| S. Kahrs. Limits of ML-definability. In H. Kuchen and S. D. Swierstra, editors, Proceedings of the 8th Symposium on Programming Language Implementations and Logic Programming, volume 1140 of LNCS, pages 17--31. Springer-Verlag, 1996. |
....call is identical to the type of the head . In Miranda or Haskell, this problem can be overcome by providing a type declaration, while in ML, the function will definitely be rejected. This limitation of 17 the ML type system, or alternatively, the ML type checker, has been studied by Kahrs [Kah96] Example 4.9 suggests that there is a certain symmetry between polymorphic recursion and violations of the head condition. 4.4 A Generalisation: Semi generic Programs To reason about the existence of a solution for the equation set of a type skeleton, we give a su#cient condition for ....
S. Kahrs. Limits of ML-definability. In H. Kuchen and S. D. Swierstra, editors, Proceedings of the 8th Symposium on Programming Language Implementations and Logic Programming, volume 1140 of LNCS, pages 17--31. Springer-Verlag, 1996.
....In doing so we get a operational semantic for the functions Bfold Bmap. Studying these functions one sees that termination for finite bushes and the subject reduction property are valid (i.e. if the arguments of the functions are well typed the result of the computation will be again well typed) [Kah96]. Polymorphic Recursion The problem is that the type inference of Haskell or ML would not accept the definition. Please recall that the definition of Bush a involves twice the use of the type constructor Bush on the right hand side. This is repeated in the definition of the function Bfold by ....
Stefan Kahrs. Limits of ML-definability. In H. Kuchen and S. Swierstra, editors, Proceedings of PLIP '96, pages 17--32, Aachen, September 1996. LNCS 1140.
....be quick to say that far from having been offered a type discipline they have been lumbered with a type bureaucracy. It is Mads Tofte s view that rejecting some sensible programs which would never go wrong is inevitable but not everyone is so willing to accept a loss such as this. Stefan Kahrs in [Kah96] discusses the notion of completeness programs which never go wrong can be type checked which complements Milner s notion of soundness type checked programs never go wrong [Mil78] CHAPTER 4. TYPES AND TYPE INFERENCE 26 We will now consider some programs which the type discipline of ....
Stefan Kahrs. Limits of ML-definability. In Proceedings of Eighth International Symposium on Programming Languages, Implementations, Logics, and Programs, September 1996.
....functions in P models. In SML, each function is modelled as a closure which contains the expression used in defining the function, so we get only the SML expressible functions [MTH90] Of course, all of these are computable, but not all computable functions of a given type are SML expressible [Kah96]. Putting these together (the decision to interpret S specifications using classes of P models and the imposition of computability and other restrictions on P models) leads to a possible problem, as the following example from [ST96] illustrates. Example 1 Let equiv be a sentence which asserts ....
S. Kahrs. Limits of ML-definability. In Proceedings of PLILP'96, volume 1140 of Lecture Notes in Computer Science, pages 17--31. Springer, 1996.
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