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Unification in a λCalculus with Intersection Types
"... We propose related algorithms for unification and constraint simplification in !& , a refinement of the simplytyped λcalculus with subtypes and bounded intersection types. !& is intended as the basis of a logical framework in order to achieve more succinct and declarative axiomatizations o ..."
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We propose related algorithms for unification and constraint simplification in !& , a refinement of the simplytyped λcalculus with subtypes and bounded intersection types. !& is intended as the basis of a logical framework in order to achieve more succinct and declarative axiomatizations of deductive systems than possible with the simplytyped λcalculus. The unification and constraint simplification algorithms described here lay the groundwork for a mechanization of such frameworks as constraint logic programming languages and theorem provers.
Program Extraction in a Logical Framework Setting
 IN PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING AND AUTOMATED REASONING
, 1994
"... This paper demonstrates a method of extracting programs from formal deductions represented in the Edinburgh Logical Framework, using the Elf programming language. Deductive systems are given for the extraction of simple types from formulas of firstorder arithmetic and of calculus terms from n ..."
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This paper demonstrates a method of extracting programs from formal deductions represented in the Edinburgh Logical Framework, using the Elf programming language. Deductive systems are given for the extraction of simple types from formulas of firstorder arithmetic and of calculus terms from natural deduction proofs. These systems are easily encoded in Elf, yielding an implementation of extraction that corresponds to modified realizability. Because extraction is itself implemented as a set of formal deductive systems, some of its correctness properties can be partially represented and mechanically checked in the Elf language.
Combinator Shared Reduction and Infinite Objects in Type Theory
, 1996
"... We will present a syntactical proof of correctness and completeness of shared reduction. This work is an application of type theory extended with infinite objects and coinduction. ..."
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We will present a syntactical proof of correctness and completeness of shared reduction. This work is an application of type theory extended with infinite objects and coinduction.
Program Extraction in a Logical Framework Setting
 In Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
, 1994
"... : This paper demonstrates a method of extracting programs from formal deductions represented in the Edinburgh Logical Framework, using the Elf programming language. Deductive systems are given for the extraction of simple types from formulas of firstorder arithmetic and of calculus terms from natu ..."
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: This paper demonstrates a method of extracting programs from formal deductions represented in the Edinburgh Logical Framework, using the Elf programming language. Deductive systems are given for the extraction of simple types from formulas of firstorder arithmetic and of calculus terms from natural deduction proofs. These systems are easily encoded in Elf, yielding an implementation of extraction that corresponds to modified realizability. Because extraction is itself implemented as a set of formal deductive systems, some of its correctness properties can be partially represented and mechanically checked in the Elf language. Keywords: Program extraction, Realisability, Typed lambda calculus, Logical framework, Higherorder logic programming language, Elf, Edinburgh Logical Framework, Natural deduction, Natural semantics (R'esum'e : tsvp) Unite de recherche INRIA SophiaAntipolis 2004 route des Lucioles, BP 93, 06902 SOPHIAANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77  ...
Silly Type Families ∗ DRAFT
, 1994
"... This paper presents an extension to standard HindleyMilner type checking that allows constructors in data types to have nonuniform result types. We use Haskell as the sample language, [Hud92], but it should work for any language using HM. It starts with some motivating examples and then shows the ..."
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This paper presents an extension to standard HindleyMilner type checking that allows constructors in data types to have nonuniform result types. We use Haskell as the sample language, [Hud92], but it should work for any language using HM. It starts with some motivating examples and then shows the type rules for a simple language. Finally, it contains a sketch of how type deduction could be done. 1
Program Derivation by Proof Transformation
, 1993
"... In the proofsasprograms methodology, verified programs are developed through theoremproving in a constructive logic. Under this approach, the theoremproving process can be regarded as a program derivation process. The merits of this approach to programming are twofold. First, working with proofs ..."
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In the proofsasprograms methodology, verified programs are developed through theoremproving in a constructive logic. Under this approach, the theoremproving process can be regarded as a program derivation process. The merits of this approach to programming are twofold. First, working with proofs instead of programs concentrates the developer's effort on the intellectually difficult part of the development process: understanding, solving, and explaining the solution to a mathematical problem. Second, the proof provides a formal and trustworthy basis for an explanation of the program. This thesis investigates the use of proof transformations as a way to address important concerns in program derivation that are not addressed by theoremproving alone. One difficulty with the proofsasprograms strategy arises from the conflict between elegance and efficiency. A simple, elegant proof may lead to an inefficient program. A more complex proof that corresponds to a more efficient program ma...