K. Crary and S. Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, Sept. 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... to type indexed functions, see Dubois et al. [8] Jay et al. [22] and Yang [36] but none of them mentions user de ned type indexed data types (Yang does mention value indexed types, usually called dependent types) Type indexed data types, however, appear in the work on intensional type analysis [11, 6, 5, 33, 35]. Intensional type analysis is used in typed intermediate languages in compilers for polymorphic languages, among others to be able to optimize code for polymorphic functions. This work di ers from our work in several aspects: typed intermediate languages are expressive, but rather complex ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings ICFP 1999: International Conference on Functional Programming, pages 233-248. ACM Press, 1999.

....of correspondence assertions for communication protocols [15] However, neither refinement types nor the many type ande #ect systems attempt to provide a general purpose logical framework for reasoning about e#ectful computations. Xi and Pfenning s dependent type system and related work [8, 2, 5, 6] only seek to capture properties of values and pure computations, rather than properties of e#ectful computations. For example, they are unable to describe protocols that require e#ectful functions to be used in a specified order. Therefore, these systems cannot be used to enforce important ....

K. Crary and S. Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, Sept. 1999.

....in formalizing a multistage language, and proving its safety under a sophisticated dependent type system. We do this by capitalizing on the recent work by Shao, Saha, Trifonov and Papaspyrou s on the TL system [44] which in turn builds on a number of recent works on typed intermediate languages [20, 7, 59, 43, 9, 57, 44]. 1.6 Organization of this Paper Section 2 shows how to take our motivating example and turn it into a tagless staged interpreter in a dependently typed setting. First, we present the syntax and semantics of a simple typed language and show how these can be implemented in a direct fashion in ....

....our type checking function, as it produces a term whose type depends on the value of its argument. A standard solution to is to introduce a mechanism that allows only a limited kind of dependency between values and types. This limited dependency uses so called singleton or representation types [60, 7, 9, 57]. The basic idea is to allow bijections on ground terms between the value and type world. Now, we can rewrite our interpreter so that its type does not depend on runtime values, which may introduce effects into the typechecking phase. Any computation in the type checking phase can now be ....

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Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the Fourth ACM SIGPLAN International Conference on Functional Programming (ICFP-99), volume 34.9 of ACM Sigplan Notices, pages 233--248, N.Y., September 27--29 1999. ACM Press.

....statically typed dynamics and implementing intensional polymorphism. Explicit type representations are not new either: they were introduced by Crary, Weirich, and Morrisett [9] the authors also observed that representations could be used to implement an explicit Dynamic type. Crary and Weirich [8] and Weirich [33] have also considered encodings of type representations in the more powerful type systems LX , which includes function, sum, product, and recursive kinds, and LU , which includes impredicative kind polymorphism. Baars and Swierstra [4] have independently discovered the type ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the ACM SIGPLAN International Conference on Functional Programming (ICFP '99), Paris, France, volume (34)9 of ACM SIGPLAN Notices, pages 233-248. ACM Press, September 1999.

.... to type indexed functions, see Dubois et al. [7] Jay et al. [21] and Yang [36] but none of them mentions user defined type indexed data types (Yang does mention value indexed types, usually called dependent types) Type indexed data types, however, appear in the work on intensional type analysis [10, 6, 5, 32, 34]. Intensional type analysis is used in typed intermediate languages in compilers for polymorphic languages, among others to be able to optimize code for polymorphic functions. This work di#ers from our work in several aspects: typed intermediate languages are expressive, but rather complex ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings ICFP 1999: International Conference on Functional Programming, pages 233--248. ACM Press, 1999.

....While an ad hoc treatment of arrays can be fairly easily integrated into the language, this is highly unsatisfactory since the intention is to make all allocation explicit through the same mechanism. A more elegant possibility is to use a dependent type formalism [25] or a type analysis formalism [5] to introduce a notion of dynamic extent into the type system. We hope to explore this avenue further in the future. Another important area for future research is to attempt to account for pointers into the frontier itself. As we saw in Section 5 we are forced to allocate an object into the heap ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999.

....DML(C) can incorporate semantically rich constraint theories and thus guarantee a decidable type checking algorithm, our constraint theory is in principle fixed but still variable due to the underlying term rewriting system and the choice of strategy for each function. Intensional type analysis [21, 7, 6, 50] is an approach to defining functions by induction on the structure of types. These works are closer to generic programming [22, 25] The commonality is that their scheme of function definition is much more rigid than with our approach. Usually, the inspection of the type structure is limited to a ....

