On Wed, 23 Dec 2020, Lawrence Bottorff
I have these three versions of addition
addA x y = x + y addB x = \y -> x + y addC = \x -> \y -> x + y
and all three add two arguments just fine
addA 2 3 5 addB 2 3 5 addC 2 3 5
but I can't see how addB and addC are actually accomplishing this. addA is currying, which I don't fully follow. addC I understand beta reduction-wise
(\x -> \y -> x + y) 2 3 (\y -> 2 + y) 3 (2 + 3) 5
but I don't understand addB and what steps are happening currying/beta reduction-wise. Can someone break down the steps with addA and addB?
LB
Dear Lawrence Bottorf, your questions are delightful! Heaven forwarding, I will respond more fully and clearly. The questions you ask strike at the heart of the issue: Why is Haskell so hard to learn? I offer no decent answer here, but I give below a transcript of an incoherent session with ghci on panix3.panix.com, panix3% ghci --version The Glorious Glasgow Haskell Compilation System, version 7.8.4 panix3% uname -a NetBSD panix3.panix.com 9.0 NetBSD 9.0 (PANIX-XEN-USER) #1: Sun May 3 21:15:18 EDT 2020 root@juggler.panix.com:/misc/obj64/misc/devel/netbsd/9.0/src/sys/arch/amd64/compile/PANIX-XEN-USER amd64 panix3% Below is the whole transcript of the session. Note two things: 1. I do not know ghci. 2. I failed to ask the ':t" questions in the right order, for a good training video. But I hope the transcript is helpful. oo--JS. bash-5.0$ ghci GHCi, version 7.8.4: http://www.haskell.org/ghc/ :? for help Loading package ghc-prim ... linking ... done. Loading package integer-gmp ... linking ... done. Loading package base ... linking ... done. Prelude> let addA x y = x + y Prelude> addA <interactive>:6:1: No instance for (Show (a0 -> a0 -> a0)) arising from a use of `print' In a stmt of an interactive GHCi command: print it Prelude> print addA <interactive>:7:1: No instance for (Show (a0 -> a0 -> a0)) arising from a use of `print' In the expression: print addA In an equation for `it': it = print addA <interactive>:7:7: No instance for (Num a0) arising from a use of `addA' The type variable `a0' is ambiguous Note: there are several potential instances: instance Num Double -- Defined in `GHC.Float' instance Num Float -- Defined in `GHC.Float' instance Integral a => Num (GHC.Real.Ratio a) -- Defined in `GHC.Real' ...plus three others In the first argument of `print', namely `addA' In the expression: print addA In an equation for `it': it = print addA Prelude> let addA x y = x + y Prelude> print it <interactive>:9:7: Not in scope: `it' Perhaps you meant `id' (imported from Prelude) Prelude> addA <interactive>:10:1: No instance for (Show (a0 -> a0 -> a0)) arising from a use of `print' In a stmt of an interactive GHCi command: print it Prelude> addA 7 <interactive>:11:1: No instance for (Show (a0 -> a0)) arising from a use of `print' In a stmt of an interactive GHCi command: print it Prelude> addA 7 5 12 Prelude> (addA 7) <interactive>:13:1: No instance for (Show (a0 -> a0)) arising from a use of `print' In a stmt of an interactive GHCi command: print it Prelude> :t (addA 7) (addA 7) :: Num a => a -> a Prelude> :t addA addA :: Num a => a -> a -> a Prelude> :t addA 7 addA 7 :: Num a => a -> a Prelude> :t addA 7 5 addA 7 5 :: Num a => a Prelude> let addB x = \y -> x + y Prelude> :t addB addB :: Num a => a -> a -> a Prelude> :t addB 7 addB 7 :: Num a => a -> a Prelude> :t (addB 7) (addB 7) :: Num a => a -> a Prelude> :t addB 7 5 addB 7 5 :: Num a => a Prelude> let addC = \x -> \y -> x + y Prelude> :t addC addC :: Num a => a -> a -> a Prelude> :t (addC) (addC) :: Num a => a -> a -> a Prelude> :t addC 7 addC 7 :: Num a => a -> a Prelude> :t (addC 7) (addC 7) :: Num a => a -> a Prelude> :t addC 7 5 addC 7 5 :: Num a => a Prelude> addC 7 5 12 Prelude> (addC 7 5) 12 Prelude> (exit) <interactive>:31:2: Not in scope: `exit' Prelude> Leaving GHCi. bash-5.0$