Issues with quickSort in chapter 6 about liquidhaskell-tutorial

[skyzh]

I've also tested my code on the online version, which caused the same issue. http://ucsd-progsys.github.io/liquidhaskell-tutorial/07-measure-int.html#/program-40

[ranjitjhala]

thanks for posting this! Indeed The issue here is that ++ is defined using “Len” not “size”. Two solutions: 1 use “Len” instead of “size” In the spec of “partition” 2 tell LH that “Len” is the same as “size” by specifying that Size :: xs:_ -> {v:Nat| v= Len xs} Does that help? output type of size :: You can tell LH that len and size are the same th

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On Fri, Feb 15, 2019 at 9:10 PM Alex Chi ***@***.***> wrote: Hello! I encountered some problems when I was trying solving exercise 6.6 Exercise 6.6 (QuickSort). Use partition to implement quickSort. -- >> quickSort [1,4,3,2] -- [1,2,3,4] {-@ quickSort :: (Ord a) => xs:List a -> ListX a xs @-} quickSort [] = [] quickSort (x:xs) = undefined {-@ test10 :: ListN String 2 @-} test10 = quickSort test4 Here's my implementation: {-@ partition :: _ -> xs:_ -> {v:_ | Sum2 v (size xs)} @-} {-@ predicate Sum2 X N = size (fst X) + size (snd X) = N @-} partition :: (a -> Bool) -> [a] -> ([a], [a]) partition _ [] = ([], []) partition f (x:xs) | f x = (x:ys, zs) | otherwise = (ys, x:zs) where (ys, zs) = partition f xs -- exercise 6.6 {-@ quickSort' :: (Ord a) => xs:List a -> ListX a xs @-}quickSort' :: (Ord a) => [a] -> [a] quickSort' [] = [] quickSort' (x:xs) = let (l, r) = partition cmp xs cmp t = t < x in quickSort' l ++ [x] ++ quickSort' r Which I got the following error: /Users/skyzh/Work/playground/src/Ex06.hs:152:6-17: Error: Liquid Type Mismatch 152 | quickSort' l ++ [x] ++ quickSort' r ^^^^^^^^^^^^ Inferred type VV : {v : [a##xo] | len v >= 0 && v == fst ?a && v /= ?b && Ex06.size v >= 0} not a subtype of Required type VV : {VV : [a##xo] | len VV < len ?b && len VV >= 0} In Context xs : {v : [a##xo] | Ex06.size v >= 0 && len v >= 0} ?b : {?b : [a##xo] | Ex06.size ?b >= 0 && len ?b >= 0} x : a##xo ?a : {?a : ([a##xo], [a##xo]) | Ex06.size (fst ?a) + Ex06.size (snd ?a) == Ex06.size xs} /Users/skyzh/Work/playground/src/Ex06.hs:152:6-40: Error: Liquid Type Mismatch 152 | quickSort' l ++ [x] ++ quickSort' r ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Inferred type VV : {v : [a##xo] | len v == len ?f + len ?b && Ex06.size v >= 0 && len v >= 0} not a subtype of Required type VV : {VV : [a##xo] | Ex06.size VV == Ex06.size ?e} In Context ?g : {?g : [a##xo] | (Ex06.notEmpty ?g <=> false) && Ex06.size ?g == 0 && len ?g == 0 && Ex06.size ?g >= 0 && len ?g >= 0} xs : {v : [a##xo] | Ex06.size v >= 0 && len v >= 0} ?f : {?f : [a##xo] | Ex06.size ?f == Ex06.size (fst ?c) && Ex06.size ?f >= 0 && len ?f >= 0} ?c : {?c : ([a##xo], [a##xo]) | Ex06.size (fst ?c) + Ex06.size (snd ?c) == Ex06.size xs} ?e : {?e : [a##xo] | Ex06.size ?e >= 0 && len ?e >= 0} ?b : {?b : [a##xo] | len ?b == len ?a + len ?d && Ex06.size ?b >= 0 && len ?b >= 0} x : a##xo ?d : {?d : [a##xo] | Ex06.size ?d == Ex06.size (snd ?c) && Ex06.size ?d >= 0 && len ?d >= 0} ?a : {?a : [a##xo] | tail ?a == ?g && head ?a == x && (Ex06.notEmpty ?a <=> true) && Ex06.size ?a == 1 + Ex06.size ?g && len ?a == 1 + len ?g && Ex06.size ?a >= 0 && len ?a >= 0} /Users/skyzh/Work/playground/src/Ex06.hs:152:29-40: Error: Liquid Type Mismatch 152 | quickSort' l ++ [x] ++ quickSort' r ^^^^^^^^^^^^ Inferred type VV : {v : [a##xo] | len v >= 0 && v == snd ?a && v /= ?b && Ex06.size v >= 0} not a subtype of Required type VV : {VV : [a##xo] | len VV < len ?b && len VV >= 0} In Context xs : {v : [a##xo] | Ex06.size v >= 0 && len v >= 0} ?b : {?b : [a##xo] | Ex06.size ?b >= 0 && len ?b >= 0} x : a##xo ?a : {?a : ([a##xo], [a##xo]) | Ex06.size (fst ?a) + Ex06.size (snd ?a) == Ex06.size xs} And I suspect that Liquid Haskell may fail to deduce the size of operator ++. Then I made an experiment to test. {-@ (+++) :: xs: List a -> ys: List a -> ListN a {size xs + size ys} @-}(+++) :: [a] -> [a] -> [a] a +++ b = a ++ b And certainly I got the following error: /Users/skyzh/Work/playground/src/Ex06.hs:143:11-16: Error: Liquid Type Mismatch 143 | a +++ b = a ++ b ^^^^^^ Inferred type VV : {v : [a##xo] | len v == len a + len b && Ex06.size v >= 0 && len v >= 0} not a subtype of Required type VV : {VV : [a##xo] | Ex06.size VV == Ex06.size a + Ex06.size b} In Context a : {a : [a##xo] | Ex06.size a >= 0 && len a >= 0} b : {b : [a##xo] | Ex06.size b >= 0 && len b >= 0} Is there anyway to make Liquid Haskell deduce that ++ can correctly add up size? Thank you for reading this issue! — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#79>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ABkuOA8YXdTX67XcotN8eqqdQb6OASB0ks5vN5KKgaJpZM4a-yhy> .

