#### DMCA

## Forum: A multiple-conclusion specification logic (1996)

### Cached

### Download Links

- [www.lix.polytechnique.fr]
- [www.lix.polytechnique.fr]
- [www.lix.polytechnique.fr]
- [citeseerx.ist.psu.edu]
- [www.disi.unige.it]
- DBLP

### Other Repositories/Bibliography

Venue: | Theoretical Computer Science |

Citations: | 96 - 12 self |

### Citations

1714 | The Definition of Standard ML.
- Milner, Tofte, et al.
- 1997
(Show Context)
Citation Context ...level programs using meta-level resolution, as in the last section, should be applicable here as well. In the [5], Chirimar presents a specification of a programming language motivated by Standard ML =-=[28]-=-. In particular, a specification for the call-by-value λ-calculus is provided, and then modularly extended with the specifications of references, exceptions, and continuations: each of these features ... |

1182 | A calculus of mobile processes
- MILNER, PARROW, et al.
- 1989
(Show Context)
Citation Context ...adigm [19, 32]. 2 Design issues The following generalization of the definition of uniform proof was introduced in [23] where it was shown that a certain logic specification inspired by the π-calculus =-=[27]-=- can be seen as a logic program. Definition 1 A cut-free sequent proof Ξ is uniform if for every subproof Ξ ′ of Ξ and for every non-atomic formula occurrence B in the right-hand side of the end-seque... |

995 |
A Formulation of the Simple Theory of Types
- Church
- 1940
(Show Context)
Citation Context ...ons simple and natural, is used in this paper. We employ the logical connectives of Girard [9] (typeset as in that paper) and the quantification and term structures of Church’s Simple Theory of Types =-=[6]-=-. A signature Σ is a finite set of pairs, written c : τ, where c is a token and 2sτ is a simple type (over some fixed set of base types). We assume that a given token is declared at most one type in a... |

827 | Light Linear Logic.
- Girard
- 1998
(Show Context)
Citation Context ...evel judgment that a sequent is provable: that is, ∆ ⊢ Γ means that the two-sided sequent ∆ −→ Γ has a linear logic proof. The sequents of F are similar to those used in the LU proof system of Girard =-=[10]-=- except that we have followed the tradition of [1, 14] in writing the “classical” context (here, Ψ and Υ) on the outside of the sequent and the “linear” context (here, ∆ and Γ) nearest the sequent arr... |

794 | A framework for defining logics
- Harper, Honsell, et al.
- 1993
(Show Context)
Citation Context ...r the specification of the NM1 natural deduction proof system given in Figure 4. The specification there is similar to those given using intuitionistic meta-logics [7, 29] and dependent typed calculi =-=[3, 13]-=-. Proposition 8 (Correctness of NM1) The formula B0 has an NM1 proof from the assumptions B1, . . . , Bn (n ≥ 0) if and only if has a proof in F. Σ1: NM1, right B1, . . . , right Bn; · −→ right B0; · ... |

470 | Isabelle: A Generic Theorem Prover
- Paulson
- 1994
(Show Context)
Citation Context ... ˆ ∀R) and ( ˆ ∀L), the type of B is i → bool. This style representation of quantification is familiar from Church [6] and has been used to advantage in computer systems such as λProlog [7], Isabelle =-=[29]-=-, and Elf [30]. This style of representing object-level syntax is often called higher-order abstract syntax. To illustrate how these clauses specify the corresponding object-level inference rule, cons... |

428 | A.: Uniform Proofs as a Foundation for Logic Programming,
- Miller, Nadathur, et al.
- 1991
(Show Context)
Citation Context ...e also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum. This paper will appear in Theoretical Computer Science. 1s1 Introduction In =-=[25]-=- a proof theoretic foundation for logic programming was proposed in which logic programs are collections of formulas used to specify the meaning of non-logical constants and computation is identified ... |

419 | Logic Programming with Focusing Proofs in Linear Logic,
- Andreoli
- 1992
(Show Context)
Citation Context ...essiveness of full logic by introducing non-logical constants and programs to describe their meaning. Felty in [7] uses a meta-logical presentation to specify full logic at the object-level. Andreoli =-=[1]-=- provides a “compilationlike” translation of linear logic into LinLog (of which LO is a subset). Forum has a more immediate relationship to all of linear logic since no non-logical symbols need to be ... |

340 | Logic programming in a fragment of intuitionistic linear logic.
- Hodas, Miller
- 1994
(Show Context)
Citation Context ...∆ ⊢ Γ means that the two-sided sequent ∆ −→ Γ has a linear logic proof. The sequents of F are similar to those used in the LU proof system of Girard [10] except that we have followed the tradition of =-=[1, 14]-=- in writing the “classical” context (here, Ψ and Υ) on the outside of the sequent and the “linear” context (here, ∆ and Γ) nearest the sequent arrow: in LU these conventions are reversed. Given the in... |