K. Crary and S. Weirich. Flexible type analysis. In P. Lee, editor, Proc. International Conference on Functional Programming 1999.

....equality testers, debuggers, and marshallers (a.k.a. serializers or picklers) Juan Chen and I have developed an implementation of polytypic primitives as a transformation on the typed intermediate representation in the SML NJ compiler [6] Like the l R transformation of Crary and Weirich [8] it allows these polytypic functions to be typechecked, but unlike their calculus, ours does not require dependent types in the typed intermediate language and is thus simpler to implement. 7 Conclusion Our goal is to reduce the size of the trusted computing base of systems that run machine code ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In ACM SIGPLAN International Conference on Functional Programming Languages, September 1999.

....2, 26, 8, 15] were introduced back in the nineties. There exist other approaches to type indexed functions, see Dubois et al. [7] Jay et al. [20] and Yang [33] but none of them mentions user de ned type indexed data types. Type indexed data types appear in the work on intensional type analysis [9, 6, 5, 30, 32]. Intensional type analysis is used in typed intermediate languages in compilers for polymorphic languages, among others to be able to optimize code for polymorphic functions. This work di ers from our work in that typed intermediate languages are expressive, but rather complex languages not ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings ICFP 1999: International Conference on Functional Programming, pages 233-248. ACM Press, 1999.

....vanishes when it reaches a type variable. However this would break the confluence of the type language the application of ## :# . Typerec # of . to # would reduce in general to different types if we perform the # reduction step first or eliminate the iterator first. Crary and Weirich [1] propose another method for solving this problem. Their language LX allows the representation of terms with bound variables using deBruijn notation and an encoding of natural numbers as types. To analyze quantified types, the iterator carries an environment mapping indices to types; when the ....

....to resolve this problem by generalizing the negative occurrence of# to an arbitrary kind; however such an approach is doomed in the case of recursive types since the argument of l u must have identical domain and range. One possibility is to follow the approach outlined by Crary and Weirich in [1] for quantified types; since type variables bound by the fixpoint operator must be of kind# , an environment can be used to map them to types of kind# without kind mismatches. While plausible and perhaps efficient, this approach (as pointed out in Section 2.4) gives no protection against some ....

[Article contains additional citation context not shown here]

K. Crary and S. Weirich. Flexible type analysis. In Proc. 1999 ACM SIGPLAN International Conf. on Functional Programming, pages 233--248. ACM Press, Sept. 1999.

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Crary, K. and Weirich, S. 1999. Flexible type analysis. In 1999 ACM International Conference on Functional Programming. Paris, 233--248.

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Crary, K. and Weirich, S. 1999. Flexible type analysis. In 1999 ACM SIGPLAN International Conference on Functional Programming. ACM Press, New York, NY, USA. To appear.

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K. Crary and S. Weirich. Flexible type analysis. In Proceedings of the Fourth International Conference on Functional Programming (ICFP), pages 233--248, Paris, Sept. 1999.

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Karl Crary and Stephanie Weirich. Flexible Type Analysis. In Proceedings of the Fourth ACM SIGPLAN International Conference on Functional Programming, pages 233--248, Paris, September 1999.

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K. Crary and S. Weirich. Flexible type analysis. In Proceedings of theFourth International Conference on Functional Programming (ICFP), pages 233--248, Paris, Sept. 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the Fourth ACM SIGPLAN International Conference on Functional Programming, pages 233-- 248, Paris, September 1999.

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K. Crary and S. Weirich. Flexible type analysis. In Proceedings of the Fourth International Conference on Functional Programming (ICFP), pages 233--248, Paris, Sept. 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999 ACM International Conference on Functional Programming, pages 233#248, Paris, September 1999.

....rule that precisely describes the required structure of the stack, we must enrich the constructor level of our language. For this purpose, we add a number of constructs from ## Figure 3: Kinds and Constructors from LX Crary and Weirich s LX type theory [3]. These additions to our language are shown in Figure 3. In addition to function spaces, products and sums over kinds (k1 k2 , k1 k2 , k1 k2 ) LX provides inductive kinds j.k, where j is a kind variable that may appear in positive positions within k. At the type constructor level, we ....