[ranjitjhala]

But this is not something you should have to worry about for this exercise — I think some of the LH defaults have changed since I wrote it so don’t close the issue, I’ll fix the tutorial. Than again!

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On Fri, Feb 15, 2019 at 9:25 PM Ranjit Jhala ***@***.***> wrote: thanks for posting this! Indeed The issue here is that ++ is defined using “Len” not “size”. Two solutions: 1 use “Len” instead of “size” In the spec of “partition” 2 tell LH that “Len” is the same as “size” by specifying that Size :: xs:_ -> {v:Nat| v= Len xs} Does that help? output type of size :: You can tell LH that len and size are the same th On Fri, Feb 15, 2019 at 9:10 PM Alex Chi ***@***.***> wrote: > Hello! I encountered some problems when I was trying solving exercise 6.6 > > Exercise 6.6 (QuickSort). Use partition to implement quickSort. > -- >> quickSort [1,4,3,2] > -- [1,2,3,4] > {-@ quickSort :: (Ord a) => xs:List a -> ListX a xs @-} > quickSort [] = [] > quickSort (x:xs) = undefined > {-@ test10 :: ListN String 2 @-} > test10 = quickSort test4 > > Here's my implementation: > > {-@ partition :: _ -> xs:_ -> {v:_ | Sum2 v (size xs)} @-} > {-@ predicate Sum2 X N = size (fst X) + size (snd X) = N @-} > partition :: (a -> Bool) -> [a] -> ([a], [a]) > partition _ [] = ([], []) > partition f (x:xs) > | f x = (x:ys, zs) > | otherwise = (ys, x:zs) > where > (ys, zs) = partition f xs > -- exercise 6.6 > {-@ quickSort' :: (Ord a) => xs:List a -> ListX a xs @-}quickSort' :: (Ord a) => [a] -> [a] > quickSort' [] = [] > quickSort' (x:xs) = let > (l, r) = partition cmp xs > cmp t = t < x in > quickSort' l ++ [x] ++ quickSort' r > > Which I got the following error: > > /Users/skyzh/Work/playground/src/Ex06.hs:152:6-17: Error: Liquid Type Mismatch > > 152 | quickSort' l ++ [x] ++ quickSort' r > ^^^^^^^^^^^^ > > Inferred type > VV : {v : [a##xo] | len v >= 0 > && v == fst ?a > && v /= ?b > && Ex06.size v >= 0} > > not a subtype of Required type > VV : {VV : [a##xo] | len VV < len ?b > && len VV >= 0} > > In Context > xs : {v : [a##xo] | Ex06.size v >= 0 > && len v >= 0} > > ?b : {?b : [a##xo] | Ex06.size ?b >= 0 > && len ?b >= 0} > > x : a##xo > > ?a : {?a : ([a##xo], [a##xo]) | Ex06.size (fst ?a) + Ex06.size (snd ?a) == Ex06.size xs} > > > /Users/skyzh/Work/playground/src/Ex06.hs:152:6-40: Error: Liquid Type Mismatch > > 152 | quickSort' l ++ [x] ++ quickSort' r > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > > Inferred type > VV : {v : [a##xo] | len v == len ?f + len ?b > && Ex06.size v >= 0 > && len v >= 0} > > not a subtype of Required type > VV : {VV : [a##xo] | Ex06.size VV == Ex06.size ?e} > > In Context > ?g : {?g : [a##xo] | (Ex06.notEmpty ?g <=> false) > && Ex06.size ?g == 0 > && len ?g == 0 > && Ex06.size ?g >= 0 > && len ?g >= 0} > > xs : {v : [a##xo] | Ex06.size v >= 0 > && len v >= 0} > > ?f : {?f : [a##xo] | Ex06.size ?f == Ex06.size (fst ?c) > && Ex06.size ?f >= 0 > && len ?f >= 0} > > ?c : {?c : ([a##xo], [a##xo]) | Ex06.size (fst ?c) + Ex06.size (snd ?c) == Ex06.size xs} > > ?e : {?e : [a##xo] | Ex06.size ?e >= 0 > && len ?e >= 0} > > ?b : {?b : [a##xo] | len ?b == len ?a + len ?d > && Ex06.size ?b >= 0 > && len ?b >= 0} > > x : a##xo > > ?d : {?d : [a##xo] | Ex06.size ?d == Ex06.size (snd ?c) > && Ex06.size ?d >= 0 > && len ?d >= 0} > > ?a : {?a : [a##xo] | tail ?a == ?g > && head ?a == x > && (Ex06.notEmpty ?a <=> true) > && Ex06.size ?a == 1 + Ex06.size ?g > && len ?a == 1 + len ?g > && Ex06.size ?a >= 0 > && len ?a >= 0} > > > /Users/skyzh/Work/playground/src/Ex06.hs:152:29-40: Error: Liquid Type Mismatch > > 152 | quickSort' l ++ [x] ++ quickSort' r > ^^^^^^^^^^^^ > > Inferred type > VV : {v : [a##xo] | len v >= 0 > && v == snd ?a > && v /= ?b > && Ex06.size v >= 0} > > not a subtype of Required type > VV : {VV : [a##xo] | len VV < len ?b > && len VV >= 0} > > In Context > xs : {v : [a##xo] | Ex06.size v >= 0 > && len v >= 0} > > ?b : {?b : [a##xo] | Ex06.size ?b >= 0 > && len ?b >= 0} > > x : a##xo > > ?a : {?a : ([a##xo], [a##xo]) | Ex06.size (fst ?a) + Ex06.size (snd ?a) == Ex06.size xs} > > And I suspect that Liquid Haskell may fail to deduce the size of > operator ++. Then I made an experiment to test. > > {-@ (+++) :: xs: List a -> ys: List a -> ListN a {size xs + size ys} @-}(+++) :: [a] -> [a] -> [a] > a +++ b = a ++ b > > And certainly I got the following error: > > /Users/skyzh/Work/playground/src/Ex06.hs:143:11-16: Error: Liquid Type Mismatch > > 143 | a +++ b = a ++ b > ^^^^^^ > > Inferred type > VV : {v : [a##xo] | len v == len a + len b > && Ex06.size v >= 0 > && len v >= 0} > > not a subtype of Required type > VV : {VV : [a##xo] | Ex06.size VV == Ex06.size a + Ex06.size b} > > In Context > a : {a : [a##xo] | Ex06.size a >= 0 > && len a >= 0} > > b : {b : [a##xo] | Ex06.size b >= 0 > && len b >= 0} > > Is there anyway to make Liquid Haskell deduce that ++ can correctly add > up size? > > Thank you for reading this issue! > > — > You are receiving this because you are subscribed to this thread. > Reply to this email directly, view it on GitHub > <#79>, or mute > the thread > <https://github.com/notifications/unsubscribe-auth/ABkuOA8YXdTX67XcotN8eqqdQb6OASB0ks5vN5KKgaJpZM4a-yhy> > . >

