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It's one of the simple ones: f˙𝕩 is f. And 𝕨f˙𝕩? It's f. Like the identity functions, Constant doesn't compute anything but just returns one of its inputs. It's somewhat different in that it's a deferred modifier, so you have to first apply Constant to its operand and then to some arguments for that non-event to happen.
The design of BQN makes Constant unnecessary in most cases, because when a non-operation (number, character, array, namespace) is applied it already returns itself: π˙ is the same function as π. If you've used much tacit programming, you've probably written a few trains like 2×+ (twice the sum), which is nicer than the equivalent 2˙×+. However, a train has to end with a function, so you can't just put a number at the end. Applying ˙ is a convenient way to change the number from a subject to a function role.
+÷2 # A number
+÷2˙ # A function
3 (+÷2˙) 7
When programming with first-class functions, the constant application shortcut becomes a hazard! Consider the program {𝕨⌾(2⊸⊑) 𝕩} to insert 𝕨 into an array 𝕩 as an element. It works fine with a number, but with a function it's broken:
∞ {𝕨⌾(2⊸⊑) 𝕩} 1‿2‿3‿4
M ← -
m {𝕨⌾(2⊸⊑) 𝕩} 1‿2‿3‿4
Here m is applied to 2⊑𝕩 even though we want to discard that value. Spelled as m, our context-free grammar knows it's a function argument, but this doesn't affect later usage. Under always applies 𝔽 as a function. The proper definition of the insertion function should use a ˙, like this:
m {𝕨˙⌾(2⊸⊑) 𝕩} 1‿2‿3‿4