => P ! x

A => F {w(Fw}

A => F(P!z)

A => ($F)FV

A => ("V)P!V

A => ("V)FV

S => A

S => A = A

S => A ó A

S => A & A

S => ~A

F => f

F => g

P => p

P => q

C => c

C => d

V => x

V => y