[skyzh]

Thank you for your response! I've just figured out a working example by defining pivApp similar to http://goto.ucsd.edu/~gridaphobe/liquid/haskell/blog/blog/2013/07/29/putting-things-in-order.lhs/

https://github.com/SkyZH/introliquid.hs/blob/master/src/Ex06.hs#L150

[ranjitjhala]

Excellent!!

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On Fri, Feb 15, 2019 at 9:33 PM Alex Chi ***@***.***> wrote: Thank you for your response! I've just figured out a working example by defining pivApp similar to http://goto.ucsd.edu/~gridaphobe/liquid/haskell/blog/blog/2013/07/29/putting-things-in-order.lhs/ https://github.com/SkyZH/introliquid.hs/blob/master/src/Ex06.hs#L150 — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#79 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ABkuOPa1l1BfIL46FG5wXW6h5oqwuvDWks5vN5gIgaJpZM4a-yhy> .

[skyzh]

I've missed your first reply...

1. use “Len” instead of “size” In the spec of “partition” does not help, because ListN is defined by size...

2. tell LH that “Len” is the same as “size” by specifying that does not help.

{-@ measure size @-}
{-@ size :: xs:[a] -> {v:Nat | v = len xs} @-}
size :: [a] -> Int
size [] = 0
size (_:rs) = 1 + size rs

/Users/skyzh/Work/playground/src/Ex06.hs:157:5-17: Error: Liquid Type Mismatch

 157 |     l ++ [x] ++ r
           ^^^^^^^^^^^^^

   Inferred type
     VV : {v : [a##xo] | len v == len (Ex06.fst ?f) + len ?b
                         && Ex06.size v >= 0
                         && len v >= 0}

   not a subtype of Required type
     VV : {VV : [a##xo] | Ex06.size VV == Ex06.size ?e}

   In Context
     xs : {v : [a##xo] | Ex06.size v >= 0
                         && len v >= 0}

     ?f : {?f : ([a##xo], [a##xo]) | Ex06.size (fst ?f) + Ex06.size (snd ?f) == Ex06.size xs
                                     && len (fst ?f) + len (snd ?f) == Ex06.size xs}

     ?c : {?c : [a##xo] | tail ?c == ?a
                          && head ?c == x
                          && (Ex06.notEmpty ?c <=> true)
                          && Ex06.size ?c == 1 + Ex06.size ?a
                          && len ?c == 1 + len ?a
                          && Ex06.size ?c >= 0
                          && len ?c >= 0}

     ?e : {?e : [a##xo] | Ex06.size ?e >= 0
                          && len ?e >= 0}

     ?b : {?b : [a##xo] | len ?b == len ?c + len (Ex06.snd ?f)
                          && Ex06.size ?b >= 0
                          && len ?b >= 0}

     x : a##xo

     ?a : {?a : [a##xo] | (Ex06.notEmpty ?a <=> false)
                          && Ex06.size ?a == 0
                          && len ?a == 0
                          && Ex06.size ?a >= 0
                          && len ?a >= 0}

3. replace all size with len this is ok 💯, here's the working example https://github.com/SkyZH/introliquid.hs/blob/master/src/Ex06len.hs

[skyzh]

2. tell LH that “Len” is the same as “size” by specifying that still does not help if I change the definition from the one in the previous comment into:

  {-@ measure size @-}
- {-@ size :: xs::[a]-> {v:Nat | v = len xs} @-}
+ {-@ size :: xs:_ -> {v:Nat | v = len xs} @-}
  size :: [a] -> Int
  size [] = 0
  size (_:rs) = 1 + size rs

which yields exactly the same error.