## Proof search for programming in Intuitionistic Linear Logic (Extended Abstract) (1994)

Venue: | CADE-12 Workshop on Proof Search in Type-Theoretic Languages |

Citations: | 8 - 3 self |

### BibTeX

@INPROCEEDINGS{Galmiche94proofsearch,

author = {D. Galmiche and E. Boudinet},

title = {Proof search for programming in Intuitionistic Linear Logic (Extended Abstract)},

booktitle = {CADE-12 Workshop on Proof Search in Type-Theoretic Languages},

year = {1994},

pages = {24--30}

}

### OpenURL

### Abstract

Introduction Linear logic (denoted LL) [6] is a powerful and expressive logic with connections to a variety of topics in computer science as logic programming, concurrency or functional programming. From the logical side, LL combines the constructive content of Intuitionistic Logic with the symmetries of Classical Logic and from the computation side, it offers a control on resource management and evaluation order. Concerning functional programming, applications of LL to computation can be seen through the Curry-Howard isomorphism in which propositions are interpreted as types, proofs as programs and proof normalization process as computation. Works have been recently devoted to term assignment for intuitionistic linear logic (ILL) [3, 12] and full LL [1] with proposals of linear lambda calculi having important properties as subject-reduction or substitution property. Having natural deduction and sequent calculus proof systems of ILL (that are proved equivalent), we can investi

### Citations

331 | Logic programming with focusing proofs in linear logic
- Andréoli
(Show Context)
Citation Context ...ogic basis for optimizations in functional programming language implementations by using linear logic as a type system [1, 12]. Other applications include generalized and concurrent logic programming =-=[2, 9, 10]-=-. From specification point of view, ILL provides a natural and simple encoding of Petri net reachability [13] that can be extended to high-level nets [11]. For example, the formula !((a\Omega c)\Gamma... |

303 | D.: Logic programming in a fragment of intuitionistic linear logic
- Hodas, Miller
- 1994
(Show Context)
Citation Context ...r predicate ILL and high-level nets [11] illustrates the interest of proof search methods for proving specifications (and synthesizing programs). Let us mention that works on linear logic programming =-=[9]-=- and on concurrent programming based on proof construction as computation involve also specific logical ILL fragments. Thus, the study of proof search methods for automatic or interactive theorem prov... |

281 | Computational interpretations of linear logic
- Abramsky
- 1993
(Show Context)
Citation Context ... interpreted as types, proofs as programs and proof normalization process as computation. Works have been recently devoted to term assignment for intuitionistic linear logic (ILL) [3, 12] and full LL =-=[1]-=- with proposals of linear lambda calculi having important properties as subject-reduction or substitution property. Having natural deduction and sequent calculus proof systems of ILL (that are proved ... |

72 | A term calculus for intuitionistic linear logic
- Benton, Bierman, et al.
- 1993
(Show Context)
Citation Context ...ich propositions are interpreted as types, proofs as programs and proof normalization process as computation. Works have been recently devoted to term assignment for intuitionistic linear logic (ILL) =-=[3, 12]-=- and full LL [1] with proposals of linear lambda calculi having important properties as subject-reduction or substitution property. Having natural deduction and sequent calculus proof systems of ILL (... |

67 |
From Petri nets to linear logic
- Martí-Oliet, Meseguer
- 1991
(Show Context)
Citation Context ...tem [1, 12]. Other applications include generalized and concurrent logic programming [2, 9, 10]. From specification point of view, ILL provides a natural and simple encoding of Petri net reachability =-=[13]-=- that can be extended to high-level nets [11]. For example, the formula !((a\Omega c)\Gammaffib) is used to encode a Petri net transition taking tokens from place a and c and adding a token to place b... |

46 | ACL — A concurrent linear logic programming paradigm
- Kobayashi, Yonezawa
- 1993
(Show Context)
Citation Context ...ogic basis for optimizations in functional programming language implementations by using linear logic as a type system [1, 12]. Other applications include generalized and concurrent logic programming =-=[2, 9, 10]-=-. From specification point of view, ILL provides a natural and simple encoding of Petri net reachability [13] that can be extended to high-level nets [11]. For example, the formula !((a\Omega c)\Gamma... |

44 | Operational aspects of linear lambda calculus
- Lincoln, Mitchell
- 1992
(Show Context)
Citation Context ...ich propositions are interpreted as types, proofs as programs and proof normalization process as computation. Works have been recently devoted to term assignment for intuitionistic linear logic (ILL) =-=[3, 12]-=- and full LL [1] with proposals of linear lambda calculi having important properties as subject-reduction or substitution property. Having natural deduction and sequent calculus proof systems of ILL (... |

20 | Foundations of proof search strategies design in linear logic
- Galmiche, Perrier
- 1994
(Show Context)
Citation Context ...[10, 13]. These various results are based on different fragments of (intuitionistic or not) LL, different proof search approaches (top-down or bottom-up proof construction, goal-oriented proof search)=-=[4, 5, 14]-=- and lead to proposals for designing automated proof search procedures. The main point is to define subclasses of proofs, in the LL fragment, that are complete and tractable. Here, we have adapted rec... |

16 | On resolution in fragments of classical linear logic
- Harland
- 1992
(Show Context)
Citation Context ...Omega d, considering a goal-oriented proof search. But, for this example, it leads to a failure. It means that we cannot use the notion of uniform proof, issued from works on linear logic programming =-=[8, 9]-=-, to prove such ILL sequents. Thus we have to define adequate proof search methods for ILL theorem proving (dedicated here to program synthesis) but also applicable to applications based on proof-sear... |

14 | A proof-theoretic analysis of goal-directed provability
- Harland
- 1994
(Show Context)
Citation Context ...as computation paradigm. 4 Proof search in ILL Recent works have been devoted to proof search methods and to their applications to various topics of computer science as logic (concurrent) programming =-=[2, 7, 10]-=- or concurrency [10, 13]. These various results are based on different fragments of (intuitionistic or not) LL, different proof search approaches (top-down or bottom-up proof construction, goal-orient... |

11 |
High-level nets and linear logic
- Lilius
- 1992
(Show Context)
Citation Context ...the latter. In this case, proof search corresponds to program synthesis and proof normalization to computation. The correspondence between ILL and Petri nets [13] or predicate ILL and high-level nets =-=[11]-=- illustrates the interest of proof search methods for proving specifications (and synthesizing programs). Let us mention that works on linear logic programming [9] and on concurrent programming based ... |

10 |
Proof search strategies in linear logic
- Tammet
- 1994
(Show Context)
Citation Context ...[10, 13]. These various results are based on different fragments of (intuitionistic or not) LL, different proof search approaches (top-down or bottom-up proof construction, goal-oriented proof search)=-=[4, 5, 14]-=- and lead to proposals for designing automated proof search procedures. The main point is to define subclasses of proofs, in the LL fragment, that are complete and tractable. Here, we have adapted rec... |

3 |
On proof normalisation in linear logic. Research report 93-R059
- Galmiche, Perrier
- 1993
(Show Context)
Citation Context ...[10, 13]. These various results are based on different fragments of (intuitionistic or not) LL, different proof search approaches (top-down or bottom-up proof construction, goal-oriented proof search)=-=[4, 5, 14]-=- and lead to proposals for designing automated proof search procedures. The main point is to define subclasses of proofs, in the LL fragment, that are complete and tractable. Here, we have adapted rec... |