Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....types, subtyping and bounded type labels. We have a type checker for Talx86 object files, a link compatibility and program completeness checker, and two front ends for toy languages meant to demonstrate the viability of Talx86 as a target language. We are also working on a front end for KML [Cra98], a variant of ML with higher order modules, full polymorphism, and subtyping among other features. 256 Conclusion This paper presents MTAL a calculus that formalises a low level notion of linking similar to the linker tools of modern operating systems. MTAL extends the earlier work of Cardelli ....

Karl Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 4130 Upson Hall, Ithaca, NY 14853-7501, USA, August 1998.

....David Aspinall [1] studied a calculus fg with singleton types and fi equivalence. Labelled singletons are primitive notions in this system# in the absence of j equivalence the encoding of Section 2.3 does not work. He conjectured that equivalence in this system was decidable. Karl Crary [4] studied an extension of with subtyping and power kinds and also conjectured that typechecking was decidable. 7 Conclusion and Future Work Wehave confirmed that fij equivalence for well formed constructors is decidable in the presence of singleton kinds by providing a sound, complete, and ....

Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

....David Aspinall [1] studied a calculus fg with singleton types and fi equivalence. Labelled singletons are primitive notions in this system; in the absence of j equivalence the encoding of Section 2.3 does not work. He conjectured that equivalence in this system was decidable. Karl Crary [4] studied an extension of with subtyping and power kinds and also conjectured that typechecking was decidable. 7 Conclusion and Future Work We have confirmed that fij equivalence for well formed constructors is decidable in the presence of singleton kinds by providing a sound, complete, and ....

Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

....Types The notion of subtype is not very thoroughly presented in the literature. There is the article by Constable and Hickey [39] which cites the basic literature. Another key paper is by Pierce and Turner [91] The PhD theses from Cornell and Edinburgh deal with this subject, especially Crary [46], Hickey [63] and Hofmann [65] 12 COMPUTATIONAL COMPLEXITY 37 Section 3 Pairs Cartesian products are standard, even in the earliest type theories, such as Curry [47] and deBruijn [49] Section 4 Union and Intersection The intersection type is deeply studied in the lambda calculus. ....

....operations to families. Each set is either true or false, and each sentence is a name for a set. REFERENCES 38 Section 10 Structures, Records and Classes The approach to records and classes developed here is based entirely on the work of Constable, Hickey and Crary. The basic papers are [39, 46]. The account by Betarte and Tasistro [15] is related. There is an etensive literature cited in the books of Gunter and Mitchell [56] The treatment of inductive classes is based on Basin and Constable [9] Section 11 The Axiom of Choice There are many books about the axiom of choice. One of ....

Karl Crary. Type--Theoretic Methodology for Practical Programming Languages. PhD thesis, Cornell University, Ithaca, NY, August 1998.

....David Aspinall [1] studied a calculus fg with singleton types and fi equivalence. Labelled singletons are primitive notions in this system; in the absence of j equivalence the encoding of Section 2.3 does not work. He conjectured that equivalence in this system was decidable. Karl Crary [4] studied an extension of Pi SigmaS with subtyping and power kinds and also conjectured that typechecking was decidable. 7 Conclusion and Future Work We have confirmed that fij equivalence for well formed constructors is decidable in the presence of singleton kinds by providing a sound, ....

Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

....Aspinall [1] studied a calculus fg with singleton types and equivalence between terms. Labelled singletons are primitive notions in this system; in the absence of equivalence the encoding of Section 2.3 does not work. He conjectured that equivalence in this system was decidable. Karl Crary [4] studied an extension of S with subtyping and power kinds and also conjectured that typechecking was decidable. Singleton kinds should not be confused with the identity types of extensional Martin L of type theory [13] There the type I(K; A; B) represents the type of proofs that A B : ....

Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

....David Aspinall [1] studied a calculus fg with singleton types and fi equivalence. Labelled singletons are primitive notions in this system; in the absence of j equivalence the encoding of Section 2.3 does not work. He conjectured that equivalence in this system was decidable. Karl Crary [4] studied an extension of Pi SigmaS with subtyping and power kinds and also conjectured that typechecking was decidable. 7 Conclusion and Future Work We have confirmed that fij equivalence for well formed constructors is decidable in the presence of singleton kinds by providing a sound, ....

Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

....David Aspinall [1] studied a calculus fg with singleton types and fi equivalence. Labelled singletons are primitive notions in this system; in the absence of j equivalence the encoding of Section 2.3 does not work. He conjectured that equivalence in this system was decidable. Karl Crary [4] studied an extension of Pi SigmaS with subtyping and power kinds and also conjectured that typechecking was decidable. 7 Conclusion and Future Work We have confirmed that fij equivalence for well formed constructors is decidable in the presence of singleton kinds by providing a sound, ....

Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

....types, subtyping and bounded type labels. We have a type checker for Talx86 object files, a link compatibility and program completeness checker, and two front ends for toy languages meant to demonstrate the viability of Talx86 as a target language. We are also working on a front end for KML [Cra98] a variant of ML with higher order modules, full polymorphism, and subtyping among other features. 7 Conclusion This paper presents MTAL a calculus that formalises a low level notion of linking similar to the linker tools of modern operating systems. MTAL extends the earlier work of Cardelli ....

Karl Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 4130 Upson Hall, Ithaca, NY 14853-7501, USA, August 1998.

