Multiple parameters vs anonymous syntax

Wink Saville

17 Oct 2017 17 Oct '17

1:28 p.m.

I'm going through "Haskell Programming from first principles" and in section 7.3 Anonymous Functions there is an exercise on converting multiple parameters to anonymous functions, and it asks: 1. Which (two or more) of the following are equivalent? mTh1 x y z = x * y * z mTh2 x y = \z -> x * y * z mTh3 x = \y -> \z -> x * y * z mTh4 = \x -> \y -> \z -> x * y * z So I created a file, anon.hs (attached): module Anon where mTh1 x y z = x * y * z mTh2 x y = \z -> x * y * z mTh3 x = \y -> \z -> x * y * z mTh4 = \x -> \y -> \z -> x * y * z I load that into ghci and check the function types: $ ghci anon.hs GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help [1 of 1] Compiling Anon ( anon.hs, interpreted ) Ok, 1 module loaded. *Anon> :t mTh1 mTh1 :: Num a => a -> a -> a -> a *Anon> :t mTh2 mTh2 :: Num a => a -> a -> a -> a *Anon> :t mTh3 mTh3 :: Num a => a -> a -> a -> a *Anon> :t mTh4 mTh4 :: Integer -> Integer -> Integer -> Integer Why is mTh4 different from the rest? On the flip side If I enter "mTh4 = \x -> \y -> \z -> x * y * z" directly in ghci command line then it has same type as the others: $ ghci GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help Prelude> mTh4 = \x -> \y -> \z -> x * y * z Prelude> :t mTh4 mTh4 :: Num a => a -> a -> a -> a -- Wink

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David McBride

17 Oct 17 Oct

1:52 p.m.

It is because of NoMomomorphismRestriction

...

let mTh4 = \x -> \y -> \z -> x * y * z :t mTh4 mTh4 :: Integer -> Integer -> Integer -> Integer :set -XNoMonomorphismRestriction let mTh4 = \x -> \y -> \z -> x * y * z :t mTh4 mTh4 :: Num a => a -> a -> a -> a

I'm not going into it too deeply, as it is somewhat involved and you can read about it but I believe when a function "takes no arguments", it is allowed to specialize polymorphic variables to defaults, and due to the Num constraint it chooses Integer. On Tue, Oct 17, 2017 at 1:28 PM, Wink Saville wrote:

...

I'm going through "Haskell Programming from first principles" and in section 7.3 Anonymous Functions there is an exercise on converting multiple parameters to anonymous functions, and it asks:

1. Which (two or more) of the following are equivalent?

mTh1 x y z = x * y * z mTh2 x y = \z -> x * y * z mTh3 x = \y -> \z -> x * y * z mTh4 = \x -> \y -> \z -> x * y * z

So I created a file, anon.hs (attached):

module Anon where

mTh1 x y z = x * y * z mTh2 x y = \z -> x * y * z mTh3 x = \y -> \z -> x * y * z mTh4 = \x -> \y -> \z -> x * y * z

I load that into ghci and check the function types:

$ ghci anon.hs GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help [1 of 1] Compiling Anon ( anon.hs, interpreted ) Ok, 1 module loaded. *Anon> :t mTh1 mTh1 :: Num a => a -> a -> a -> a *Anon> :t mTh2 mTh2 :: Num a => a -> a -> a -> a *Anon> :t mTh3 mTh3 :: Num a => a -> a -> a -> a *Anon> :t mTh4 mTh4 :: Integer -> Integer -> Integer -> Integer

Why is mTh4 different from the rest?

On the flip side If I enter "mTh4 = \x -> \y -> \z -> x * y * z" directly in ghci command line then it has same type as the others:

$ ghci GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help Prelude> mTh4 = \x -> \y -> \z -> x * y * z Prelude> :t mTh4 mTh4 :: Num a => a -> a -> a -> a

-- Wink

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Wink Saville

2:30 p.m.

Thank you, my head's spinning just starting to read [1] :) BTW, you led me to find the answer to why ghci was different in the interactive mode vs loading. I discovered there are two sets of options used for ghci which are controlled by ":set" and ":seti", [2]. And in the interactive mode we see -XNoMonomorphismRestriction is in effect: Prelude> :seti base language is: Haskell2010 with the following modifiers: -XExtendedDefaultRules -XNoMonomorphismRestriction -XNondecreasingIndentation GHCi-specific dynamic flag settings: other dynamic, non-language, flag settings: -fimplicit-import-qualified warning settings: But it's not in the "non-interactive" mode: Prelude> :set options currently set: none. base language is: Haskell2010 with the following modifiers: -XNondecreasingIndentation GHCi-specific dynamic flag settings: other dynamic, non-language, flag settings: -fimplicit-import-qualified warning settings: [1]: https://wiki.haskell.org/Monomorphism_restriction [2]: https://downloads.haskell.org/~ghc/7.8.4/docs/html/users_guide/ghci-set.html On Tue, Oct 17, 2017 at 10:53 AM David McBride wrote:

...

It is because of NoMomomorphismRestriction

...
let mTh4 = \x -> \y -> \z -> x * y * z

...
:t mTh4 mTh4 :: Integer -> Integer -> Integer -> Integer :set -XNoMonomorphismRestriction let mTh4 = \x -> \y -> \z -> x * y * z

...
:t mTh4 mTh4 :: Num a => a -> a -> a -> a

I'm not going into it too deeply, as it is somewhat involved and you can read about it but I believe when a function "takes no arguments", it is allowed to specialize polymorphic variables to defaults, and due to the Num constraint it chooses Integer.

On Tue, Oct 17, 2017 at 1:28 PM, Wink Saville wrote:

...
I'm going through "Haskell Programming from first principles" and in section 7.3 Anonymous Functions there is an exercise on converting multiple parameters to anonymous functions, and it asks:

1. Which (two or more) of the following are equivalent?

mTh1 x y z = x * y * z mTh2 x y = \z -> x * y * z mTh3 x = \y -> \z -> x * y * z mTh4 = \x -> \y -> \z -> x * y * z

So I created a file, anon.hs (attached):

module Anon where

mTh1 x y z = x * y * z mTh2 x y = \z -> x * y * z mTh3 x = \y -> \z -> x * y * z mTh4 = \x -> \y -> \z -> x * y * z

I load that into ghci and check the function types:

$ ghci anon.hs GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help [1 of 1] Compiling Anon ( anon.hs, interpreted ) Ok, 1 module loaded. *Anon> :t mTh1 mTh1 :: Num a => a -> a -> a -> a *Anon> :t mTh2 mTh2 :: Num a => a -> a -> a -> a *Anon> :t mTh3 mTh3 :: Num a => a -> a -> a -> a *Anon> :t mTh4 mTh4 :: Integer -> Integer -> Integer -> Integer

Why is mTh4 different from the rest?

On the flip side If I enter "mTh4 = \x -> \y -> \z -> x * y * z" directly in ghci command line then it has same type as the others:

$ ghci GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help Prelude> mTh4 = \x -> \y -> \z -> x * y * z Prelude> :t mTh4 mTh4 :: Num a => a -> a -> a -> a

-- Wink

_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

_______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners

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David McBride
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