[Haskell-cafe] QuickCheck testing of AST transformers

Thomas Schilling nominolo at googlemail.com
Mon Apr 23 18:19:59 EDT 2007

Additionally, as a safety net, you might want to type-check the code  
that's being produced by your Arbitrary instances and state some  
invariants on your code.  Also, you'll likely want to limit your  
number of evaluation steps if your language allows non-terminating  

In any case, QuickCheck may not get you far enough to gain enough  
confidence, so proving properties by hand (after you made sure that  
QuickCheck doesn't find any counter-examples, of course) can give you  
interesting insights, since, this way, you have to take a look at all  
the possible cases yourself.


On 24 apr 2007, at 00.05, Lennart Augustsson wrote:

> Without looking into your language and transformation in more  
> detail it's hard to come up with concrete suggestions.  But here  
> are some anyway:
> Write an interpreter for each of your languages (original AST,  
> transformed AST) etc, and then use a quickcheck property stating  
> that well formed programs have the same denotation before and after  
> transformation, i.e., the two interpreters give the "same" value  
> (you might need some relaxed notion of same).
> You transformations are trying to get rid of some language  
> construct, I presume.  So you can have some properties stating that  
> they will be gone in the transformed program..
> 	-- Lennart
> On Apr 23, 2007, at 22:46 , Joel Reymont wrote:
>> My previous post did not receive any replies so I thought I might  
>> try generalizing the problem a bit...
>> Suppose I'm parsing a language into a syntax tree and then  
>> transforming that tree into another AST representing a "core  
>> language". The core language is a more general AST that should  
>> help with compiling to other languages.
>> My problem is how to best structure my AST transformations to be  
>> able to test them with QuickCheck. I suspect that I'm not going  
>> about it in the most optimal way so I thought I should ask for  
>> suggestions.
>> The transformation into the core AST applies operations to  
>> simplify, or desugar, the AST of the original language. Here's  
>> sample code in the source language which, incidentally, was  
>> recently highlighted at Lambda the Ultimate [1].
>> Array: MyArray[10](10 + 2);
>> Value1 = MyArray[5][10];
>> This declares an array of 10 elements and initializes each element  
>> to 12. Value1 (a built-in variable) is then initialized to the  
>> value of element #5 as of 10 bars ago. A bar is, basically, a  
>> stock quote. The code is invoked on every bar and so "5 bars ago"  
>> can be treated as 5 invocations ago.
>> The syntax tree of the above code is a 1-1 mapping. We declare an  
>> array of integers of 10 elements. Initialize it to the sum of two  
>> integers and then assign to Value1.
>> [ ArrayDecs [ VarDecl (VarIdent "MyArray") TyInt [Int 10]
>>                           (Op Plus (Int 10) (Int 2)) ]
>> , Assign (VarIdent "Value1") [] (Var (VarIdent "MyArray") [Int 5]
>>                                          (BarsBack (Int 10))) ]
>> The "desugared" version does away with the array declaration  
>> statement and declares MyArray to be a variable of array type.  
>> Arrays in the "core language" do not remember values from one  
>> invocation to another but there's a data series type, so we  
>> declare a series variable to hold the value of element #5.
>> We must manually store the value of the array element in the data  
>> series and can then refer to the value of the series 10 data  
>> points ago.
>> vars = [ ("MyArray", VarDecl (TyArray TyInt) [Int 10]
>>                        (Just (Plus (Int 10) (Int 2))))
>>        , ("series0", VarDecl (TySeries TyInt) [] Nothing)
>>        ]
>> code = [ AddToSeries (VarIdent "series0") (Var (VarIdent  
>> "MyArray") [Int 5])
>>        , Assign (Var (VarIdent "Value1") [])
>>                     (Series (VarIdent "series0") (Int 10))
>>        ]
>> The next step would be to take the above "core syntax tree" and  
>> transform it yet again into a C# (or other target language) AST.  
>> It's assumed that all target languages have a data series type.
>> The OCaml version of my code translated directly into the C# AST  
>> but I figured an intermediate syntax tree will help me translate  
>> into other languages such as Haskell, Erlang or OCaml.
>> The part I can't figure out is how to come up with a set of  
>> invariants for my transformations.
>> Should I, for example, state that every access to an array value  
>> in a previous invocation should introduce an extra variable to  
>> hold the series plus the appropriate assignment code?
>> Should I write the translator as a series of small transformers in  
>> the ST monad that can be threaded and tested separately?
>> 	Thanks in advance, Joel
>> [1] http://lambda-the-ultimate.org/node/2201
>> --
>> http://wagerlabs.com/
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