#line 647 "/home/ubuntu/felix/src/packages/core_type_constructors.fdoc"
  
  //------------------------------------------------------------------------------
  // Class Str: convert to string
  
  // Tuple class for inner tuple listing
  class Tuple[U] {
    virtual fun tuple_str (x:U) => str x;
  }
  
  instance[U,V with Str[U], Tuple[V]] Tuple[U ** V] {
    fun tuple_str (x: U ** V) =>
      match x with
      | a ,, b => str a +", " + tuple_str b
      endmatch
    ;
  }
  
  instance[U,V with Str[U], Str[V]] Tuple[U * V] {
    fun tuple_str (x: U * V) =>
      match x with
      | a , b => str a +", " + str b
      endmatch
    ;
  }
  
  // actual Str class impl.
  instance [U, V with Tuple[U ** V]] Str[U ** V] {
    fun str (x: U ** V) => "(" + tuple_str x +")";
  }
  
  instance[T,U] Str[T*U] {
     fun str (t:T, u:U) => "("+str t + ", " + str u+")";
  }
  instance[T] Str[T*T] {
     fun str (t1:T, t2:T) => "("+str t1 + ", " + str t2+")";
  }
  
  open[U, V with Tuple[U **V]] Str [U**V];
  open[U, V with Str[U], Str[V]] Str [U*V];
  
  
  //------------------------------------------------------------------------------
  // Class Eq: Equality
  instance [T,U with Eq[T], Eq[U]] Eq[T ** U] {
    fun == : (T ** U) * (T ** U) -> bool =
    | (ah ,, at) , (bh ,, bt) => ah == bh and at == bt;
    ;
  }
  
  instance[t,u with Eq[t],Eq[u]] Eq[t*u] {
    fun == : (t * u) * (t * u) -> bool =
    | (x1,y1),(x2,y2) => x1==x2 and y1 == y2
    ;
  }
  
  instance[t with Eq[t]] Eq[t*t] {
    fun == : (t * t) * (t * t) -> bool =
    | (x1,y1),(x2,y2) => x1==x2 and y1 == y2
    ;
  }
  
  //------------------------------------------------------------------------------
  // Class Tord: Total Order
  instance [T,U with Tord[T], Tord[U]] Tord[T ** U] {
    fun < : (T ** U) * (T ** U) -> bool =
    | (ah ,, at) , (bh ,, bt) => ah < bh or ah == bh and at < bt;
    ;
  }
  
  instance[t,u with Tord[t],Tord[u]] Tord[t*u] {
    fun < : (t * u) * (t * u) -> bool =
    | (x1,y1),(x2,y2) => x1 < x2 or x1 == x2 and y1 < y2
    ;
  }
  instance[t with Tord[t]] Tord[t*t] {
    fun < : (t * t) * (t * t) -> bool =
    | (x1,y1),(x2,y2) => x1 < x2 or x1 == x2 and y1 < y2
    ;
  }
  open [T,U with Tord[T], Tord[U]] Tord[T ** U];
  open [T,U with Tord[T], Tord[U]] Tord[T * U];
  open [T with Tord[T]] Tord[T * T];
  
  /* type equality now requires type_eq!
  //------------------------------------------------------------------------------
  // Generic Field access
  fun field[n,t,u where n==0] (a:t,b:u)=>a;
  fun field[n,t,u where n==1] (a:t,b:u)=>b;
  
  fun field[n,t,u,v where n==0] (a:t,b:u,c:v)=>a;
  fun field[n,t,u,v where n==1] (a:t,b:u,c:v)=>b;
  fun field[n,t,u,v where n==2] (a:t,b:u,c:v)=>c;
  
  fun field[n,t,u,v,w where n==0] (a:t,b:u,c:v,d:w)=>a;
  fun field[n,t,u,v,w where n==1] (a:t,b:u,c:v,d:w)=>b;
  fun field[n,t,u,v,w where n==2] (a:t,b:u,c:v,d:w)=>c;
  fun field[n,t,u,v,w where n==3] (a:t,b:u,c:v,d:w)=>d;
  
  fun field[n,t,u,v,w,x where n==0] (a:t,b:u,c:v,d:w,e:x)=>a;
  fun field[n,t,u,v,w,x where n==1] (a:t,b:u,c:v,d:w,e:x)=>b;
  fun field[n,t,u,v,w,x where n==2] (a:t,b:u,c:v,d:w,e:x)=>c;
  fun field[n,t,u,v,w,x where n==3] (a:t,b:u,c:v,d:w,e:x)=>d;
  fun field[n,t,u,v,w,x where n==4] (a:t,b:u,c:v,d:w,e:x)=>e;
  */
  
  //------------------------------------------------------------------------------
  open class parallel_tuple_comp
  {
    parallel composition
    // notation: f \times g
    fun ravel[u1,u2,r1,r2] (f1:u1->r1,f2:u2->r2) : u1 * u2 -> r1 * r2 =>
      fun (x1:u1,x2:u2) => f1 x1, f2 x2;
  
    fun ravel[u1,u2,u3,r1,r2,r3] (
       f1:u1->r1,
       f2:u2->r2,
       f3:u3->r3
      ) : u1 * u2 * u3 -> r1 * r2 * r3 =>
      fun (x1:u1,x2:u2,x3:u3) => f1 x1, f2 x2, f3 x3;
  
    fun ravel[u1,u2,u3,u4,r1,r2,r3,r4] (
       f1:u1->r1,
       f2:u2->r2,
       f3:u3->r3,
       f4:u4->r4
      ) : u1 * u2 * u3 * u4 -> r1 * r2 * r3 * r4=>
      fun (x1:u1,x2:u2,x3:u3,x4:u4) => f1 x1, f2 x2, f3 x3, f4 x4;
  
    fun ravel[u1,u2,u3,u4,u5,r1,r2,r3,r4,r5] (
       f1:u1->r1,
       f2:u2->r2,
       f3:u3->r3,
       f4:u4->r4,
       f5:u5->r5
      ) : u1 * u2 * u3 * u4 * u5 -> r1 * r2 * r3 * r4 * r5 =>
      fun (x1:u1,x2:u2,x3:u3,x4:u4,x5:u5) => f1 x1, f2 x2, f3 x3, f4 x4, f5 x5;
  
  }