Answer: Corsican mint (Mentha requienii) is a creeping, mat forming, spreading plant, growing only 1/2" high. The leaves are tiny, round, and bright green; flowers are light purple. This is an excellent groundcover plant in sunny or partly shady spots and it will spread rapidly.
Irish moss isn't a moss at all, but Sagina subulata, a moss-looking groundcover, that thrives in rich, moist soil, in full sunshine to partial shade. This plant flowers in the summer months and is useful for filling in between stepping stones. It does spread, but tends to form humps rather than hug the ground.
Your choice of plants will depend upon whether you want an undulating mat as a groundcover or one that's reasonably level. Both will fit the situation you describe.
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