Maar hoe moet het dan?


 Maurice Nelson
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1 Maar hoe moet het dan? Onderzoek naar feedback in interactieve leeromgevingen bij de Faculteit Informatica Johan Jeuring Met bijdragen van Alex Gerdes, Bastiaan Heeren, Josje Lodder, Harrie Passier, Sylvia Stuurman Open Universiteit Nederland Touwdag 2012, Amsterdam November 2012
2 Software technology for learning and teaching The software technology group has worked on interactive learning environments since 2005: The logic tutor Feedback in mathematical learning environments AskElle: a programming tutor for Haskell
3 Demos!
4 Main ideas behind AskElle A teacher specifies model solutions for an exercise, and possibly adapts the feedback AskElle compares possibly partial student solutions against model solutions As long as a student follows a model solution, AskElle can give hints
5 And what if a student makes an error, or takes a step that the tutor doesn t recognize? You have made a, possibly incorrect, step that does not follow the strategy.
6 And what if a student makes an error, or takes a step that the tutor doesn t recognize? You have made a, possibly incorrect, step that does not follow the strategy.
7 Our goals Increase the number of recognized good programs Report more errors, as precisely as possible
8 Report more errors, as precisely as possible Specify the properties a solution should satisfy Test the properties using QuickCheck Express the properties a solution should satisfy as a contract Use contract inference to infer contracts for userdefined functions Use contract checking to report property violations as precisely as possible
9 The problem Write a function that sorts a list sort :: Ord a => [a] > [a] For example: Data.List> sort [1,2,1,3,2,4] [1,1,2,2,3,4]
10 Sorting: a model solution sort = foldr insert [ ] insert x [ ] = [x] insert x (y : ys) x y = x : y : ys otherwise = y : insert x ys
11 An error in sorting sort = foldr insert [ ] insert x [ ] = [x] insert x (y : ys) x y = y : x : ys otherwise = y : insert x ys
12 Sorting: a property propsort xs = isnondesc (sort xs) isnondesc (x : y : xs) = x y isnondesc (y : xs) isnondesc = True
13 Running QuickCheck main = do quickcheck propsort *Main> main *** Failed! Falsifiable (after...): [0,1] But where is the error?
14 Running QuickCheck main = do quickcheck propsort *Main> main *** Failed! Falsifiable (after...): [0,1] But where is the error?
15 Contracts... Contracts to the rescue.
16 A contracted sort sortc = assert ([true] { zs isnondesc zs }) (λxs sort xs)
17 Blaming blamesort = sortc 0 [0, 1] *** Exception: contract failed: the expression sort is to blame. But where is the error?
18 Blaming blamesort = sortc 0 [0, 1] *** Exception: contract failed: the expression sort is to blame. But where is the error?
19 A more precise location To get a more precise location for the error: replace all functions in the definition of sort by their contracted counterparts.
20 A contracted insert insertc = assert (true { xs isnondesc xs } { xs isnondesc xs }) (λx λxs insert x xs)
21 A contracted foldr foldrc ca cb = assert ((ca cb cb) cb [ca] cb) (λf λe λxs foldr (λa λb f 1 a 2 b) e xs)
22 Blaming II blamesort = sortc 0 [0, 1] *** Exception: contract failed: the expression insert is to blame.
23 But wait In the context of the tutor, we only know the contract for sort A student can implement sort in many different ways We want to infer the contracts for the components of a function
24 The inferring contracts problem: Given A welltyped program A contract for the toplevel function determine the contracts for the components of the function.
25 range Write a function which enumerates all numbers contained in a given range. range :: Int Int [Int] For example, range 2 5 gives [2, 3, 4, 5]
26 Some solutions for range range 1 x y = if x y then [x] else x : range 1 (x + 1) y range 2 x y = if y x then [x] else x : range 2 (x + 1) y range 3 x y = if x y then x : range 3 (x + 1) y else [x] range 4 x y = if y x then x : range 4 (x + 1) y else [x] range 5 x y = if x y then x : range 5 (1 + x) y else [x]  and the 3 variants range 6 x = λy if x y then [x] else x : range 6 (x + 1) y  and the 7 variants range 7 = λx λy if x y then [x] else x : range 7 (x + 1) y  and the 7 variants
27 A procedure for determining equality A procedure for determining whether or not two programs are equal is necessarily going to have some limitations But surely each pair of range programs can pass the test How can determine many of these equalities? What program transformations can I specify to steer this procedure?
28 I need a normal form! Remove syntactic sugar Normalization by Evaluation normalizes based on types, so a function of type a b c always has the form λx λy... Normal forms for integer expressions, boolean expressions, string expressions, taking into account algebraic properties of the operators Inlining? let duplicate x = [x, x] in concatmap duplicate concatmap (λx [x, x]) Fusion? map f. map g = map (f. g)
29 The functional programming normal form problem Highlevel: how can I determine equality of (functional) programs? What is a normal form of a program? What sequence of steps do I use for determining a normal form of a program? How can I influence the computation of a normal form of a program?
30 Conclusions Interesting problems remain to be solved for AskElle: Inferring contracts Normal forms of programs More info: General information: Experiment online:
arxiv: v1 [cs.cy] 14 Jul 2015
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