....proof in this paper. An operational semantics is completely straightforward, except that the two rules that perform heap allocation must each have an additional side condition requiring that the stack be parsable. A type safety proof is boilerplate, based on the proof for LX by Crary and Weirich [3], except that in the cases of injection and allocation it must be shown that the typing conditions on the stack imply that it is parsable. However, it is not clear how to give a formal definition of parsability that is any simpler than our specification in Appendix B, so such a proof would be ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the Fourth ACM SIGPLAN International Conference on Functional Programming (ICFP), pages 233--248, September 1999.

....While an ad hoc treatment of arrays can be fairly easily integrated into the language, this is unsatisfactory since the intention is to make all allocation explicit through the same mechanism. A more interesting possibility is to use a dependent type formalism [23] or a type analysis formalism [4] to introduce a notion of dynamic extent into the type system. We intend to explore this avenue further in the future. Another important area for future research is to attempt to account for pointers into the frontier itself. As we saw in Section 5 we are forced to allocate an object into the ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999.

....operations as primitives (including the allocation and initialization operations) This is highly unsatisfactory since the intention is to make all allocation explicit through the same mechanism. A more elegant possibility is to use a dependent type formalism [25] or a type analysis formalism [5] to introduce a notion of dynamic extent into the type system. The size of an object can then be expressed as depending on the runtime value of an index object for allocation purposes, and inductive operations for traversing and initializing such objects using their indices could be defined. ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999.

....operations as primitives (including the allocation and initialization operations) This is highly unsatisfactory since the intention is to make all allocation explicit through the same mechanism. A more elegant possibility is to use a dependent type formalism [25] or a type analysis formalism [5] to introduce a notion of dynamic extent into the type system. The size of an object can then be expressed as depending on the runtime value of an index object for allocation purposes, and inductive operations for traversing and initializing such objects using their indices could be de ned. ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999.

....investigated and may be di#cult. On the other hand, Inductive Constructions supports primitive recursion, which 10 LF does not (as such a construct would destroy LF s notion of canonical forms) Consequently, SSTP can use primitive recursion on encoded types to support intensional type analysis [9, 5], which LTT cannot. Various proposals have been made for extending LF with primitive recursion [6, 20, 19] and we are exploring integrating one of these into LTT. LTT provides the power for very expressive type systems by allowing operations to demand proofs of arbitrary propositions (thereby ....

K. Crary and S. Weirich. Flexible type analysis. In 1999.

....and may be difficult to extend to more complicated type systems. The complexity of this proof is probably the source of the common misconception that singleton kinds make typechecking difficult. The latter phases of a type preserving compiler may involve some very complicated type systems indeed [15, 3, 4, 20]. Extending Stone and Harper s proof to these type systems, some of which already have nontrivial decidability proofs, is a daunting prospect. Moreover, there already exist a variety of tools for manipulating low level typed languages that, by and large, do not support singleton kinds. In this ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In

....software by allowing functions to automatically adapt to changes in the representation of data. Other classic examples of polytypic operations include debuggers, comparison functions and mapping functions. The theory behind describing such operations has been developed in a variety of frameworks [1, 2, 4, 8, 12, 14, 17, 18, 27, 28, 30, 31]. Nevertheless, no single existing framework encompasses all polytypic de nitions. These systems are limited by what polytypic operations they may express and by what types they may examine. These de ciencies are unfortunate because advanced languages depend crucially on these features. Only some ....

.... to functional programming languages, such as ML [21] and Haskell [24] and also extremely important to imperative languages such as Ada [16] and Java [3, 11] Furthermore, only some frameworks for polytypism may examine types with binding structure, such as polymorphic or existential types [2, 4, 30]. However, these types are becoming increasingly more important. Current implementations of the Haskell language [19, 29] include a form of existential type and rst class polymorphism. Existential types are particularly useful for implementing dynamically extensible systems that may be augmented ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the Fourth ACM SIGPLAN International Conference on Functional Programming, pages 233-248, Paris, September 1999.

....of a type environment. The work of Minamide et al. arose from the TIL compiler [Morrisett et al. 1996] which uses run time type information to optimize data layout [Tarditi et al. 1996] At first, it seems that a type erasure semantics precludes these optimizations. However, recent work of Crary et al. 1998; 1999] shows how to encode run time type information in a type erasure language. Rather than manipulating types directly, programs manipulate values that represent types. Using this device, the type environment can become part of the value environment and closure conversion may be performed in a similar ....

