Final answer:
In the context of a functional programming language, p1 ... pn in match e with | p1 -> e1 | p2 -> e2 | ... | pn -> en are patterns against which an input e is matched to perform different actions based on the pattern it matches.
Step-by-step explanation:
The expression you've posted looks like a pattern matching construct from a functional programming language, such as OCaml or Haskell. In such constructs, p1 ... pn represent different patterns that the input e can match against. When e matches the pattern p1, the expression e1 is evaluated; if it matches pattern p2, then expression e2 is evaluated, and so on, until pn. This kind of construct is typically used in decision making, where based on the pattern that the input e matches, the code takes different actions.
For example, in a program, you might have a situation where based on the type of message received - which could be an error, a warning, or information - you want to perform different actions. This is where pattern matching can be very effective.