Y combinator and C preprocessor
The Y combinator is a higher order function, and support for higher order functions in the language is required to support explicit recursive substitution. Therefore, for specific tasks, this can be done in Scheme, SML and other functional languages.
Talk about the C preprocessor later, but what about C? Higher-order functions could be used in C since we can pass function references as arguments to functions and return them to emulate higher-order functions. However, the lack of support for closures in the language prevents the Y combinator from being implemented.
Since the preprocessor is even more restrictive, there is no way for C to implement the Y combinator that is based on the concepts of lambda calculus. The use of the Y combinator can only be achieved in functional programming languages with full support for higher-order functions.
PreprocessorC is very simple as it only does line replacements in the text. I would not apply any concepts from lambda calculus and functional programming to it.
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Actually it is possible, see my CSP Git Repo project , it is a LISP interpreter, FULLY implemented in C, and of course you can implement the Y combinator on it.
I hope you enjoy some tests / examples as well if you are interested in it.
Here's the most important part. (from csp.h) It successfully implements closure and lambda, giving support for implementing fixed point combinators.
#define EVAL_e(x) x
#define _be(y) y)
#define ZIP(x) _n() (x,_be
#define _PAIR(x,y) _e( __PAIR(x,y))
#define __PAIR(x,y) _E COND((NULL SAFE_CDR(x)((SAFE_CAR(x) SAFE_CAR(y))))((T)((SAFE_CAR (x) SAFE_CAR (y)) _e(_PAIR2(_e SAFE_CDR(x),_e SAFE_CDR(y))))))
#define _PAIR2(x,y) _E COND((NULL SAFE_CDR(x)((SAFE_CAR(x) SAFE_CAR(y))))((T)((SAFE_CAR (x) SAFE_CAR (y)) _e(_PAIR3(_e SAFE_CDR(x),_e SAFE_CDR(y))))))
#define _PAIR3(x,y) _E COND((NULL SAFE_CDR(x)((SAFE_CAR(x) SAFE_CAR(y))))((T)((SAFE_CAR (x) SAFE_CAR (y)) _e(_PAIR4(_e SAFE_CDR(x),_e SAFE_CDR(y))))))
#define _PAIR4(x,y) _E COND((NULL SAFE_CDR(x)((SAFE_CAR(x) SAFE_CAR(y))))((T)((SAFE_CAR (x) SAFE_CAR (y)) _e(DELAY_INT_54(__PAIR_R) ()(SAFE_CDR(x) SAFE_CDR(y))))))
#define __PAIR_R() _$pair
#define TEST_R() TEST
#define TEST(x) test
#define _PAIR_e(x) x
#define _$pair(x) _PAIR_e(_PAIR ZIP x)
#define PAIR_EVAL(...) PAIR_EVAL2(PAIR_EVAL2(PAIR_EVAL2(__VA_ARGS__)))
#define PAIR_EVAL2(...) PAIR_EVAL3(PAIR_EVAL3(PAIR_EVAL3(__VA_ARGS__)))
#define PAIR_EVAL3(...) PAIR_EVAL4(PAIR_EVAL4(PAIR_EVAL4(__VA_ARGS__)))
#define PAIR_EVAL4(...) PAIR_EVAL_E(PAIR_EVAL_E(PAIR_EVAL_E(__VA_ARGS__)))
#define PAIR_EVAL_E(...) __VA_ARGS__
#define $pair(x) PAIR_EVAL(_$pair(x))
#define $zipped_evlis_R() $zipped_evlis
#define EVLIS_e_R() EVLIS_e
#define EVLIS_e(x) x
#define _EVLIS_ZIP(...) _n() (__VA_ARGS__,_BE
#define _BE(...) __VA_ARGS__)
#define _EVLIS_R() _EVLIS
#define _EVLIS_E(...) __VA_ARGS__
#define _EVLIS_N(...)
#define _EVLIS_B _EVLIS_E (_EVLIS_N,_EVLIS_E(_EVLIS_N,_EVLIS_N))
#define ___EVLIS(a,b,k,...) k($zipped_eval((b),(a)) DELAY_INT_2(_EVLIS_R)()(a))
#define __EVLIS(a,b,...) ___EVLIS(a,b,__VA_ARGS__ _EVLIS_E)
#define _EVLIS_EVAL_E(...) __VA_ARGS__
#define _EVLIS_EVAL_5(...) _EVLIS_EVAL_E(_EVLIS_EVAL_E(_EVLIS_EVAL_E(__VA_ARGS__)))
#define _EVLIS_EVAL_4(...) _EVLIS_EVAL_5(_EVLIS_EVAL_5(_EVLIS_EVAL_5(__VA_ARGS__)))
#define _EVLIS_EVAL_3(...) _EVLIS_EVAL_4(_EVLIS_EVAL_4(_EVLIS_EVAL_4(__VA_ARGS__)))
#define _EVLIS_EVAL_2(...) _EVLIS_EVAL_3(_EVLIS_EVAL_3(_EVLIS_EVAL_3(__VA_ARGS__)))
#define _EVLIS_EVAL(...) _EVLIS_EVAL_2(_EVLIS_EVAL_2(_EVLIS_EVAL_2(__VA_ARGS__)))
#define _EVLIS(x) __EVLIS _EVLIS_ZIP(x)
#define $zipped_evlis(x,y) _EVLIS_EVAL(_EVLIS y x (_EVLIS_B))
#define $zipped_eval_R() $zipped_eval
#define $zipped_eval(e,a) /**sth irrelevant**/
($eq(SAFE_CAR SAFE_CAR e (lambda))\
(DELAY_INT_26(EVAL_e_R)() DELAY_INT_23($zipped_eval_R)()(\
EVAL_e(EVAL_e(EVAL_e(EVAL_e(SAFE_CAR SAFE_CDR SAFE_CDR SAFE_CAR e)))),\
EVAL_e(APPEND DELAY_INT_13($pair_R)()(EVAL_e(EVAL_e(EVAL_e(SAFE_CAR SAFE_CDR SAFE_CAR e)))\
(DELAY_INT_19($zipped_evlis_R)()(EVAL_e(_e EVAL_e(SAFE_CDR e)), a)))a)))\
/**end of eval recursion**/
#define $pair_R() $pair
#define EVAL_e_R() EVAL_e
#define $eval_E(...) __VA_ARGS__
#define $eval_expand5(...) $eval_E($eval_E($eval_E(__VA_ARGS__)))
#define $eval_expand4(...) $eval_expand5($eval_expand5($eval_expand5(__VA_ARGS__)))
#define $eval_expand3(...) $eval_expand4($eval_expand4($eval_expand4(__VA_ARGS__)))
#define $eval_expand2(...) $eval_expand3($eval_expand3($eval_expand3(__VA_ARGS__)))
#define $eval_expand(...) $eval_expand2($eval_expand2($eval_expand2(__VA_ARGS__)))
#define $zeval(x,y) $eval_expand($zipped_eval(x,y))
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