....compatible with the type erasure interpretation adopted here. To make such optimizations permissible, we are augmenting the TALx86 language so that TAL programs can construct values that represent 32 Delta Morrisett et al. types and analyze those values when necessary, following the work of Crary et al. 1998; 1999]. Although we believe our translations are operationally correct, we are still searching for robust proofs of correctness. Similar CPS [Danvy and Filinski 1992] and closure conversion [Minamide et al. 1996] translations have already been proven correct, but these results do not easily extend to ....

Crary, K. and Weirich, S. 1999. Flexible type analysis. In 1999 ACM SIGPLAN International Conference on Functional Programming. ACM Press, New York, NY, USA. To appear.

....in System F using equality [21] A stronger equational theory for U , perhaps one incorporating a parametricity principle [19] might solve this problem. However, a simpler way to support primitive recursion would be to include a primitive for primitive recursion directly in the language [12, 18, 3, 4]. 4.2 Impredicativity and Non termination Another issue with this encoding is that the target language must have impredicative polymorphism at the type and kind level. However, impredicativity at the kind level destroys strong normalization [2] 4 In practice, this property may be acceptable in ....

....theorem [20] forming an isomorphism between a set and its double power set. such as type directed partial evaluation [6] Because core ML does not support higher order polymorphism, he presented his encoding within the ML module system. At the type constructor level, Crary and Weirich [4] encoded the Typerec construct with a language supporting product, sum and inductive kinds. Their aim was to support type analysis in type preserving compilation. Because various intermediate languages do not share the same type system, they needed some way to express the analysis of source level ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999 ACM International Conference on Functional Programming, pages 233-248, Paris, September 1999.

....and may be difficult to extend to more complicated type systems. The complexity of this proof is probably the source of the common misconception that singleton kinds make typechecking difficult. The latter phases of a type preserving compiler may involve some very complicated type systems indeed [15, 3, 4, 20]. Extending Stone and Harper s proof to these type systems, some of which already have nontrivial decidability proofs, is a daunting prospect. Moreover, there already exist a variety of tools for manipulating low level typed languages that, by and large, do not support singleton kinds. In this ....

Karl Crary and Stephanie Weirich. Flexible type analysis. In 1999 ACM International Conference on Functional Programming, pages 233--248, Paris, September 1999.

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K. Crary and S. Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, Sept. 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, September 1999.

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K. Crary and S. Weirich. Flexible type analysis. In International Conference on Functional Programming, 1999.

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K. Crary and S. Weirich. Flexible type analysis. In International Conference on Functional Programming, 1999.

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K. Crary and S. Weirich. Flexible type analysis. In International Conference on Functional Programming, pages 233--248, 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the Fourth ACM SIGPLAN International Conference on Functional Programming (ICFP-99), volume 34.9 of ACM Sigplan Notices, pages 233--248, N.Y., September 27--29 1999. ACM Press.

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K. Crary and S. Weirich. Flexible Type Analysis. In Proceedings of International Conference on Functional Programming (ICFP '99), Paris, France, 1999.

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Karl Crary and Stephanie Weirich. Flexible Type Analysis. In Proceedings of International Conference on Functional Programming (ICFP '99), Paris, France, 1999.

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K. Crary, S. Weirich, Flexible type analysis, in: Proceedings ICFP 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In International Conference on Functional Programming, pages 233--248, 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, September 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In 4th ACM International Conference on Functional Programming, pages 233--248, 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings of the ACM SIGPLAN International Conference on Functional Programming (ICFP '99), Paris, France, volume (34)9 of ACM SIGPLAN Notices, pages 233-248. ACM Press, September 1999.

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Karl Crary and Stephanie Weirich. Flexible Type Analysis. In Proceedings of International Conference on Functional Programming (ICFP '99), Paris, France, 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In Proceedings ICFP 1999.

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K. Crary and S. Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, Sept. 1999.

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K. Crary and S. Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, Sept. 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In International Conference on Functional Programming, 1999.

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K. Crary, S. Weirich, Flexible type analysis, in: Proceedings ICFP 1999.

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Karl Crary and Stephanie Weirich. Flexible type analysis. In ACM International Conference on Functional Programming, pages 233--248, Paris, September 1999.

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K. Crary and S. Weirich. Flexible Type Analysis. In Proceedings of International Conference on Functional Programming (ICFP '99), Paris, France, 1999.

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