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Simplifying and Improving Qualified Types
 IN FPCA ’95
, 1995
"... Qualified types provide a general framework for constrained type systems, with applications including type class overloading, subtyping and record calculi. This paper presents an extended version of the type inference algorithm used in previous work, that can take account of the satisfiability of co ..."
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Cited by 50 (3 self)
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Qualified types provide a general framework for constrained type systems, with applications including type class overloading, subtyping and record calculi. This paper presents an extended version of the type inference algorithm used in previous work, that can take account of the satisfiability of constraints to obtain more accurate principal types. The new algorithm is obtained by adding two new rules, one for simplification and one for improvement of constraint sets. In particular, it permits a better treatment of the previously troublesome multiple parameter extensions of Haskell type classes, generalizing the system of parametric type classes proposed by Chen, Hudak and Odersky.
Natural Semantics and Some of its MetaTheory in Elf
 PROCEEDINGS OF THE SECOND INTERNATIONAL WORKSHOP ON EXTENSIONS OF LOGIC PROGRAMMING
, 1991
"... Operational semantics provide a simple, highlevel and elegant means of specifying interpreters for programming languages. In natural semantics, a form of operational semantics, programs are traditionally represented as firstorder tree structures and reasoned about using natural deductionlike meth ..."
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Cited by 44 (14 self)
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Operational semantics provide a simple, highlevel and elegant means of specifying interpreters for programming languages. In natural semantics, a form of operational semantics, programs are traditionally represented as firstorder tree structures and reasoned about using natural deductionlike methods. Hannan and Miller combined these methods with higherorder representations using Prolog. In this paper we go one step further and investigate the use of the logic programming language Elf to represent natural semantics. Because Elf is based on the LF Logical Framework with dependent types, it is possible to write programs that reason about their own partial correctness. We illustrate these techniques by giving type checking rules and operational semantics for MiniML, a small functional language based on a simply typed calculus with polymorphism, constants, products, conditionals, and recursive function definitions. We also partially internalize proofs for some metatheoretic properti...
Compiler Verification in LF
 Seventh Annual IEEE Symposium on Logic in Computer Science
, 1992
"... We sketch a methodology for the verification of compiler correctness based on the LF Logical Framework as realized within the Elf programming language. We have applied this technique to specify, implement, and verify a compiler from a simple functional programming language to a variant of the Catego ..."
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Cited by 41 (11 self)
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We sketch a methodology for the verification of compiler correctness based on the LF Logical Framework as realized within the Elf programming language. We have applied this technique to specify, implement, and verify a compiler from a simple functional programming language to a variant of the Categorical Abstract Machine (CAM). 1 Introduction Compiler correctness is an essential aspect of program verification as almost all programs are compiled before being executed. Unfortunately, even for small languages and simple compilers, proving their correctness can be an enormous task, and verifying these proofs becomes an equally difficult task. Our goal is to develop techniques for mechanizing proofs of compiler correctness. To this end we employ 1. the LF Logical Framework [13] to specify relationships between source and target languages; 2. the Elf programming language [21] to provide an operational semantics for these relationships; and 3. a related metatheory [22] to reason about the ...
Extension of ML Type System with a Sorted Equational Theory on Types
, 1992
"... We extend the ML language by allowing a sorted regular equational theory on types for which unification is decidable and unitary. We prove that the extension keeps principal typings and subject reduction. A new set of typing rules is proposed so that type generalization is simpler and more efficient ..."
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Cited by 34 (11 self)
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We extend the ML language by allowing a sorted regular equational theory on types for which unification is decidable and unitary. We prove that the extension keeps principal typings and subject reduction. A new set of typing rules is proposed so that type generalization is simpler and more efficient. We consider typing problems as general unification problems, which we solve with a formalism of unificands. Unificands naturally deal with sharing between types and lead to a more efficient type inference algorithm. The use of unificands also simplifies the proof of correctness of the algorithm by splitting it into more elementary steps. Extension du syst`eme de type de ML par une th'eorie 'equationnelle avec sortes sur les types R'esum'e Le typage du langage ML est 'etendu en consid'erant les types modulo une th'eorie 'equationnelle r'eguli`ere avec sortes pour laquelle l'unification est d'ecidable. Cette extension conserve la propri'et'e d'avoir un type principal ainsi que la conservatio...
Ordersorted polymorphism in isabelle
 Logical Environments
, 1993
"... MLstyle polymorphism can be generalized from a singlesorted algebra of types to an ordersorted one by adding a partially ordered layer of “sorts ” on top of the types. Type inference proceeds as in the Hindley/Milner system, except that ordersorted unification of types is used. The resulting sys ..."
