Domains

• A domain exports a collection of related constants.

  #include "algebra"
  macro Z == Integer;
  Utils == add {
        import from Z;
        pi: Fraction(Z) == 355/113;
        fib(n:Z): Z ==       ................
        factorial(n:Z): Z ==       ................
        ............................................
  }
  

• All constants defined within a domain are exported by default unless declared local.
• Constants exported by domains may be imported into a program's scope.
• Within a domain-valued expression, the name ``%'' refers to the domain being computed.
• A type Rep is defined to give a representation for %.
• rep and per are type conversions:

  rep: % -> Rep
  per: Rep -> %
  

  Complex == add {
      R  == DoubleFloat;
  
      Rep == Record(real: R, imag: R);
  
      import from Rep, R;
  
      real(u: %): R == rep(u).real;
      imag(u: %): R == rep(u).imag;
      complex(a: R, b: R): % == per [a, b];
  
      (u: %) + (v: %): % == complex(real u + real v, imag u + imag v);
      (k: R) * (u: %): % == complex(k * real u, k * imag u);
      abs(u: %): R       == sqrt(real(u)^2 + imag(u)^2);
      ...
  }
  

• The add operator may be used to build on an existing domain.

  Polygon == add {
      Rep == List Complex;
      new(l: List Complex): % == per l;
      vertex(p: %, i: Integer): Complex == rep(p).i;
  }
  
  Square == Polygon add {
      area(s: %): DoubleFloat == {
          s1 := vertex(s,1) - vertex(s,0);
          s2 := vertex(s,2) - vertex(s,0);
          abs(vectorial(s1,s2));
      }
  }