[clean-list] Handling of reals & boolean expressions?

[G.W.M. Vissers]

Hello,

Consider the following program:


module tst

import StdReal, StdBool, StdClass

::Complex = { re :: Real, im :: Real }

absreal :: !Complex -> Real
absreal {re=re, im=im}
| mna == 0.0 = mxa
= mxa * sqrt (1.0 + u * u)
where
  ax = abs re
  ay = abs im

  mna = min ax ay
  mxa = max ax ay

  u = mna / mxa

less :: !Complex !Complex -> Bool
less z1 z2 = az1 < az2
where
  az1 = absreal z1
  az2 = absreal z2

less2 :: !Complex !Complex -> Bool
less2 z1 z2 = az1 < az2 || az1 == az2
where
  az1 = absreal z1
  az2 = absreal z2

less3 :: !Complex !Complex -> Bool
less3 z1 z2 = az1 < az2 || False
where
  az1 = absreal z1
  az2 = absreal z2

Start = (less ip im, less2 ip im, less3 ip im)
where
  ip = {re=2.0, im=1.0}
  im = {re=2.0, im=(-1.0)}


When calling the function less, less2, less3 with complex numbers with the 
same absolute value (as in the program above), I get the result
(True,False,True).

My two questions are then of course
a) why is in the functions less and less3 az1 < az2 evaluated to True?
b) if the behaviour in less and less3 is correct, then why is the result 
   of less2 False? 

Using the three functions with complex numbers of different magnitude 
results in the behaviour one expects, i.e. all three functions give the 
same answer.

Thanks in advance for possible explanations, 

Gé Vissers