# Why Logic Programming?

Why? Always a good question, to understand logic programming, need to
realize what we gain from it. Normally, if we want to solve a
computational problem, we make a sequential command to get an answer.
For example, what is Fibonacci's number at `3`

? We can have a racket
program for this:

#lang racket (define (fib n) (match n [0 1] [1 1] [n (+ (fib (- n 1)) (fib (- n 2)))])) (fib 3)

However, some questions aren't that easy to be resolved since need some
synthesis, but we can take a look at how to resolve the Fibonacci
problem via logic programming(use `Datalog`

):

#lang datalog (racket/base). fib(0, 0). fib(1, 1). fib(N, F) :- N != 1, N != 0, N1 :- -(N, 1), N2 :- -(N, 2), fib(N1, F1), fib(N2, F2), F :- +(F1, F2). fib(3, F)?

In Fibonacci this example they actually the same thing, but if I ask: g(x) is under f(x) follows the Big-O definition.

C : Real(\(\gt 0\)), N : Integer(\(\ge 0\)), \(\forall n \ge N, \exists C, g(N) < C \cdot f(N)\)

Does that still easy to answer? Solve this problem in Racket is really
hard, but simple in `Rosette`

:

#lang rosette/safe (define-symbolic C N integer?) (define (O f g) (solve (begin (assert (>= N 0)) (assert (positive? C)) (assert (< (g N) (* C (f N)))))))

Can see all need to do is point out constraints. The only problem is we
cannot use `C : Real`

this definition since `Real`

is not constructible.
However, the power of logic programming already shows there. Hope you
also like it ^{_}.