The code is illegal, but in accordance with the error message.
You need to set WHICH to 1 via either

        INTEGER :: which = 1

or
        which = 1

This however doesn't fix the problem.  If you change the call to

          CALL set_bound(the_beta%parameters(1))

then it compiles.  So, it looks as if gfortran isn't
properly evaluating the derived type arguments.

Created attachment 13618 [details]
decl.c patch (not check-gfortran tested)

Erik, are you still working on this?

One should also check that:
          CALL set_bound(the_beta%parameters(1:which))
is rejected. (This does not seem to call compare_parameter).

First step, to get it further is to modify compare_parameter (see attachment).
However, this then crashes in trans-expr.c's gfc_conv_function_call (l.2148) [invalid memory access].

(In reply to comment #2)
> Created an attachment (id=13618) [edit]
> decl.c patch (not check-gfortran tested)
> 
> Erik, are you still working on this?

Officially, yes :-)
I.e., I began, but now I haven't had time to look at it for a couple of weeks.  Just go ahead  and fix it if you are interested.

(In reply to comment #3)
> (In reply to comment #2)
> > Created an attachment (id=13618) [edit]
> > decl.c patch (not check-gfortran tested)
> > 
> > Erik, are you still working on this?
> 
> Officially, yes :-)
> I.e., I began, but now I haven't had time to look at it for a couple of weeks. 
> Just go ahead  and fix it if you are interested. 

Just to add one more data point: It's not just procedure arguments that are problematic; it's expression like

    foo%array(variable)

in general, where foo is a PARAMETER.  E.g. this piece of code is also rejected:

SUBROUTINE cdf_beta()

    TYPE :: the_distribution
        INTEGER :: parameters(1)
    END TYPE the_distribution

    TYPE (the_distribution), PARAMETER :: the_beta = the_distribution((/0/))
    INTEGER :: which, pooh

    which = 1

    pooh = the_beta%parameters(which)
END SUBROUTINE cdf_beta

erik:~/gcc$ gfortran pr31564.f90 
pr31564.f90:12.8:

    pooh = the_beta%parameters(which)
       1
Error: Incompatible ranks 0 and 1 in assignment at (1)

I never seem to get time to do anything about this bug, so I'll better unassign it from me.

This one is a real head-banger.  The array element reference is being completely ignored in translation.  I tried simplifying it by grabbing out the array component and attaching the array reference to it.  The resulting expression looks fine but the reference is ignore further downstream; I have run out of time to look at this, for a while.  Note that replacing the array component of a derived type parameter with a parameter array works fine.

Just for the record, my attempt to fix this by simplification appears below.

Paul

Index: gcc/fortran/expr.c
===================================================================
*** gcc/fortran/expr.c  (revision 127505)
--- gcc/fortran/expr.c  (working copy)
*************** simplify_ref_chain (gfc_ref *ref, int ty
*** 1461,1466 ****
--- 1461,1535 ----
  }


+ /* Simplify structure references.  */
+
+ static void
+ simplify_structure_refs (gfc_expr *e)
+ {
+   int n;
+   bool seen_array_ref;
+   bool reduced_structure = false;
+   gfc_ref *ref;
+   gfc_component *cmp;
+   gfc_constructor *ctr;
+   gfc_expr *p = e;
+   gfc_symtree *st;
+
+   if (e->expr_type != EXPR_STRUCTURE)
+     return;
+
+ start:
+   seen_array_ref = false;
+   ref = p->ref;
+
+   for (; ref; ref = ref->next)
+     {
+       switch (ref->type)
+       {
+       case REF_COMPONENT:
+         if (p->symtree
+               && p->symtree->n.sym->ts.derived
+               && !p->ts.derived)
+           p->ts = p->symtree->n.sym->ts;
+
+         if (seen_array_ref || !p->ts.derived)
+           break;
+
+         ctr = p->value.constructor;
+         cmp = p->ts.derived->components;
+         for (;ctr; ctr = ctr->next, cmp = cmp->next)
+           {
+             if (ref->u.c.component != cmp || ctr->expr == NULL)
+               continue;
+             p = ctr->expr;
+             p->ts = cmp->ts;
+             ctr->expr = NULL;
+             p->ref = ref->next;
+             ref->next = NULL;
+             gfc_free_expr (e);
+             *e = *p;
+             reduced_structure = true;
+             goto start;
+           }
+         break;
+
+       case REF_ARRAY:
+         for (n = 0; n < ref->u.ar.dimen; n++)
+           {
+             if (reduced_structure
+                   && ref->u.ar.dimen_type[n] == DIMEN_ELEMENT)
+               p->rank--;
+           }
+         seen_array_ref = true;
+         break;
+
+       default:
+         break;
+       }
+     }
+ }
+
+
  /* Try to substitute the value of a parameter variable.  */

  static try
*************** gfc_simplify_expr (gfc_expr *p, int type
*** 1604,1609 ****
--- 1673,1681 ----
        if (simplify_ref_chain (p->ref, type) == FAILURE)
        return FAILURE;

+       if (p->ref)
+         simplify_structure_refs (p);
+
        if (simplify_constructor (p->value.constructor, type) == FAILURE)
        return FAILURE;

*************** gfc_check_pointer_assign (gfc_expr *lval
*** 2749,2755 ****

    is_pure = gfc_pure (NULL);

!   if (is_pure && gfc_impure_variable (lvalue->symtree->n.sym))
      {
        gfc_error ("Bad pointer object in PURE procedure at %L", &lvalue->where)
;
        return FAILURE;
--- 2821,2828 ----

    is_pure = gfc_pure (NULL);

!   if (is_pure && gfc_impure_variable (lvalue->symtree->n.sym)
!       && lvalue->symtree->n.sym->value != rvalue)
      {
        gfc_error ("Bad pointer object in PURE procedure at %L", &lvalue->where)
;
        return FAILURE;

To my surprise, I have a fix for this one.  I'll post it to the list in the next 48 hours.

Paul

Subject: Bug 31564

Author: pault
Date: Wed Sep  5 13:34:25 2007
New Revision: 128130

URL: http://gcc.gnu.org/viewcvs?root=gcc&view=rev&rev=128130
Log:
2007-09-05  Paul Thomas  <pault@gcc.gnu.org>

	PR fortran/31564
	* primary.c (gfc_match_rvalue): Make expressions that refer
	to derived type parameters that have array references into
	variable expressions.  Remove references to use association
	from the symbol.

	PR fortran/33241
	* decl.c (add_init_expr_to_sym): Provide assumed character
	length parameters with the length of the initialization
	expression, if a constant, or that of the first element of
	an array.

2007-09-05  Paul Thomas  <pault@gcc.gnu.org>

	PR fortran/31564
	* gfortran.dg/derived_comp_array_ref_2.f90: New test.

	PR fortran/33241
	* gfortran.dg/char_length_10.f90: New test.

Added:
    trunk/gcc/testsuite/gfortran.dg/char_length_10.f90
    trunk/gcc/testsuite/gfortran.dg/derived_comp_array_ref_2.f90
Modified:
    trunk/gcc/fortran/ChangeLog
    trunk/gcc/fortran/decl.c
    trunk/gcc/fortran/primary.c
    trunk/gcc/testsuite/ChangeLog

Fixed on trunk.

Paul

Subject: Bug number PR31564

A patch for this bug has been added to the patch tracker.
The mailing list url for the patch is http://gcc.gnu.org/ml/gcc-patches/2007-09/msg00319.html