From: tjroberts137@sbcglobal.net   
      
   On 7/21/17 7/21/17   7:29 PM, rockbrentwood@gmail.com wrote:   
   > Physical quantities form a TYPED ALGEBRA.   
   >   
   > The system of types form an Abelian group with the identity 1   
   > standing for the type of dimensionless quantities   
   >   
   > A type judgement e: T means quantity e has type T, which in dimensional   
   > analysis means [e] = T.   
   >   
   > Addition and subtraction are subject to type-restriction: e + f and   
   > e - f are only defined if e:T and f:T, in which case (e +/- f): T.   
      
   OK, except there is also the concept of compatible types: cm and inches (in)   
   are   
   not equal (same type), but are compatible:   
   	1cm + 1in = 3.54cm   
   	1in - 1cm = .606in   
   	1in / 1cm = 2.54   
   	2 * 1cm = 2cm   
   	1cm / 2 = 0.5cm   
   	convert(1in,cm) = 2.54cm   
   	convert(1cm,in) = 0.394in   
   	... etc.   
      
   Tom Roberts   
      
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