306 | Investigations into logical deductions. - Gentzen - 1969 |

230 |
CML: A higher-order concurrent language
- Reppy
- 1991
(Show Context)
Citation Context ...the π-calculus were shown in [23] to be expressible naturally in a fragment of linear logic subsumed by Forum. Below we show how concurrency primitives, inspired by those found in Concurrent ML (CML) =-=[31]-=- can be specified in Forum. Consider the specification in Figure 10. The first eight clauses specify the straightforward evaluation rules for the corresponding eight data constructors. The next three ... |

206 | Linear objects: logical processes with built-in inheritance - Andreoli, Pareschi - 1990 |

166 |
A Logical Analysis of Modules in Logic Programming.
- Miller
- 1989
(Show Context)
Citation Context ...on θ over the variables ¯x. Such a clause provides no overt clues as to when it can be effectively used to prove a given goal: backchaining using a clause with an empty head is always successful. See =-=[21]-=- for a discussion of a similar problem when negated clauses are allowed in logic programming based on minimal or intuitionistic logic. As we shall see in the next section, the specification of the cut... |

165 | Higher-order logic programming.
- Miller, Nadathur
- 1986
(Show Context)
Citation Context ...mulas are from L1 and are also Σ-formulas. (The introduction of signatures into sequents is not strictly necessary but is desirable when this proof system is used for logic programming specifications =-=[22]-=-.) The intended meanings of these two sequents in linear logic are ! Ψ, ∆ −→ Γ, ? Υ and ! Ψ, ∆, B −→ Γ, ? Υ, respectively. In the proof system of Figure 1, the only right rules are those for sequents ... |

113 | The pi-calculus as a theory in linear logic: Preliminary results
- Miller
- 1992
(Show Context)
Citation Context ...programming and used linear logic connectives to extend previous languages in this paradigm [19, 32]. 2 Design issues The following generalization of the definition of uniform proof was introduced in =-=[23]-=- where it was shown that a certain logic specification inspired by the π-calculus [27] can be seen as a logic program. Definition 1 A cut-free sequent proof Ξ is uniform if for every subproof Ξ ′ of Ξ... |

93 | Using Typed Lambda Calculus to Implement Formal Systems on a Machine.
- Avron, Honsell, et al.
- 1992
(Show Context)
Citation Context ...r the specification of the NM1 natural deduction proof system given in Figure 4. The specification there is similar to those given using intuitionistic meta-logics [7, 29] and dependent typed calculi =-=[3, 13]-=-. Proposition 8 (Correctness of NM1) The formula B0 has an NM1 proof from the assumptions B1, . . . , Bn (n ≥ 0) if and only if has a proof in F. Σ1: NM1, right B1, . . . , right Bn; · −→ right B0; · ... |

87 | A multiple-conclusion meta-logic
- Miller
- 1994
(Show Context)
Citation Context ...the problem of code rescheduling. His proofs and analyses made use of familiar aspects of proof theory and linear logic. Acknowledgments. This paper is an extended version of a paper that appeared as =-=[24]-=- and which was also presented at the 1994 Joint Meeting of ALP and PLILP, Madrid, September 1994. I benefited from discussions with Jawahar Chirimar and Bob Harper. Thanks also to Bow-Yaw Wang for his... |

80 | Elf: a language for logic definition and verified metaprogramming
- Pfenning
(Show Context)
Citation Context ... ∀L), the type of B is i → bool. This style representation of quantification is familiar from Church [6] and has been used to advantage in computer systems such as λProlog [7], Isabelle [29], and Elf =-=[30]-=-. This style of representing object-level syntax is often called higher-order abstract syntax. To illustrate how these clauses specify the corresponding object-level inference rule, consider in more d... |

68 | Implementing tactics and tacticals in a higher-order logic programming language
- Felty
- 1993
(Show Context)
Citation Context ... The other logic programming languages we have mentioned can, of course, capture the expressiveness of full logic by introducing non-logical constants and programs to describe their meaning. Felty in =-=[7]-=- uses a meta-logical presentation to specify full logic at the object-level. Andreoli [1] provides a “compilationlike” translation of linear logic into LinLog (of which LO is a subset). Forum has a mo... |

63 | Lexical scoping as universal quantification
- Miller
- 1989
(Show Context)
Citation Context ...res the counter’s value is itself local to the counter’s specification (such existential quantification of predicates is a familiar technique for implementing abstract data types in logic programming =-=[20]-=-). The first two specifications store the counter’s value on the right of the sequent arrow, and reading and incrementing the counter occurs via a synchronization between an eval-atom and an r-atom. I... |

