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Encoding a dependent-type -calculus in a logic programming language

Amy Felty 1 Dale Miller 1
1 CROAP - Design and Implementation of Programming Tools
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Various forms of typed l-calculi have been proposed as specification languages for representing wide varieties of object logics. The logical framework, LF is an example of such a dependent-type l-calculus. A small subset of intuitionistic logic with quantification over simply typed l-calculus has also been proposed as a framework for specifying general logics. The logic of hereditary Harrop formulas with quantification at all non-predicate types, denoted here as hhw is such a meta-logic that has been implemented in both the Isabelle theorem prover and the lProlog logic programming language. In this paper, we show how LF can be encoded into hhw in a direct and natural way by mapping the typing judgments in LF into propositions in the logic of hhw. This translation establishes a strong connection between these two languages : the order of quantification in an LF signature is exactly the order of a set of hhw clauses and the proofs in one system correspond directly to proofs in the other system.
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https://hal.inria.fr/inria-00075299
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Submitted on : Wednesday, May 24, 2006 - 5:54:02 PM
Last modification on : Tuesday, December 1, 2020 - 7:58:04 AM
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  • HAL Id : inria-00075299, version 1

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Amy Felty, Dale Miller. Encoding a dependent-type -calculus in a logic programming language. [Research Report] RR-1259, INRIA. 1990, pp.15. ⟨inria-00075299⟩

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