α lean TA P: A declarative theorem prover for first-order classical logic. Near, J., P., Byrd, W., E., & Friedman, D., P. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 5366 LNCS:238-252, 2008.
Website doi abstract bibtex We present α lean TA P, a declarative tableau-based theorem prover written as a pure relation. Like lean TA P, on which it is based, α lean TA P can prove ground theorems in first-order classical logic. Since it is declarative, α lean TA P generates theorems and accepts non-ground theorems and proofs. The lack of mode restrictions also allows the user to provide guidance in proving complex theorems and to ask the prover to instantiate non-ground parts of theorems. We present a complete implementation of α lean TA P, beginning with a translation of lean TA P into αKanren, an embedding of nominal logic programming in Scheme. We then show how to use a combination of tagging and nominal unification to eliminate the impure operators inherited from lean TA P, resulting in a purely declarative theorem prover. © 2008 Springer Berlin Heidelberg.
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title = {α lean TA P: A declarative theorem prover for first-order classical logic},
type = {article},
year = {2008},
keywords = {Classical logic; First order; Nominal logic; Prov,Computer programming; Logic programming; Programmi,Program translators; Theorem proving},
pages = {238-252},
volume = {5366 LNCS},
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notes = {cited By 1; Conference of 24th International Conference on Logic Programming, ICLP 2008 ; Conference Date: 9 December 2008 Through 13 December 2008; Conference Code:75119},
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abstract = {We present α lean TA P, a declarative tableau-based theorem prover written as a pure relation. Like lean TA P, on which it is based, α lean TA P can prove ground theorems in first-order classical logic. Since it is declarative, α lean TA P generates theorems and accepts non-ground theorems and proofs. The lack of mode restrictions also allows the user to provide guidance in proving complex theorems and to ask the prover to instantiate non-ground parts of theorems. We present a complete implementation of α lean TA P, beginning with a translation of lean TA P into αKanren, an embedding of nominal logic programming in Scheme. We then show how to use a combination of tagging and nominal unification to eliminate the impure operators inherited from lean TA P, resulting in a purely declarative theorem prover. © 2008 Springer Berlin Heidelberg.},
bibtype = {article},
author = {Near, J P and Byrd, W E and Friedman, D P},
doi = {10.1007/978-3-540-89982-2_26},
journal = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}
}