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Q&A Where does the name of the `pure` function in the `Applicative` type class come from?

A direct answer to your question of where the name comes from is the paper that introduced Applicative functors, Applicative programming with effects (PDF). Quoting from there: The idea is that ...

posted 6mo ago by Derek Elkins‭  ·  edited 6mo ago by Derek Elkins‭

Answer
#2: Post edited by user avatar Derek Elkins‭ · 2024-06-02T20:55:22Z (6 months ago)
  • A direct answer to your question of where the name comes from is the paper that introduced Applicative functors, [Applicative programming with effects](https://dl.acm.org/doi/10.1017/S0956796807006326) ([PDF](https://www.staff.city.ac.uk/~ross/papers/Applicative.pdf)). Quoting from there:
  • > The idea is that `pure` embeds pure computations into the pure fragment of an effectful world[.]
  • I would say this is indeed the intuition many Haskell (and presumably PureScript) programmers have for it.
  • The intuition is that a type like `F a` for a monad or applicative functor `F` *models* a computation that may have effects. `pure x` then models the "effectful computation" that happens to have no effects and returns `x`, i.e. is pure in the sense of "pure functional programming".
  • A direct answer to your question of where the name comes from is the paper that introduced Applicative functors, [Applicative programming with effects](https://dl.acm.org/doi/10.1017/S0956796807006326) ([PDF](https://www.staff.city.ac.uk/~ross/papers/Applicative.pdf)). Quoting from there:
  • > The idea is that `pure` embeds pure computations into the pure fragment of an effectful world[.]
  • I would say this is indeed the intuition many Haskell (and presumably PureScript) programmers have for it.
  • The intuition is that a type like `F a` for a monad or applicative functor `F` *models* a computation that may have effects. `pure x` then models the "effectful computation" that happens to have no effects and returns `x`, i.e. is pure in the sense of "pure functional programming". The "lifting" intuition should also be reasonably clear here. We're "lifting" "pure" computations into the world of effectful computations.
#1: Initial revision by user avatar Derek Elkins‭ · 2024-06-02T20:54:13Z (6 months ago)
A direct answer to your question of where the name comes from is the paper that introduced Applicative functors, [Applicative programming with effects](https://dl.acm.org/doi/10.1017/S0956796807006326) ([PDF](https://www.staff.city.ac.uk/~ross/papers/Applicative.pdf)). Quoting from there:

> The idea is that `pure` embeds pure computations into the pure fragment of an effectful world[.]

I would say this is indeed the intuition many Haskell (and presumably PureScript) programmers have for it.

The intuition is that a type like `F a` for a monad or applicative functor `F` *models* a computation that may have effects. `pure x` then models the "effectful computation" that happens to have no effects and returns `x`, i.e. is pure in the sense of "pure functional programming".