lambda-calculus in C: Booleans and NOT operator

I wanted to give implementations in different programming languages of the lambda-calculus construction of the booleans and the NOT operator.

These are:

TRUE = lx.ly. x
FALSE = lx.ly. y
NOT = lx. x FALSE TRUE

It's trivial to do in Javascript and Python say, like

var TRUE = function(x,y){ return x;} 
var FALSE = function(x,y){ return y;}
var NOT = function(b){ return b(FALSE,TRUE) ; } 

but I can't figure out how to do it in C.

The naive idea of implementing something like this

lambda true(lambda x, lambda y){ return x ; }
lambda false(lambda x, lambda y){ return y ; }

lambda not(lambda (b)(lambda, lambda) ){ return b(false,true) ;}

doesn't seem possible in C, as typedef doesn't allow a recursive definition

typedef void (*lambda)(lambda,lambda) ;not valid in C

Is there a way to do it in C? and is there a way to do it that is meaningful to use as an educational example? That is, if the syntax starts getting to cumbersome it ends up defeating its purpose...

Finally, if C ends up being too limited in any way, an answer in C++ would also work for me, albeit with the same "complexity" constraint

I may be expecting too much of C.

EDIT: Following the suggestion by Tom in the comments, the following definitions do compile

typedef void *(*bol)() ;

bol true(bol x, bol y){ return x ; }
bol false(bol x, bol y){ return y ; }

bol not(bol b ){ return b(false,true) ;}



int main(){
 bol p = not((bol)true);
 
 return 0;
}

EDIT2: This, however, is not strictly conforming as Tom and others have pointed out.

Furthermore, as @Antti Haapala, and @n.m point out, this may be asking too much of C.

At this point I'm skeptical that there could be a simple enough implementation in C++.

The only way I know in C to declare recursive declarations is by using struct, like this:

#include <stdio.h>
#include <stdarg.h>

typedef struct LAMBDA {
    struct LAMBDA * (*function)(struct LAMBDA *, ...);
} *lambda;

lambda trueFunction(lambda x, ...) {return x;}
lambda true = &(struct LAMBDA) {.function = trueFunction};

lambda falseFunction(lambda x, ...) {va_list argp; va_start(argp, x); lambda y = va_arg(argp, lambda); va_end(argp); return y;}
lambda false = &(struct LAMBDA) {.function = falseFunction};

lambda notFunction(lambda b, ...) {return b->function(false, true);}
lambda not = &(struct LAMBDA) {.function = notFunction};

int main() {
    lambda p1 = not->function(true);
    lambda p2 = not->function(false);
    printf("%p %p %p %p", true, p1, false, p2);
    return 0;
}

Its hard for me to judge whether such syntax is too cumbersome or not, obviously less clear than dynamic languages.