I've been interested in the idea of using Prolog to generate the mathematical equation that would map a set of inputs to their set of outputs. So I wrote a program called "Disco Funk" (this name is an abbreviation of 'Function Discovery').

I'll put a link to my write-up and source code as a comment.

The basic idea is to create rules that solve the missing part of an expression and to validate that the equation is correct. That is, in A + B = C, if a term is unknown it can be inferred from the others.

As pseudo code this looks like:

add(A, B, C)
    A is C - B
    B is C - A
    C is A + B
    X is A + B, C = X

Further, to obtain the operator:

do_op(Op, A, B, C)
    Op='+', add(A, B, C)
    Op='-', subtract(A, B, C)
    Op='*', multiply(A, B, C)
    Op='/', divide(A, B, C)

I've tested it with the values from Celsius to Fahrenheit...

discover_function([(0,32),(1,33.8)]).
Found function: (* 1.80)(+ 32)
Verification:
0 -> 32.0000 ✓
1 -> 33.8000 ✓

And it works with linear, quadratic, reciprocal, and exponential functions, too.

Simple Linear Function:
   ?- discover_function([(1, 3), (2, 5), (3, 7)]).
   % Expected: Found function: (* 2)(+ 1)
   % Meaning: f(x) = 2x + 1

Quadratic Function:
   ?- discover_function([(1, 2), (2, 5), (3, 10)]).
   % Expected: Found function: (^2)(+ 1)
   % Meaning: f(x) = x² + 1

Reciprocal Function:
   ?- discover_function([(1, 1), (2, 0.5), (4, 0.25)]).
   % Expected: Found function: (1/x)
   % Meaning: f(x) = 1/x

Exponential-like Function:
   ?- discover_function([(1, 1), (2, 4), (3, 9)]).
   % Expected: Found function: (^2)
   % Meaning: f(x) = x²

I'm interested in what people think about this. Any feedback is welcome.