No.
Some may be considered as leaves but not really. Christmas cactus for instance grows in thin segmented stalks reminiscent of leaves. Cactus flowers have petal that are leafy and green like leaves but not really leaves. barrel cactus and saquaros obviously have no leafy protrusions beyond their flowers.
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actually, One defining feature of cacti is having clusters of spines. Numerous plants have spines of course, but in cacti, spines occur in clusters in the axil of leaves, even though the leaves are usually microscopic. Most cactus morphologists have concluded that cactus spines are either modified leaves or modified bud scales (the difference is inconsequential because bud scales themselves are modified leaves).
Cactus have leaves. But their leaves are special, that their leaves are needle-like leaves. It is because, it prevents the cactus from losing water.
By evolution
Extremely carefully.
Plants in different environments makes changes in its structure when it starts growing. These are adaptations. For example Cactus are made up of a fleshy leaves with no leaves except for thorns which plays an important role in reducing water through evaporation (transpiration). Pine trees as we know are conical and its leaves are needle-shaped so as to reduce water loss. Under various changes, their normal disposition changes. Their structure changes for the worse.
A cactus is a carnivore; they enjoy eating desert foxes and the odd rat or two.
An example of mutualism in a desert biome is the desert is the relationship between Saguaro cacti and the Gila woodpecker. This bird finds food like parasites and insects on the cactus. It also nests on cacti. While the cacti provide food and shelter for this bird, the bird in turn helps cacti when it spreads pollen to other cacti. Mutualism refers to a relationship in which both parties benefit from their interaction.