Draft

• https://eli.thegreenplace.net/2007/11/24/the-context-sensitivity-of-cs-grammar/
• The lexer hack https://en.wikipedia.org/wiki/The_lexer_hack
• Clang use a thin lexer to avoid this problem, which is what I'm going to use as well

Here is the C lexer rule and grammar for yacc

• lex: http://www.quut.com/c/ANSI-C-grammar-l.html
• yacc: http://www.quut.com/c/ANSI-C-grammar-y.html

Calculus has two main branches:

• differential calculus
  • it is mainly about derivative. The process of finding a derivative is called differentiation.
  • \(\frac{dy}{dx}|_{a}\) is Leibniz's notation
  • f'(a) is Lagrange's notation
• integral calculus
  • definite integral
  • indefinite integral (also antiderivative)

When solving a maxima of a function, with subject to a constraint, we often use Lagrange multiplier. Say:

• maximize \(f(x,y)\)
• subject to \(g(x,y)=0\)

We are going to introduce the Lagrange multiplier \(\lambda\) such that

• \(L(x,y,\lambda) = f(x,y) - \lambda g(x,y)\) is called Lagrange function.
• Compute the gradient of L, and compute the stationary points. Those points will be the space of the solution to the original maxima problem.

The intuition: at a maximum, f(x,y) cannot be increasing in the direction of any neighboring point where g = 0.