Appeared in J. Theoretical Computer Science, 117 (1993), 23-38.
Identities are the icing on the mathematical cake. Our puritan mathematical education made us feel guilty of licking the icing without eating the cake. But sometimes only tasting the icing would not only give us more enjoyment, but could lead to better cakes and better icings.
This article is based in my invited lecture at the historical FPSAC III (May 2-4 1991) conference, organized so efficiently and pleasantly by the Bordelaise. A highlight of this conference was Mireille Bousquet-Melou's defense of her thesis.
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