50 | Acl - a concurrent linear logic programming paradigm. In
- Kobayashi, Yonezawa
- 1993
(Show Context)
Citation Context ...ased on linear logic, there have been other linear logic programming languages proposed that it does not extend or otherwise relate directly. In particular, the language ACL by Kobayashi and Yonezawa =-=[17, 18]-=- captures simple notions of asynchronous communication by identifying the send and read primitives with two complementary linear logic connectives. Also, Lincoln and Saraswat have developed a linear l... |

47 | Proof Theoretic Approach to Specification Languages
- Chirimar
- 1995
(Show Context)
Citation Context ... anything formal, although it should be clear that the approach to reasoning about object-level programs using meta-level resolution, as in the last section, should be applicable here as well. In the =-=[5]-=-, Chirimar presents a specification of a programming language motivated by Standard ML [28]. In particular, a specification for the call-by-value λ-calculus is provided, and then modularly extended wi... |

34 | Permutabilities of inferences in gentzen’s calculi LK and LJ - Kleene - 1952 |

27 |
Type-Theoretic Foundations for Concurrent Object-Oriented Programming
- Kobayashi, Yonezawa
- 1994
(Show Context)
Citation Context ...ased on linear logic, there have been other linear logic programming languages proposed that it does not extend or otherwise relate directly. In particular, the language ACL by Kobayashi and Yonezawa =-=[17, 18]-=- captures simple notions of asynchronous communication by identifying the send and read primitives with two complementary linear logic connectives. Also, Lincoln and Saraswat have developed a linear l... |

24 |
Towards foundations for concurrent objectoriented programming – types and language design. Theory and Practice of Object Systems
- Kobayashi, Yonezawa
- 1995
(Show Context)
Citation Context ...ased on linear logic, there have been other linear logic programming languages proposed that it does not extend or otherwise relate directly. In particular, the language ACL by Kobayashi and Yonezawa =-=[17, 18]-=- captures simple notions of asynchronous communication by identifying the send and read primitives with two complementary linear logic connectives. Also, Lincoln and Saraswat have developed a linear l... |

19 |
Extended natural semantics
- Hannan
- 1993
(Show Context)
Citation Context ...and the possibility of handling some substructural object-logics. 6 Operational Semantics Examples Evaluation of pure functional programs has been successfully specified in intuitionistic meta-logics =-=[11]-=- and type theories [4, 30] using structured operational semantics and natural semantics. These specification systems are less successful at providing natural specifications of languages that incorpora... |

18 |
Program Transformations and WAM-support for the Compilation of Definite Metaprograms
- Tarau
- 1992
(Show Context)
Citation Context ...this specification must be made more explicit: in particular, the exact order in which M, N, and (R U) are evaluated must be specified. Using a “continuation-passing” technique from logic programming =-=[33]-=-, this ordering can be made explicit using the following two clauses, this time using the predicate eval at type tm → tm → o → o. eval (app M N) V K ◦− eval M (abs R) (eval N U (eval (R U) V K)). eval... |

8 |
A brief introduction to linear concurrent constraint programming. Xerox PARC
- Saraswat
- 1993
(Show Context)
Citation Context ...ogic connectives. Also, Lincoln and Saraswat have developed a linear logic version of concurrent constraint programming and used linear logic connectives to extend previous languages in this paradigm =-=[19, 32]-=-. 2 Design issues The following generalization of the definition of uniform proof was introduced in [23] where it was shown that a certain logic specification inspired by the π-calculus [27] can be se... |

7 |
A natural deduction treatment of operational semantics
- Burstall, Honsell
- 1988
(Show Context)
Citation Context ...handling some substructural object-logics. 6 Operational Semantics Examples Evaluation of pure functional programs has been successfully specified in intuitionistic meta-logics [11] and type theories =-=[4, 30]-=- using structured operational semantics and natural semantics. These specification systems are less successful at providing natural specifications of languages that incorporate references and 26sconcu... |

5 | On Goal-directed Provability in Classical Logic
- Harland, Pym
- 1992
(Show Context)
Citation Context ...omic formulas, how should the logical connectives at the head of those formulas be introduced? There seems to be two choices. One choice simply requires that one of the possible introductions be done =-=[12]-=-. This choice has the disadvantage that there might be interdependencies between right-introduction rules: thus, the meaning of the logical connectives in the goal would not be reflected directly and ... |

2 |
concurrent constraint programming. Available as file://parcftp.xerox.com/pub/ccp/lcc/hlcc.dvi
- Higher-order
- 1993
(Show Context)
Citation Context ...ogic connectives. Also, Lincoln and Saraswat have developed a linear logic version of concurrent constraint programming and used linear logic connectives to extend previous languages in this paradigm =-=[19, 32]-=-. 2 Design issues The following generalization of the definition of uniform proof was introduced in [23] where it was shown that a certain logic specification inspired by the π-calculus [27] can be se... |