The PREDICATE macro is there to make your code look nice, taking care of the interface to the C-defined SWI-Prolog kernel as well as mapping exceptions. Using the macro
PREDICATE(hello, 1)
is the same as writing:30There 
are a few more details, such as catching std::bad_alloc.:
static foreign_t pl_hello__1(PlTermv PL_av);
static foreign_t
_pl_hello__1(term_t t0, int arity, control_t ctx)
{ (void)arity; (void)ctx;
  try
  { return pl_hello__1(PlTermv(1, t0));
  } catch( PlFail& )
  { return false;
  } catch ( PlException& ex )
  { return ex.plThrow();
  }
}
static PlRegister _x_hello__1("hello", 1, _pl_hello__1);
static foreign_t
pl_hello__1(PlTermv PL_av)
The first function converts the parameters passed from the Prolog 
kernel to a PlTermv instance and maps exceptions raised in 
the body to simple failure or Prolog exceptions. The PlRegister 
global constructor registers the predicate. Finally, the function header 
for the implementation is created.
The PREDICATE() macros have a number of variations that deal with special cases.
A1, A2, 
etc.PL_av is not used.
    NAMED_PREDICATE("#", hash, 2)
    { return A2.unify_string(A1.as_string());
    }
    
Non-deterministic predicates are defined using PREDICATE_NONDET(plname, cname, arity) or NAMED_PREDICATE_NONDET(plname, cname, arity).
A non-deterministic predicate returns a “context” , which 
is passed to a subsequent retry. Typically, this context is allocated on 
the first call to the predicate and freed when the predicate either 
fails or does its last successful return (the context is nullptr 
on the first call). To simplify this, a template helper function 
PlControl::context_unique_ptr<ContextType>() provides a “smart 
pointer” that frees the context on normal return or an exception; 
when used with PL_retry_address(), the context's std:unique_ptr<ContextType>::release() 
is used to pass the context to Prolog for the next retry, and to prevent 
the context from being freed. If the predicate is called with PL_PRUNE, 
the normal return true will implicitly free the context.
The skeleton for a typical non-deterministic predicate is as follows. 
The test for PL_PRUNED is done first to avoid an unneeded
PlFrame and also to ensure that A1, A2, 
etc. aren't used when they have the value
PlTerm::null.31This 
code could be structured as a switch statement, but 
typically the PL_FIRST_CALL case falls through to the PL_REDO 
case. There are a number of examples of non-deterministic 
predicates in the test code test_cpp.cpp.
struct PredContext { ... }; // The "context" for retries
PREDICATE_NONDET(pred, <arity>)
{ // "ctxt" must be acquired so that the destructor deletes it
  auto ctxt = handle.context_unique_ptr<PredContext>();
  const auto control  = handle.foreign_control();
  if ( control == PL_PRUNED )
    return true;
  // Can use A1, A2, etc. after we know control != PL_PRUNED
  if ( ... ) // deterministic result
  { assert(control == PL_FIRST_CALL);
    if ( ... )
      return true;  // Success (and no more solutions)
    else
      return fase;
  }
  if ( control = PL_FIRST_CALL )
  { ctxt.reset(new PredContext(...));
    ...
  } else
  { assert(control == PL_REDO);
  }
  PlFrame fr;
  for ( ; ctxt->valid(...) ; ctxt->next() )
  { if ( ... unify a result ... )
    { ctxt->next();
      if ( ctxt->valid(...) )
        PL_retry_addresss(ctxt.release()); // Succeed with a choice point
      else
        return true; // deterministic success
    }
    fr.rewind();
  }
  return false;
}
With no special precautions, the predicates are defined into the 
module from which load_foreign_library/1 
was called, or in the module
user if there is no Prolog context from which to deduce the 
module such as while linking the extension statically with the Prolog 
kernel.
Alternatively, before loading the SWI-Prolog include file, the macro PROLOG_MODULE may be defined to a string containing the name of the destination module. A module name may only contain alpha-numerical characters (letters, digits, _). See the example below:
#define PROLOG_MODULE "math"
#include <SWI-Prolog.h>
#include <math.h>
PREDICATE(pi, 1)
{ A1 = M_PI;
}
?- math:pi(X). X = 3.14159