μ4

A esolang based on μ6

Flags

By default, μ4 executes the ASCII version of the code. E.g.

python3 mu4.py test.m4

Executes the contents of test.m4 as an ASCII file.

Two flags are supported:

• -t: Converts the given file to the octal encoding of the program.
  • (Note: You might need to use > to write its output to a file.)
• -b: Reads the program from an octal encoding.

Execution

The program takes a list of integers from STDIN (space-separated), as the arguments to the function.

Then, the program is parsed into a function. The result of calling the function with the argument(s) is printed.

Unlike μ6, μ4 encodes the characters in octets. All allowed characters:

0 1 2 3 ; ( ) !

Grammar

Functions

• N Constant function. Takes any number of arguments, and returns N, decoded from base-4.
• ;N Projection. Takes any number of arguments, and returns the Nth argument. (base-4 decoded)
  • (Indexing starts at 1.)
• ; Successor. Takes 1 argument. Returns the successor of its argument.

Operators

Here, h1, g, f1, etc. all represent functions.

a1, a2, .. an represents an arbitrary number of the same type of argument (i.e. numbers/functions). This list can be empty.

• ( h1 h2 .. hn g ) Composition. Defines a function which:
  • Takes any number of arguments [a1, a2, .. an].
  • Returns g(h1([a1, a2, .. an]), h2([a1, a2, .. an]), .. hn([a1, a2, .. an])).
• ! g h Primitive recursion. Defines a function which:
  • Takes any number of arguments [n, a1, a2, .. an].
    • If n == 0: Returns g([a1, a2, .. an]).
    • Else. Returns h([n-1, ! g h([n-1, a1, ... an]), a1, .. an]).
• ! f Minimization. Defines a function which:
  • Takes any number of arguments [a1, a2, .. an].
  • Return the smallest natural number x where f([x, a1, a2, .. an]) = 0.

Examples

Addition: !;1(;2;)

Double: (;1;1!;1(;2;))

Multiplication: !0(;2;3!;1(;2;))

Predecessor: !0;1

Monus (reversed args): !;1(;2!0;1)

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Minimization test: !(;1!0;0)