It is without doubt Cyaniris or Cupido.
The upperside looks like nothing you have ever seen before:
Note the very white ground colour, the basal spot in the cell of the hindwing and the small submarginal grey spot on the hindwing. All of these are visible in the picture below, which shows two little blues (Cupido minimus) at another site in Switzerland:
Here is another, more complete view of the underside of the mystery blue, taken into the light and therefore looking darker - this is an illusion. The very straight lines suggested Cupido osiris to me (which is why some of these pictures are labelled 'osiris1' &c.:
In fact, the two underside shots were taken 2 days apart (Sunday and Tuesday irrespectively) but I am fairly certain all pictures are of the same insect.
What sex is it? On the Sunday (the upperside pictures above) I firmly believed it was female, from the abdomen shape. The picture below was taken on Tuesday and I was not so sure:
Here is a close-up of the abdomen, in case anyone can tell me for certain what sex this insect is:
If you know what this species is, please contact me. I think the choices are: extreme variation of male Cupido minimus, extreme variation of female Cupido osiris, melanic male Cyaniris semiargus or a species hitherto unknown to science, Cupido maximus (Padfield 2005). This last is the least likely option! Truthfully, it has to be one of the first three but I have simply no idea which...