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Cited by 33 (2 self)
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MLstyle polymorphism can be generalized from a singlesorted algebra of types to an ordersorted one by adding a partially ordered layer of “sorts ” on top of the types. Type inference proceeds as in the Hindley/Milner system, except that ordersorted unification of types is used. The resulting system has been implemented in Isabelle to permit type variables to range over userdefinable subsets of all types. Ordersorted polymorphism allows a simple specification of type restrictions in many logical systems. It accommodates userdefined parametric overloading and allows for a limited form of abstract axiomatic reasoning. It can also explain type inference with Standard ML’s equality types and Haskell’s type classes. 1
Implementing the MetaTheory of Deductive Systems
 Proceedings of the 11th International Conference on Automated Deduction
, 1992
"... . We exhibit a methodology for formulating and verifying metatheorems about deductive systems in the Elf language, an implementation of the LF Logical Framework with an operational semantics in the spirit of logic programming. It is based on the mechanical verification of properties of transformatio ..."
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Cited by 32 (9 self)
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. We exhibit a methodology for formulating and verifying metatheorems about deductive systems in the Elf language, an implementation of the LF Logical Framework with an operational semantics in the spirit of logic programming. It is based on the mechanical verification of properties of transformations between deductions, which relies on type reconstruction and schemachecking. The latter is justified by induction principles for closed LF objects, which can be constructed over a given signature. We illustrate our technique through several examples, the most extensive of which is an interpretation of classical logic in minimal logic through a continuationpassingstyle transformation on proofs. 1 Introduction Formal deductive systems have become an important tool in computer science. They are used to specify logics, type systems, operational semantics and other aspects of languages. The role of such specifications is threefold. Firstly, inference rules serve as a highlevel notation w...
Type Checking Type Classes
 IN PROC. 20TH ACM SYMP. PRINCIPLES OF PROGRAMMING LANGUAGES
, 1993
"... We study the type inference problem for a system with type classes as in the functional programming language Haskell. Type classes are an extension of MLstyle polymorphism with overloading. We generalize Milner's work on polymorphism by introducing a separate context constraining the type variables ..."
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Cited by 31 (3 self)
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We study the type inference problem for a system with type classes as in the functional programming language Haskell. Type classes are an extension of MLstyle polymorphism with overloading. We generalize Milner's work on polymorphism by introducing a separate context constraining the type variables in a typing judgement. This leads to simple type inference systems and algorithms which closely resemble those for ML. In particular we present a new unification algorithm which is an extension of syntactic unification with constraint solving. The existence of principal types follows from an analysis of this unification algorithm.
Closed Types as a Simple Approach to Safe Imperative MultiStage Programming
, 2000
"... Safely adding computational eects to a multistage language has been an open problem. In previous work, a closed type constructor was used to provide a safe mechanism for executing dynamically generated code. This paper proposes a general notion of closed type as a simple approach to safely intro ..."
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Cited by 27 (14 self)
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Safely adding computational eects to a multistage language has been an open problem. In previous work, a closed type constructor was used to provide a safe mechanism for executing dynamically generated code. This paper proposes a general notion of closed type as a simple approach to safely introducing computational eects into multistage languages. We demonstrate this approach formally in a core language called MiniML BN ref . This core language combines safely multistage constructs and MLstyle references. In addition to incorporating state, MiniML BN ref also embodies a number of technical improvements over previously proposed core languages for multistage programming.
Rank 2 Type Systems and Recursive Definitions
, 1995
"... We demonstrate an equivalence between the rank 2 fragments of the polymorphic lambda calculus (System F) and the intersection type discipline: exactly the same terms are typable in each system. An immediate consequence is that typability in the rank 2 intersection system is DEXPTIMEcomplete. We int ..."
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Cited by 26 (1 self)
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We demonstrate an equivalence between the rank 2 fragments of the polymorphic lambda calculus (System F) and the intersection type discipline: exactly the same terms are typable in each system. An immediate consequence is that typability in the rank 2 intersection system is DEXPTIMEcomplete. We introduce a rank 2 system combining intersections and polymorphism, and prove that it types exactly the same terms as the other rank 2 systems. The combined system suggests a new rule for typing recursive definitions. The result is a rank 2 type system with decidable type inference that can type some interesting examples of polymorphic recursion. Finally,we discuss some applications of the type system in data representation optimizations such as unboxing and overloading.