What is the correct definition of a Cartesian closed category?

MacLane ("Categories for the Working Mathematician") and many other standard texts do not assume equalizers in a CCC, nor in a Cartesian category. If your interest in CCCs is that they provide categorical models for the typed lambda calculus, then you don't need equalizers (see Lambek and Scott, "Intro. to Higher Order Categorical Logic"), and many of the standard examples in computer science don't have them. I can recall only one case of the other usage, where CCCs have all finite limits, and even there it was explained as a nonstandard convention. Freyd and Scedrov ("Categories - Allegories") define "Cartesian" to mean having all finite limits. Obviously one associates Cartesian coordinates with finite products, but they point out that Descartes was also concerned with equationally defined subsets, and those are equalizers. They avoid the phrase "Cartesian closed category". If you want my personal opinion, it's that neither CCCs nor - despite the force of Freyd and Scedrov's comment - Cartesian categories are exected to have limits other than finite products. Steve Vickers.