....in other contexts. This paper is not the first to discuss language features in ML2000. Many possible design alternatives have been explored elsewhere by various members of the group, e.g. higher order modules [20, 25, 26, 30] classes and objects [14, 15, 43, 44] and type theoretic foundations [10, 22, 45]. The 1997 revision of SML [34] is one of the more visible outgrowths of the discussions. Simplifications and improvements made in this revision, including type abbreviations in signatures, value polymorphism, lack of structure sharing, restrictions to local datatype declarations, and others, are ....

....concrete syntax design influences, and must be influenced by, the formal definition and experience in programming with ML2000. Fortunately, the tools and techniques for these pieces already exist: formal definition techniques exist in the definition of SML [34] and in type theoretic semantics [10, 22], and concrete syntax and implementations can borrow ideas from SML, Objective Caml, and MOBY. Much of what we have learned goes beyond the design of the language. In the original ML2000 Manifesto from 1992, the original members of the working group wrote that The ML2000 project is largely a ....

K. Crary, D. Walker, and G. Morrisett. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Cornell University, August 1998.

....27] We briefly summarize Nuprl in Sections 2.1. This starting theory is essentially a theory of total functions only, but it may be extended to a theory of partial computable functions by adding partial types (types containing divergent terms) and a fixpoint rule for typing recursive functions [11, 12, 42, 41, 4, 17]. We use Crary s account [17] of type theory augmented by partial functions because that account is unique in providing an equality assertion within the logic, which we require in order to support extensional reasoning. 2.1 Type Theory Preliminaries As data types, the theory contains integers ....

.... This starting theory is essentially a theory of total functions only, but it may be extended to a theory of partial computable functions by adding partial types (types containing divergent terms) and a fixpoint rule for typing recursive functions [11, 12, 42, 41, 4, 17] We use Crary s account [17] of type theory augmented by partial functions because that account is unique in providing an equality assertion within the logic, which we require in order to support extensional reasoning. 2.1 Type Theory Preliminaries As data types, the theory contains integers (denoted by Z) disjoint unions ....

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Karl Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, August 1998.

....the only type constructor. These restrictions are quite strong; dependent products are used in encodings of modules [18] objects [20] algebras [17] and even such simple devices as variant records. Furthermore, ruling out dependent products disallows reasoning using fixpoint induction as in LCF [24, 11]. Finally, the restriction is particularly unsatisfying since most types used in practice do turn out to be admissible, and may be shown so by metatheoretical reasoning. In this paper I present a very wide class of admissible types using two devices, a condition called predicate admissibility and ....

....Concluding remarks appear in Section 5. 2 The Type Theory The type theory in which I formalize the results of this paper is a variant of the Nuprl type theory [5] extended with partial types (that is, types containing possibly divergent objects) This theory is a subset of the type theory of Crary [11] and is similar to Smith s theory [24] The major difference between the theory used here and Smith s is that the latter does not provide a notion of equality; the ramifications of handling equality are discussed in Crary [11] 2.1 Preliminaries As data types, the theory contains natural numbers ....

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Karl Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, August 1998.

....t in T Fig. 1. Type Theory Syntax 2 The Type Theory The type theory in which I formalize the results of this paper is a variant of the Nuprl type theory [5] extended with partial types (that is, types containing possibly divergent objects) This theory is a subset of the type theory of Crary [11] and is similar to Smith s theory [24] The major difference between the theory used here and Smith s is that the latter does not provide a notion of equality; the ramifications of handling equality are discussed in Constable and Crary [6] and at greater length in Crary [11] 2.1 Preliminaries ....

.... type theory of Crary [11] and is similar to Smith s theory [24] The major difference between the theory used here and Smith s is that the latter does not provide a notion of equality; the ramifications of handling equality are discussed in Constable and Crary [6] and at greater length in Crary [11]. 2.1 Preliminaries As data types, the theory contains natural numbers (denoted by N) disjoint unions (denoted by T 1 T 2 ) dependent products 1 (denoted by Sigma x:T 1 :T 2 ) and dependent function spaces (denoted by Pi x:T 1 :T 2 ) When x does not appear free in T 2 , I write T 1 ....

K. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, 1998. Forthcoming.

....Section 5 discusses promising directions for future work. Finally, Section 6 contains brief concluding remarks. 2 The Lambda K Programming Calculus As a case study to illustrate my technique, I use a predicative variant of K , the high level typed intermediate language in the KML compiler [17]. In this section I discuss K . In the interest of brevity, the discussion assumes knowledge of several well known programming constructs. Further discussion of the design of K appears in Crary [17] The syntax rules of K appear in Figure 1. The overall structure of the core calculus ....

....a predicative variant of K , the high level typed intermediate language in the KML compiler [17] In this section I discuss K . In the interest of brevity, the discussion assumes knowledge of several well known programming constructs. Further discussion of the design of K appears in Crary [17]. The syntax rules of K appear in Figure 1. The overall structure of the core calculus (that is, K minus modules and signatures) is similar to the higher order polymorphic lambda calculus [19, 20] augmented with records at the term and type constructor level (and their corresponding types ....

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Karl Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, Ithaca, New York, 1998. Forthcoming.

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Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

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Karl F. Crary. Type-Theoretic Methodology for Practical Programming Languages. PhD thesis, Department of Computer Science, Cornell University, 1998.

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Karl Crary. Type-theoretic Methodology for Practical Programming Languages. PhD thesis, Cornell University, 1998.

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Karl Crary. Type-theoretic Methodology for Practical Programming Languages. PhD thesis, Cornell University, 1998. 42

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