# [racket-users] Understanding P. Ragde's Proust

```Hi all,

I'm a mathematician delving into type theory and proof assistants and with
special interests in Racket.```
```
I'm now trying to understand and implement P. Ragde's Proust
<https://arxiv.org/abs/1611.09473> "nano proof assistant" and work through
the examples in his article. However, I'm pretty much a beginner in Racket
and I'm getting some errors. Particularly in the type-infer function,
that's also used in the type-check function.

Here is the code in the article:

(define (type-check ctx expr type)
(match expr
[(Lam x t)                           ; lambda expression
(match type
[(Arrow tt tw) (type-check (cons `(,x ,tt) ctx) t tw)]     ;
arrow type
[else (cannot-check ctx expr type)])]
[else (if (equal? (type-infer ctx expr) type) true (cannot-check ctx
expr type))]))

(define (type-infer ctx expr)
(match expr
[(Lam _ _) (cannot-infer ctx expr)]
[(Ann e t)  (type-check ctx e t) t]
[(App f a)                            ; function application
(define tf (type-infer ctx f))
(match tf
[(Arrow tt tw) #:when (type-check ctx a tt) tw]
[else (cannot-infer ctx expr)])]
[(? symbol? x)
(cond
[(assoc x ctx) => second]
[else (cannot-infer ctx expr)])]))

The first question I have is: what's the (Ann e t) supposed to mean,
because I'm getting a syntax error? Is it a type annotation? If so,
shouldn't everything be inside the #lang typed/racket module and type
annotations everywhere?

Secondly, the functions don't seem to work like this, as I'm getting failed
me clarify the code there or maybe it's already available somewhere?
Because just typing in the examples in the article simply doesn't work. I
can understand what they are supposed to do, but I lack the skills to fix
things myself.

Thank you!

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