let , equations, and monads

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let , equations, and monads

Patrick Browne

{- From Learn Haskell Fast and Hard : 4.3.1.  Maybe is a monad
 http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/#maybe-monad
 
 Concerning the code below I have the following questions:
 1) Are eligibleLet and eligibleEquational operationally equivalent (i.e. perform the same operations) and/or semantically equivalent(i.e. Church-Rosser)?
 2) Apart from the return type of Maybe instead of Bool how does eligibleMonad differ from eligibleLet?
 
 Regards,
 Pat
 -}

deposit  value account = account + value
withdraw value account = account - value

-- You are eligible for a bonus only if your sequence of transactions stays out of the red.
eligibleLet :: (Num a,Ord a) => a -> Bool
eligibleLet account =
  let account1 = deposit 100 account in
    if (account1 < 0)
    then False
    else
      let account2 = withdraw 200 account1 in
      if (account2 < 0)
      then False
      else
        let account3 = deposit 100 account2 in
        if (account3 < 0)
        then False
        else
          let account4 = withdraw 300 account3 in
          if (account4 < 0)
          then False
          else
            let account5 = deposit 1000 account4 in
            if (account5 < 0)
            then False
            else
              True

-- No let expressions, hence intermediate calculations are performed multiple times.
-- Should terminates on first point of failure    
eligibleEquational :: (Num a,Ord a) => a -> Bool
eligibleEquational account =  if (deposit 100 account) < 0 then False else
                              if (withdraw 200 (deposit 100 account)) < 0  then False  else
                              if (deposit 100 (withdraw 200 (deposit 100 account))) < 0  then False else
                              if (withdraw 300 (deposit 100 (withdraw 200 (deposit 100 account)))) < 0 then False else
                              if (deposit 1000 (withdraw 300 (deposit 100 (withdraw 200 (deposit 100 account))))) < 0 then False else
                               True
    


-- Monadic version    
depositM :: (Num a) => a -> a -> Maybe a
depositM value account = Just (account + value)

withdrawM :: (Num a,Ord a) => a -> a -> Maybe a
withdrawM value account = if (account < value)
                         then Nothing
                         else Just (account - value)

eligibleMonad :: (Num a, Ord a) => a -> Maybe Bool
eligibleMonad account = do
  account1 <- depositM 100 account
  account2 <- withdrawM 200 account1
  account3 <- depositM 100 account2
  account4 <- withdrawM 300 account3
  account5 <- depositM 1000 account4
  Just True

main = do
  print $ eligibleLet 300 -- True
  print $ eligibleLet 299 -- Falsen
  print $ eligibleEquational 300 -- True
  print $ eligibleEquational 299 -- False
  print $ eligibleMonad 300 -- Just True
  print $ eligibleMonad 299 -- Nothing
 
 


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Re: let , equations, and monads

Chaddaï Fouché
Hello,

Le mer. 28 oct. 2015 à 15:59, PATRICK BROWNE <[hidden email]> a écrit :

{- From Learn Haskell Fast and Hard : 4.3.1.  Maybe is a monad
 http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/#maybe-monad
 
 Concerning the code below I have the following questions:
 1) Are eligibleLet and eligibleEquational operationally equivalent (i.e. perform the same operations) and/or semantically equivalent(i.e. Church-Rosser)?


A priori, they're only semantically equivalent since in eligibleEquational intermediary computation are repeated whereas in eligibleLet they're only effectued once.
 

 2) Apart from the return type of Maybe instead of Bool how does eligibleMonad differ from eligibleLet?


eligibleMonad is nice and readable while eligibleLet is a tiresome mess to write and maintain...
Basically in eligibleMonad the logic that checks whether  an operation is possible is rolled into the monadic operations themselves whereas in eligibleLet you have to check every operation validity yourself (so you can forget one or do it incorrectly).

Note that with more familiarity with monads, you would probably rewrite eligibleMonad to avoid naming the intermediary account (and thus avoid any confusion between versions) :

eligibleMonad account = depositM 100 account
  >>= withdrawM 200
  >>= depositM 100
  >>= withdrawM 300
  >>= depositM 1000
  >> Just True

This would make it very easy to add or remove operations.


