μ-recursive functions execution.

Requires:

• C++ compiler (GCC)
• Boost (Tokenizer library)
• QT (but can be used separately)

Notes:

• all commas are optional, and can be added anywhere (f,(x y) = ,Sc(x,,,) is valid code)

Planned:

• saving and manipulating numbers in factorized form
• optimizations:
  • if induction step case doesn't depend on f(y ...), run just the y-th iteration

Builtin functions:

• sc : N -> N, Sc(x) = x + 1
• (.0, .1, .2, ...) .k : N -> N, .k(x_0 ... x_n) = x_k (requires k < n)
• z : N -> N, z(x) = 0

• Writing functions, basic case

  function_name var_1 ... var_n = expression

  Expressions are defined as: expression ::= bounded variable | function_name(expression_1 ... expression_k)

  For example, f x y z = .1(z .0(y))

• Writing functions, primitive recursion case

  • Base case:

    f 0 var_1 ... var_n = expression

  • Induction step case:

    f y + 1 var_1 ... var_n = expression

  Base case must appear before induction step case. Induction step case can only refer to f by f(y, x). The name and the position of 'y' is fixed, but you can always create a wrapper function:

  g something counter something_else = f counter something something_else

• Macros Syntax: { macro_parameters | statement1 ... statementn } (see example)