[Haskell-cafe] Is it possible to change the environment (reader) in applicative style?

[Tom Ellis]

On Tue, Sep 11, 2018 at 10:50:41PM -0300, Rodrigo Stevaux wrote:
> It is easy to read an environment in applicative style, ie:
> 
> type Env = [(String, Int)]
> data Term = Add Term Term | Number Int | Var String deriving Show
> eval :: Term -> Env -> Int
> eval (Add a b) = (+) <$> eval a <*> eval b
> eval (Var name) = fetch name
> eval (Number i) = pure i
> 
> fetch :: String -> Env -> Int
> fetch name = fromJust . lookup name
> 
> But can the eval function change the Env being passed, as to implement
> a "let" operation, without using monads? I tried I lot but ultimately
> I resorted to (>>=) in the function monad:
> 
> bind f k = \r -> k (f r) r

I'm confused by this.  Your `bind` doesn't seem to change the Env being
passed.  Can you explain?

> I do not think so, because in applicative style each operand can have
> an effect (reading the environment) but can not affect other operands
> (including the next ones), i.e., there is no notion of sequencing in
> applicatives
> 
> Is this reasoning right?

Your conclusion may be right but I don't think that your reasoning is. 
Certainly an applicative action can affect the subsequent operations.  State
is Applicative after all!

Tom