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## Open proofs and open terms: a basis for interactive logic (2002)

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Venue: | Computer Science Logic: 16th International Workshop, CLS 2002, Lecture Notes in Computer Science 2471 (2002 |

Citations: | 16 - 1 self |

### Citations

1266 |
The Lambda Calculus – Its Syntax and Semantics
- Barendregt
- 1981
(Show Context)
Citation Context ...utations with terms containing meta-variable declarations are limited as such terms are not allowed to leak into types. Bognar [4] generalizes the concept of context as used in the untyped λ-calculus=-= [3] -=-and introduces the λ[ ]-cube. Along with the local declarations of meta-variables, these systems have explicit operators for instantiation. For other related work the reader is referred to the papers... |

606 | Lambda Calculi with Types
- Barendregt
(Show Context)
Citation Context ...tions is done in type theory where a number of systems of open terms in (dependently) typed λcalculus exist [16, 10, 4, 12, 9, 6] . They have evolved from existing typing systems (the Barendregt cube=-= [2],-=- ECC [7], Martin-Löf type theory, etc.) when their application in (interactive) theorem proving required formalization of the notion of incomplete term. TypeLab [16] is based on ECC and represents un... |

467 | The Foundation of a Generic Theorem Prover
- Paulson
- 1989
(Show Context)
Citation Context ...eta-variables, these systems have explicit operators for instantiation. For other related work the reader is referred to the papers on λProlog, Isabelle and Twelf and the work of Miller [11], Paulson=-= [13] and-=- Pfenning [14]. The rest of this paper is organized as follows: In Section 2 we treat a number of examples of ‘open proofs’. The examples have been chosen to be quite trivial,sOpen Proofs and Open... |

314 | A logic programming language with lambda-abstraction, function variables, and simple unification
- Miller
- 1991
(Show Context)
Citation Context ...larations of meta-variables, these systems have explicit operators for instantiation. For other related work the reader is referred to the papers on λProlog, Isabelle and Twelf and the work of Miller=-= [11], Pa-=-ulson [13] and Pfenning [14]. The rest of this paper is organized as follows: In Section 2 we treat a number of examples of ‘open proofs’. The examples have been chosen to be quite trivial,sOpen P... |

237 | A Linear Logical Framework
- Cervesato, Pfenning
- 2002
(Show Context)
Citation Context ...se systems have explicit operators for instantiation. For other related work the reader is referred to the papers on λProlog, Isabelle and Twelf and the work of Miller [11], Paulson [13] and Pfenning=-= [14]. Th-=-e rest of this paper is organized as follows: In Section 2 we treat a number of examples of ‘open proofs’. The examples have been chosen to be quite trivial,sOpen Proofs and Open Terms: A Basis fo... |

99 | Logics and Type systems
- Geuvers
- 1993
(Show Context)
Citation Context ...roofs, o-HOL. As usual, we first define the language, then the derivation rules and then the notion of derivability. We show that o-HOL is conservative over HOL, ordinary higher order predicate logic =-=[2, 5]-=-. This means that, if we have derived the higher order formula A in o-HOL without unfinished subproofs, then A is derivable in HOL. Most of o-HOL is the same as HOL, but we present it nevertheless. De... |

90 | An Extended Calculus of Constructions
- Luo
- 1990
(Show Context)
Citation Context ...done in type theory where a number of systems of open terms in (dependently) typed λcalculus exist [16, 10, 4, 12, 9, 6] . They have evolved from existing typing systems (the Barendregt cube [2], ECC=-= [7],-=- Martin-Löf type theory, etc.) when their application in (interactive) theorem proving required formalization of the notion of incomplete term. TypeLab [16] is based on ECC and represents unknown ter... |

81 | Dependently Typed Functional Programs and their proofs
- McBride
- 2000
(Show Context)
Citation Context ...overs – quitewellwhatwewanttobeabletodo. Most of the work in the area of incomplete constructions is done in type theory where a number of systems of open terms in (dependently) typed λcalculus exi=-=st [16, 10, 4, 12, 9, 6] -=-. They have evolved from existing typing systems (the Barendregt cube [2], ECC [7], Martin-Löf type theory, etc.) when their application in (interactive) theorem proving required formalization of the... |

61 | Proof-assistants using dependent type systems
- Barendregt, Geuvers
- 2001
(Show Context)
Citation Context ...‘universes’: Type, the type of all domains (D in the logic), and Prop, the type of all formulas. (Hence Prop : Type.) We do not give a definition of the type system λHOL but refer the reader to [=-=5] or[1]-=-. A central point in this mapping is that all elements of the language and all the variables in a HOL derivation can be systematically given bindings that form a context in type theory and that the de... |

48 |
and Gérard Huet. The calculus of constructions
- Coquand
- 1988
(Show Context)
Citation Context ...deduce C by implication-elimination of the new goals A and B. The first one is solved in (4) by the assumption A and the second by introducing a new goal A and eliminating the assumption A→B. Finally =-=(5)-=- we solve A trivially by the hypothesis A and we have a complete derivation of A→C from A→B→C and A→B. 1. A→B→C A→B 2. A→B→C A→B [A] i ? A→C 3. A→B→C A→B [A] i √ ? A A→B→C B→C C i A→C ? B ? C i A→C 4.... |

45 | The implementation of ALF - A Proof Editor based on Martin-Lof's Monomorphic Type Theory with Explicit Substitutions
- Magnusson
- 1994
(Show Context)
Citation Context ...overs – quitewellwhatwewanttobeabletodo. Most of the work in the area of incomplete constructions is done in type theory where a number of systems of open terms in (dependently) typed λcalculus exi=-=st [16, 10, 4, 12, 9, 6] -=-. They have evolved from existing typing systems (the Barendregt cube [2], ECC [7], Martin-Löf type theory, etc.) when their application in (interactive) theorem proving required formalization of the... |

27 | Pure Type Systems with definitions
- Severi, Poll
- 1994
(Show Context)
Citation Context ...for Interactive Logic 551 where t(n) signifies one specific occurrence of n in t (and similarly for t(n[r]). Details of extensions of type theory with an explicit definition mechanism can be found in =-=[15]. We-=- illustrate how the type-theoretic contexts capture the notion of proof state by the following two examples. Example 18. Consider the ’scratch-paper’ example from Section 3. We can accomodate both... |

18 | A Calculus of Substitutions for Incomplete-Proof Representation in Type Theory
- Muñoz
- 1997
(Show Context)
Citation Context ...overs – quitewellwhatwewanttobeabletodo. Most of the work in the area of incomplete constructions is done in type theory where a number of systems of open terms in (dependently) typed λcalculus exi=-=st [16, 10, 4, 12, 9, 6] -=-. They have evolved from existing typing systems (the Barendregt cube [2], ECC [7], Martin-Löf type theory, etc.) when their application in (interactive) theorem proving required formalization of the... |

12 |
Construction and Deduction in Type Theories
- Strecker
- 1998
(Show Context)
Citation Context |

8 | A lambda-free logical framework - PAL |

1 | Systems for open terms: An overview
- Jojgov
- 2001
(Show Context)
Citation Context |