Hi Matt,

Thank you very much for the details! What you're saying makes sense and is 
in accordance with my intuition. But the code doesn't work as it is.

I created a Gist for it here:


Everything is from the article, except for the (struct TA (type var)) which 
I created instead of the Ann ("type annotation") and the examples I used 
for tests.


On Sunday, March 15, 2020 at 2:10:55 PM UTC, Matt Jadud wrote:
> Hi Adrian,
> The article seems to be missing a type definition for Ann.
> Perhaps some of this you already know...
> (match expr ...)
> is a pattern matcher, working to find a pattern that 'expr' fits. 
> [(Lam _ _) ...]
> is attempting to match a pattern where a 'expr' is a struct called Lam, 
> and that structure has two fields. In this case, the value of those fields 
> is ignored, so the variable '_' is used to (by convention, not by syntax) 
> tell the programmer that these values do not matter. (At least, I'm 
> reasonably confident this is by convention and not by syntax.)
> The form
> [(Ann e t) ...] is matching the structure 'Ann', and binding the value in 
> the first field to the identifier 'e', and the second value to 't'. Then, 
> the expression following is executed (assuming the pattern matched).
> In the article, there is no struct definition for 'Ann'. I suspect it is a 
> typo/oversight. This would work:
> (struct Ann (e t))
> would be a reasonable definition. It says "Ann" is a data structure with 
> two fields, called "e" and "t".
> I haven't read the article, so "better" names for those fields is not 
> something I am going to come up with right now. The name in the definition 
> matters (to you, the programmer), but the identifier used to bind in the 
> pattern is not critical. (Or, it is again something that should be 
> important to you, but it does not need to match the names of the fields in 
> the struct definition.) 
> Hopefully that helps, and helps you move forward a bit. Ask more questions 
> if that didn't help. And, perhaps putting your code as-is in a Github Gist 
> or similar, so that others can look at exactly what you're working with 
> would be useful.
> (I have no idea how complete or incomplete the code in the article is, 
> which is why I suggest you put it in a pastebin/gist to share... there 
> might be other things that were glossed in the article? I don't know.)
> Cheers,
> Matt
> On Sun, Mar 15, 2020 at 10:01 AM Adrian Manea <adrian...@gmail.com 
> <javascript:>> wrote:
>> 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 matches for everything that's not a lambda expression. Can you 
>> please help 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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