Tock

An esolang/model of computation.

Overview

There is a collection of functions taking an integer t to a real. These functions can depend on the values that the other functions take for t-1, but not for any other input, so f(t) can be defined in terms of g(t-1) but not g(t), g(t-2), g(t+1) or g(3). Two functions, called halt and out, are special: the output of the program is the value of out(t) for the smallest t such that halt(t) is zero.

Language

A program is a collection of functions, which must include functions called halt and out. Each function is defined as follows:

<function name> <initial value> {
  <expression>
}

or:

<function name> <initial value> {
  <condition> : <expression>;
  <condition> : <expression>;
  otherwise : <expression>
}

A function name can consist of alphabetical characters and underscores only. The initial value is a number. a condition consists of two expressions related by one of =, !=, >, <, >= or <=. Clauses of a piecewise definition are checked sequentially, the otherwise clause is optional (but the program will throw an error if no clause matches).

For example, the following is a simple program that outputs 10:

halt 10 {
  halt - 1
}

out 0 {
  out + 1
}

While the following outputs 20:

halt 1 {
  counter = 10: 0;
  otherwise: 1
}

out 0 {
  counter * 2
}

counter 0 {
  counter + 1
}

Line comments are permitted using double slashes. See fractran.tock for a more involved example.

Using the Intepreter

tock.rkt provides the function run, which expects a string containing a tock program and returns the result as a number. run also takes an optional keyword argument #:trace which expects a list of strings which are the names of functions in the program. If this is provided (and nonempty) then run will print the values of those functions for each t up until the program halts. It won't handle nonexistant function names well, I'm afraid.