Proce
From Esolang
Proce (pronounced like the first syllable of "process") is an esoteric programming language by User:Ihope127. A program is a list of lines; blank lines are ignored, and # marks a line comment. The syntax:
<line> ::= name "=" <function>
<function> ::= <tfunction> {"+" <tfunction>} | {"-" <tfunction>}
<tfunction> ::= name | number | "(" <function> ")" | number "*" <tfunction> |
"d!" <tfunction> | "i!" <tfunction> | "r!" <tfunction>
'name' can contain any character not used elsewhere; letters are always valid in a name. 'number' can also contain any character not used elsewhere; numerals, - and . are always valid in a number. Whitespace can be put between tokens and is generally ignored.
A program contains a list of equations, defining functions of time. f+g is the sum of functions f and g; n*f is the product of the number n and the function f; d!f is the derivative of the function f; i!f is the definite integral of the function f from 0 to t; and r!f is f if f >= 0, 0 otherwise (the rectification of f). Since these functions are actually distributions, it's valid to, say, differentiate a step function, integrate the result, and expect to have the same step function (plus a constant). It is not possible to multiply two functions, or to access a function at any other time than the current time (except using integration).
Undefined behavior can result from doing something like differentiating a Dirac delta distribution and rectifying it, as the derivative of a Dirac delta is neither negative nor positive (or both, depending on your interpretation) at 0.
A sine wave can be made easily:
sin = i!(1 - i!sin)
This is a low-pass filter of 'sig':
low = i!(sig - low)
A high-pass filter can be made by subtracting the low-pass filter from the signal; an AM receiver can be made by taking both a high-pass filter and a low-pass filter, then rectifying, then taking a low-pass filter again.
I have found a truly marvelous way to do convolution, which this margin is too narrow to contain. Computation is almost certainly possible, and in theory, it's probably Turing-complete, but maybe not.