--
Jedaï

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Re: let , equations, and monads

Patrick Browne

Chaddaï,
Thank you very much for your response to my question. It confirms my intuition, but I was not sure.

Is it true in general that let expressions (e.g. eligibleLet) are always semantically equivalent to their equational  counterparts (e.g. eligibleEquational)? Would it be fair to say that "let" is syntactic sugar for an equational equivalent? Or is there more to it?

With respect to the ordering of the operations is generally true that a monadic version is semantically equivalent to a set of "let expressions"  in a nested if-then-else?

Thanks,
Pat

On 3 November 2015 at 06:56, Chaddaï Fouché <[hidden email]> wrote:
Hello,

Le mer. 28 oct. 2015 à 15:59, PATRICK BROWNE <[hidden email]> a écrit :

{- From Learn Haskell Fast and Hard : 4.3.1.  Maybe is a monad
 http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/#maybe-monad
 
 Concerning the code below I have the following questions:
 1) Are eligibleLet and eligibleEquational operationally equivalent (i.e. perform the same operations) and/or semantically equivalent(i.e. Church-Rosser)?


A priori, they're only semantically equivalent since in eligibleEquational intermediary computation are repeated whereas in eligibleLet they're only effectued once.
 

 2) Apart from the return type of Maybe instead of Bool how does eligibleMonad differ from eligibleLet?


eligibleMonad is nice and readable while eligibleLet is a tiresome mess to write and maintain...
Basically in eligibleMonad the logic that checks whether  an operation is possible is rolled into the monadic operations themselves whereas in eligibleLet you have to check every operation validity yourself (so you can forget one or do it incorrectly).

Note that with more familiarity with monads, you would probably rewrite eligibleMonad to avoid naming the intermediary account (and thus avoid any confusion between versions) :

eligibleMonad account = depositM 100 account
  >>= withdrawM 200
  >>= depositM 100
  >>= withdrawM 300
  >>= depositM 1000
  >> Just True

This would make it very easy to add or remove operations.


--
Jedaï


This email originated from DIT. If you received this email in error, please delete it from your system. Please note that if you are not the named addressee, disclosing, copying, distributing or taking any action based on the contents of this email or attachments is prohibited. www.dit.ie

Is ó ITBÁC a tháinig an ríomhphost seo. Má fuair tú an ríomhphost seo trí earráid, scrios de do chóras é le do thoil. Tabhair ar aird, mura tú an seolaí ainmnithe, go bhfuil dianchosc ar aon nochtadh, aon chóipeáil, aon dáileadh nó ar aon ghníomh a dhéanfar bunaithe ar an ábhar atá sa ríomhphost nó sna hiatáin seo. www.dit.ie

Tá ITBÁC ag aistriú go Gráinseach Ghormáin – DIT is on the move to Grangegorman


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Re: let , equations, and monads

Chaddaï Fouché
Le mar. 3 nov. 2015 à 13:24, PATRICK BROWNE <[hidden email]> a écrit :

Chaddaï,
Thank you very much for your response to my question. It confirms my intuition, but I was not sure.

Is it true in general that let expressions (e.g. eligibleLet) are always semantically equivalent to their equational  counterparts (e.g. eligibleEquational)?


Yes, in Haskell that is true because it is pure/referentially transparent (absent case of misuse of the "escape hatch"es like unsafePerformIO). That is one of the big advantage : that you're always able to reason equationally. (note that this remains true with monads, they're not impure, they're just a notation that can describe impure computations)
 

Would it be fair to say that "let" is syntactic sugar for an equational equivalent? Or is there more to it?


"let x = stuff in expr" is syntactic sugar for "(\x -> expr) stuff" basically. Though there's a few syntactical conveniences that complicate the translation.
 
With respect to the ordering of the operations is generally true that a monadic version is semantically equivalent to a set of "let expressions"  in a nested if-then-else?

Well with the Maybe monad like here yes, though that's more of a nested case-of. With IO this is more complicated, especially if you use forkIO (concurrency).
 

Thanks,

You're welcome !
--
Chaddaï

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