I’m going to go through the Inducing Arithmetic Functions example from Forest. Hopefully this can help you gain a little bit of familiarity with probabilistic programming. Here’s the code:

```
(define (random-arithmetic-fn)
(if (flip 0.3)
(random-combination (random-arithmetic-fn)
(random-arithmetic-fn))
(if (flip)
(lambda (x) x)
(random-constant-fn))))
(define (random-combination f g)
(define op (uniform-draw (list + -)))
(lambda (x) (op (f x) (g x))))
(define (random-constant-fn)
(define i (sample-integer 10))
(lambda (x) i))
(define (sample)
(rejection-query
(define my-proc (random-arithmetic-fn))
(my-proc 2)
(and (= (my-proc 0) 2)
(= (my-proc 1) 3))))
(sample)
```

The goal is to determine what `my-proc` is, but since Church doesn't have function pretty-printing, showing that the results of `(my-proc 2)` are consistent with what you would expect is good enough.
### `(define (sample) ...)`
Let's start with the meat: lines 17-22. This function will draw a sample from `(my-proc 2)`. In Church, the body of sampling functions (like `rejection-query`) begin with the model, followed by the query and some condition. The model is the definition of `my-proc`. The query is `(my-proc 2)`, and the condition is the `and` expression on line 21. Church will draw samples until the conditions are true.
### `random-arithmetic-fn`
With probability .3, this function will create bigger combinations of adding and subtracting further arithmetic expressions. In these recursive calls, there is a 70% chance of returning either the parameter passed in (`2` from `(my-proc 2)`) or some random integer. A couple sample calls might look like this:
```scheme
(lambda (x) x)
(lambda (x) (- (lambda (x) 2) (lambda (x) 4))) ; just (- 2 4)
(lambda (x) 0)
(lambda (x) (+ (lambda (x) x) (lambda (x) 7))) ; just (+ x 7)
```
`(my-proc)` could never be any of those values since the conditions
```scheme
(and (= (my-proc 0) 2)
(= (my-proc 1) 3)))
```
don't hold. It would keep drawing samples until it found something like:
```scheme
(lambda (x) (+ (lambda (x) x) (lambda (x) 2)))
```
At that point, calling `(my-proc 2)` would return `4`. I ran the program a few times, and that's what it always came up with.
I hope that's helpful! You can tinker with and run the code at [forestdb](http://forestdb.org/models/arithmetic.html).