The addition of salt doesn't actually melt the ice in a direct fashion (i.e. by heating it) though some salts (such as calcium chloride) do actually produce some heat when they dilute in water. Technically, the addition of any substance that dissolves in water will lower the temperature at which water freezes (this is called "freezing point depression"). There is nothing special about using salt (sodium chloride) for this purpose. Salt is used because it is inexpensive and dissolves readily in water. So when the salt is added to snow or ice, it begins to dissolve into it and that lowers the temperature at which the snow/ice freezes so if it's not too cold, it will melt and stay as a liquid.
The amount that the freezing point of water is lowered is 1.86 C/m (3.35 F/m) which basically means that adding more of a substance to water will lower its freezing point more. Of course, only so much salt can dissolve in water so the lowest possible freezing temperture for water when using salt (sodium chloride) is -21.1C (-6.0F), but in real-world environments (i.e. for pavement or roads), the practical limit is -9C (15F). This link has a table of different de-icing compounds and their lowest practical temperatures (and pros/cons). You'll note that Calcium Chloride will melt ice down to -29C (-20F). This is the same calcium chloride you can get at pool stores to add calcium to your pool (i.e. to increase Calcium Hardness), but note that surfaces are slippery below -18C (0F). I don't know what is in your expensive compound you used on your walkway, but you are right that it could have been something that dissolves into more parts than salt in water.
Richard
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