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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.
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 of deduct ..."
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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.
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.