D. McAllester. Inferring recursive data types. Unpublished, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... time and is therefore very efficient in practice [23, 8] Just like first order unification, it is PTIME complete [3] Type inference in ML may require exponential time only in the presence of polymorphic (Let) 11, 14] and this happens only in the case of programs that are arguably pathological [17]. Towards filling the huge gap between efficient typeinference with (Monorec) and undecidable type inference with (Polyrec) one of our research goals is to formulate typing rules strictly more powerful that (Monorec) In this report, we combine universal types and recursive types in order to ....

D. McAllester. Inferring recursive data types. Unpublished, 1996.

.... that have a small typing, proved that their type reconstruction is in PTIME even in so called Mycroft Milner type system, that is in ML augmented by polymorphic recursion, and suggested that this is the class of programs found in practice [8] This result was recently refined by David McAllester [23], who noted that Programmers almost never write functions with more than ten arguments or functions of order larger than three , and proved that for programs whose types are of bounded size, type reconstruction can be done in pseudo linear time, that is in time O(n#(n) where # is an inverse of ....

....corresponds exactly to path compression known form the pseudo linear implementation of the UNION FIND algorithm. Thus type reconstruction in SML of NJ somehow incorporates the UNION FIND algorithm (the question whether the UNION FIND algorithm is inherent in ML type reconstruction is discussed in [23]) If we bound the type size by b, then every single unification takes O(b 2 ) steps (because of occur check) plus time used for pruning. It seems possible to retrace the calculation of the well known bound for the running time of the UNION FIND algorithm [1, 12] and to show that n subsequent ....

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D. McAllester, Inferring Recursive Data Types, unpublished manuscript, 1996.

.... very efficient in practice [PW78, Hin97] Just like first order unification, it is PTIME complete [DKM84] Type inference in ML may require exponential time only in the presence of polymorphic (Let) KMM91, KTU94] and this happens only in the case of programs that are arguably pathological [McA96] Towards filling the huge gap between efficient type inference with (Monorec) and undecidable type inference with (Polyrec) one of our research goals is to formulate typing rules strictly more powerful that (Monorec) In this report, we combine universal types and recursive types in order to ....

D. McAllester. Inferring recursive data types. Unpublished, 1996.

.... very efficient in practice [PW78, Hin97] Just like first order unification, it is PTIME complete [DKM84] Type inference in ML may require exponential time only in the presence of polymorphic (Let) KMM91, KTU94] and this happens only in the case of programs that are arguably pathological [McA96] Towards filling the huge gap between efficient type inference with (Monorec) and undecidable type inference with (Polyrec) one of our research goals is to formulate typing rules strictly more powerful that (Monorec) In this report, we combine universal types and recursive types in order to ....

D. McAllester. Inferring recursive data types. Unpublished, 1996.

....constraints arising in the formulation of algorithm W [8] can be solved as symmetric inclusion constraints using a standard inclusion constraint solver. This approach results however in an algorithm with cubic time complexity, instead of the nearly linear time algorithm based on unification [7]. A key to the efficiency of Hindley Milner type inference is that types are terms. Terms have unique head constructors, whereas set expressions generally do not. This property whether a quantity has a unique head constructor is a prime determinant of the cost of solving type constraints. We ....

David McAllester. Inferring Recursive Data Types. http://www.ai.mit.edu/people/dam/rectypes.ps.

....many of these algorithms are inherently cubic time no sub cubic procedure has been found. Such cubic time algorithms include Shivers control flow analysis [17] the Palsberg and O Keefe method of determining typability in the Amadio Cardelli type system [15, 1] and various set based analyses [5, 10, 11]. At an intuitive level the inherent cubic complexity in all these problems arises from the need to compute a dynamic transitive closure one must compute the transitive closure of a directed graph while adding edges to the input graph as a consequence of edges derived for the output graph. Not ....

David McAllester. Inferring recursive data types. (http://www.ai.mit.edu/people/dam/rectypes.ps)

....or Jagannathan and Wright [10] but includes data constructors and union types. It can also be viewed as an extension of the recently established equivalence between flow analysis and recursive types in the absence of data constructors [3, 14, 7, 15] These connections are explored more deeply in [11]. Earlier procedures for determining SBA safety for programs with deep patterns have been based on general methods of solving set constraints [1, 2] The general set constraint solvers run in nondeterministic exponential time in the worst case. Here we show that the full power of these set ....

....the free variable of x:e to values. In the rules BETA and RETURN we require that v be a value. a definition of polyvariant SBA safety one can consider the question of the computational complexity of determining polyvariant SBA safety for a variety of programming languages. McAllester has shown [11] that even for first order programs restricted to procedures of at most one argument and shallow case statements determining polyvariant SBA safety is PSPACE hard. This is in contrast to Hindley Milner typability which can be done in nearly linear time for programs of bounded order and arity ....

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David McAllester. Inferring recursive data types. http://www.ai.mit.edu/people/dam/rectypes.ps.

.... more than, say, 20 arguments or of order greater than 3, and almost never at the same time (this is less clear for automatically generated programs) Such program classes have been particularly useful for understanding the observed linear behavior of type inference for ML [10] see for example [6, 9]. Unfortunately, for the standard CFA algorithm, this approach fails: the algorithm is cubic even if we choose some constant k and consider only programs of k bounded type size. A program is said to have k bounded type size if the size of the type tree of each program node is k or less. Section ....

D. McAllester, "Inferring Recursive Data Types", draft manuscript, July 1996.

.... methods similar to control flow analysis such as that developed by Shivers [15] This includes algorithms for inferring recursive types such as the the Palsberg and O Keefe method of determining typability in the Amadio Cardelli type system [13, 1] Cubic behavior also arises in set based analyses [4, 9, 10]. Our approach to proving cubic time hardness results is derived from a result of Radford Neal s which states that the problem of determining membership in languages defined by 2 way nondeterministic pushdown automata (2NPDA) can be reduced in linear time to the problem of monotone closure [12] ....

David McAllester. Inferring recursive data types. http://www.ai.mit.edu/people/dam/rectypes.ps.

....less clear for automatically generated programs) This class of programs has been particularly useful for understanding the observed linear behavior 3 We discuss the notion of bounded type for polymorphically typed programs (in the sense of ML) in Section 5. of type inference for ML [13] see [7, 10]. However, it cannot be used to control the complexity of the standard CFA algorithm, which is cubic even when type size is bounded. Section 10 illustrates this with an example. The main result of this paper is a linear time algorithm for bounded type programs that builds a directed graph whose ....

....assumed a bound k on the size of the monotypes in a program. Now consider polymorphically typed programs (in the sense of ML) and suppose our expression language is extended with an appropriate let construct. There are at least two notions of bounded size polymorphically typed programs. McAllester [10] defines that a polymorphically typed program P has bounded type size if there is some constant k such that the tree size of the monotypes of each expression in the let expansion of P all have size k. Alternatively, motivated by Henglein s ML programs with small types [7] we can define that a ....

D. McAllester, "Inferring Recursive Data Types", draft manuscript, July 1996.

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D. McAllester. Inferring recursive data types. Unpublished, 1996.

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David McAllester. Inferring recursive data types. Unpublished, 1996.

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David McAllester. Inferring recursive data types. Draft Manuscript, 1996.

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D. McAllester. Inferring recursive data types. Unpublished, 1996.

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David McAllester. Inferring recursive data types. Unpublished, 1996.

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David McAllester. Inferring recursive data types. Unpublished, 1996.

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David McAllester. Inferring recursive data types. Unpublished, 1996.

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D. McAllester. Inferring recursive data types. Unpublished, 1996.

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