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<div>Accchhhh</div>
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<div>Thats another level of pain, i'm not a big haskeller so i'll have to wrestle with it to get all the knobs and dials working, leave it with me for the moment and i'll start wrestling with cabal<br>
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Excuse the spelling, sent from a phone with itty bitty keys, it like trying to sow a button on a shirt with a sausage.
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On 29 Apr 2015, at 12:43, Richard Eisenberg <<a href="mailto:eir@cis.upenn.edu">eir@cis.upenn.edu</a>> wrote:<br>
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<div>Hello Mark,</div>
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<div>Your suspicion that your singleton tree type is wrong is well-founded.</div>
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<div>The problem is that, in my opinion, that exercise is mentioned too early in the tutorial. To properly implement a singleton type for a parameterized type, like a binary tree, you will need `data family Sing (a :: k)`, as explained just a little bit further
down in the post. You'll need to rewrite your definition for singleton numbers and booleans to work with `Sing` as well.</div>
<div><br>
</div>
<div>Your code except the definition for SBranch is all correct. The problem with your definition is that you don't get the right information when pattern-matching. For example, say you have x with type `SBTree a`. If you successfully pattern match against
`SBranch SZ SLeaf SLeaf`, you would want to learn `a ~ Branch Z Leaf Leaf`. But that's not what you'll get in your implementation: you'll get a type error saying that we don't know that `a0` is an `SNat`, where `a ~ Branch a0 Leaf Leaf`, or something like
that. The type-level information is simply encoded in the wrong place for this to work out.</div>
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<div>Write back and I'll give you the full answer if this isn't enough to get you moving in the right direction!</div>
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<div>Richard</div>
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<div>On Apr 28, 2015, at 10:45 AM, "Nicholls, Mark" <<a href="mailto:nicholls.mark@vimn.com">nicholls.mark@vimn.com</a>> wrote:</div>
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<div lang="EN-US" link="blue" vlink="purple" style="font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; ">
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<span style="color: rgb(31, 73, 125); ">Can someone check my answer (no I’m not doing an assessment…I’m actually learning stuff out of interest!)<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">working through<o:p></o:p></span></div>
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<span lang="EN-GB"> </span></div>
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<span lang="EN-GB"><a href="https://www.fpcomplete.com/user/konn/prove-your-haskell-for-great-safety/dependent-types-in-haskell" style="color: purple; text-decoration: underline; ">https://www.fpcomplete.com/user/konn/prove-your-haskell-for-great-safety/dependent-types-in-haskell</a><o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">still there is a section about singleton types and the exercise is<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">“Exercise: Define the binary tree type and implement its singleton type.”<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Ok, I think I’m probably wrong….a binary tree is something like…<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">> data BTree a = Leaf | Branch a (BTree a) (BTree a)<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">With DataKind<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">My logic goes…<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Leaf is an uninhabited type, so I need a value isomorphic to it….<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Easy?<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">> data SBTree a where<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">> SLeaf :: SBTree Leaf<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Things like<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Branch Integer Leaf (Branch String Leaf Leaf)<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Are uninhabited…so I need to add<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">> SBranch :: (a :: *) -> (SBTree (b :: BTree *)) -> (SBTree (c :: BTree *)) -> SBTree (Branch a b c)<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">?<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">It compiles…but….is it actually correct?<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "><o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Things like<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">> y = SBranch (SS (SS SZ)) SLeaf SLeaf<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">> z = SBranch (SS (SS SZ)) (SBranch SZ SLeaf SLeaf) SLeaf<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span style="color: rgb(31, 73, 125); ">Seem to make sense ish.<o:p></o:p></span></div>
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<span style="color: rgb(31, 73, 125); "> </span></div>
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<b><span style="font-size: 10pt; font-family: Tahoma, sans-serif; ">From:</span></b><span style="font-size: 10pt; font-family: Tahoma, sans-serif; "><span class="Apple-converted-space"> </span>Nicholls, Mark<span class="Apple-converted-space"> </span><br>
<b>Sent:</b><span class="Apple-converted-space"> </span>28 April 2015 9:33 AM<br>
<b>To:</b><span class="Apple-converted-space"> </span>Nicholls, Mark<br>
<b>Subject:</b><span class="Apple-converted-space"> </span>sds<o:p></o:p></span></div>
</div>
</div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<o:p> </o:p></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">Hello,<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">working through<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"><a href="https://www.fpcomplete.com/user/konn/prove-your-haskell-for-great-safety/dependent-types-in-haskell" style="color: purple; text-decoration: underline; ">https://www.fpcomplete.com/user/konn/prove-your-haskell-for-great-safety/dependent-types-in-haskell</a><o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">but a bit stuck...with an error...<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> {-# LANGUAGE DataKinds, TypeFamilies, TypeOperators, UndecidableInstances, GADTs, StandaloneDeriving #-}<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> data Nat = Z | S Nat<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> data Vector a n where<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> Nil :: Vector a Z<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> (:-) :: a -> Vector a n -> Vector a (S n)<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> infixr 5 :-<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">I assume init...is a bit like tail but take n - 1 elements from the front....but...<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> init' :: Vector a ('S n) -> Vector a n<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> init' (x :- Nil) = Nil<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> init' (x :- xs@(_ :- _)) = x :- (init' xs)<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> zipWithSame :: (a -> b -> c) -> Vector a n -> Vector b n -> Vector c n<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> zipWithSame f Nil Nil = Nil<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB">> zipWithSame f (x :- xs) (y :- xs@(_ :- _)) = Nil<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB"> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<b><span lang="EN-GB" style="font-size: 8pt; font-family: Tahoma, sans-serif; color: teal; ">Mark Nicholls<span class="Apple-converted-space"> </span></span></b><span lang="EN-GB" style="font-size: 8pt; font-family: Tahoma, sans-serif; color: teal; ">| Senior
Technical Director, Programmes & Development - Viacom International Media Networks</span><span lang="EN-GB" style="font-size: 8pt; color: rgb(31, 73, 125); "><br>
</span><b><span lang="EN-GB" style="font-size: 8pt; font-family: Tahoma, sans-serif; color: teal; ">A:</span></b><span lang="EN-GB" style="font-size: 8pt; color: rgb(31, 73, 125); "> </span><span lang="EN-GB" style="font-size: 8pt; font-family: Tahoma, sans-serif; color: teal; ">17-29
Hawley Crescent London NW1 8TT |<span class="Apple-converted-space"> </span><b>e:</b><span class="Apple-converted-space"> </span><a href="mailto:mik@vimn.com" style="color: purple; text-decoration: underline; ">Nicholls.Mark@vimn.com</a><span class="Apple-converted-space"> </span>T<b>:</b></span><span lang="EN-GB" style="font-size: 8pt; color: rgb(31, 73, 125); "> </span><span lang="EN-GB" style="font-size: 8pt; font-family: Tahoma, sans-serif; color: teal; ">+44
(0)203 580 2223<o:p></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB" style="font-size: 10pt; color: rgb(31, 73, 125); "> </span></div>
<div style="margin: 0cm 0cm 0.0001pt 36pt; font-size: 11pt; font-family: Calibri, sans-serif; ">
<span lang="EN-GB" style="color: rgb(31, 73, 125); "><image001.png></span><span style="color: rgb(31, 73, 125); "><o:p></o:p></span></div>
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<span lang="EN-GB"> </span></div>
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