## TAS - A Generic Window Inference System

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### BibTeX

@MISC{Lüth_tas-,

author = {Christoph Lüth and Burkhart Wolff},

title = {TAS - A Generic Window Inference System},

year = {}

}

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### Abstract

This paper presents work on technology for transformational proof and program development, as used by window inference calculi and transformation systems. The calculi are characterised by a certain class of theorems in the underlying logic. Our transformation system TAS compiles these rules to concrete deduction support, complete with a graphical user interface with command-language-free user interaction by gestures like drag&drop and proof-by-pointing, and a development management for transformational proofs. It is generic in the sense that it is completely independent of the particular window inference or transformational calculus, and can be instantiated to many different ones; three such instantiations are presented in the paper.

### Citations

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Citation Context ... the graphical user interface, e.g. as a scripting engine to check proofs. 3 Design Transformations in Classical Program Transformation In the design of algorithms, certain schemata can be identified =-=[7]-=-. When such a schema is formalised as a theorem in the form of (6), we call the resulting transformation rule a design transformation. Examples include divide and conquer [20], global search [22] or b... |

583 |
The theory and practice of concurrency
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Citation Context ...ther powerful design transformation which has already been formalised in an earlier version of TAS [13]. 4 Process Modelling with CSP This section shows how to instantiate TAS for refinement with CSP =-=[19]-=-, and will briefly present an example how the resulting system can be used. CSP is a language designed to describe systems of interacting components. It is supported by an underlying theory for reason... |

467 | The Science of Programming - Gries - 1981 |

238 | KIDS: A semiautomatic program development system
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(Show Context)
Citation Context ...s by transformation as in calculus. As a way out of this dilemma, a number of systems have been developed to support transformational development. However, many of these systems such as CIP [3], KIDS =-=[21]-=- or PROSPECTRA [12] suffered from a lack of proof support and proven correctness. On the other hand, a variety of calculi have been developed which allow formal proof in a transformational way and are... |

121 |
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(Show Context)
Citation Context ... window inference. 2.1 An Introduction to Window Inference As motivating example, consider the proof for ⊢ (A ∧ B ⇒ C) ⇒ (B ∧ A ⇒ C). In natural deduction, a proof would look like (in the notation of =-=[27]-=-; we assume that the reader is roughly familiar with derivations like this): [B ∧ A] 1 [B ∧ A]1 ∧E ∧E A B ∧I A ∧ B [A ∧ B ⇒ C] 2 ⇒ E C ⇒ I1 B ∧ A ⇒ C ⇒ I2 (A ∧ B ⇒ C) ⇒ (B ∧ A ⇒ C) The following equiv... |

61 |
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Citation Context ...ects of its behaviour, which can then be validated by a model-checker. For example, deadlock checks using CSP and FDR have been carried out in this manner, where the abstraction has been done manually=-=[4,5, 17]-=-. Thus we believe that TAS represents an important step towards our ultimate goal of a transformation system which is similarly flexible with respect to underlying specification languages and refineme... |

47 |
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Citation Context ... development, for process-oriented refinement proofs and for data-oriented refinement proofs. Sect. 6 finishes with conclusions and an outlook. 2 A Generic Scheme of Window Inference Window inference =-=[18]-=-, structured calculational proof [8, 1, 2] and transformational hierarchical reasoning [11] are closely related formalisations of proof by transformation. In this paper, we will use the format of [1],... |

47 | Algorithm theories and design tactics
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Citation Context ...ified [7]. When such a schema is formalised as a theorem in the form of (6), we call the resulting transformation rule a design transformation. Examples include divide and conquer [20], global search =-=[22]-=- or branch and bound. Recall from Sect. 2.2 that transformation rules are represented by a logical core theorem with an input pattern and an output pattern. Characteristically, design transformations ... |

28 | Refinement Calculus
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Citation Context ...finement proofs and for data-oriented refinement proofs. Sect. 6 finishes with conclusions and an outlook. 2 A Generic Scheme of Window Inference Window inference [18], structured calculational proof =-=[8, 1, 2]-=- and transformational hierarchical reasoning [11] are closely related formalisations of proof by transformation. In this paper, we will use the format of [1], although we will refer to it as window in... |

22 | Static semantic analysis and theorem proving for Casl
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(Show Context)
Citation Context ...ould like to see more instances for TAS. Transformational development and proof in the specification languages Z and CASL should not be too hard, since for both embeddings into Isabelle are available =-=[13, 16]-=-. The main step here is to formalise appropriate notions of refinement. A rather simple different instantiation is obtained by turning the refinement relation around. This amounts to abstracting a con... |

22 | A corrected failure-divergence model for CSP in Isabelle/HOL
- Tej, Wolff
- 1997
(Show Context)
Citation Context ...e systems of interacting components. It is supported by an underlying theory for reasoning about their equivalences, and in particular their refinements. In this section, we use the embedding HOL-CSP =-=[26]-=- of CSP into Isabelle/HOL. Even though shortage of space precludes us the set out the basics of CSP here, a detailed understanding of CSP is not required in the following; suffice it to say that CSP i... |

22 | On the Shape of Mathematical Arguments - Gasteren - 1988 |

19 |
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Citation Context ...s. Sect. 6 finishes with conclusions and an outlook. 2 A Generic Scheme of Window Inference Window inference [18], structured calculational proof [8, 1, 2] and transformational hierarchical reasoning =-=[11]-=- are closely related formalisations of proof by transformation. In this paper, we will use the format of [1], although we will refer to it as window inference. 2.1 An Introduction to Window Inference ... |

18 | Correct and user-friendly implementations of transformation systems
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(Show Context)
Citation Context ... in algorithm design is global search which has been investigated formally in [22]. It represents another powerful design transformation which has already been formalised in an earlier version of TAS =-=[13]-=-. 4 Process Modelling with CSP This section shows how to instantiate TAS for refinement with CSP [19], and will briefly present an example how the resulting system can be used. CSP is a language desig... |

18 | Functional design and implementation of graphical user interfaces for theorem provers
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Citation Context ... and formal methods. Reusability of components is crucial, since we hope that the considerable task of developing appropriate GUIs for formal method tools can be shared with other research groups. In =-=[15]-=-, we have proposed an open architecture to build graphical user interfaces for theorem provers in a functional language; here, we instantiate thissarchitecture with a generic transformation system whi... |

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Citation Context ...ects of its behaviour, which can then be validated by a model-checker. For example, deadlock checks using CSP and FDR have been carried out in this manner, where the abstraction has been done manually=-=[4,5, 17]-=-. Thus we believe that TAS represents an important step towards our ultimate goal of a transformation system which is similarly flexible with respect to underlying specification languages and refineme... |

17 | Teaching calculation and discrimination: A more effective curriculum - Gries - 1991 |

16 | Structured calculational proof
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(Show Context)
Citation Context ...finement proofs and for data-oriented refinement proofs. Sect. 6 finishes with conclusions and an outlook. 2 A Generic Scheme of Window Inference Window inference [18], structured calculational proof =-=[8, 1, 2]-=- and transformational hierarchical reasoning [11] are closely related formalisations of proof by transformation. In this paper, we will use the format of [1], although we will refer to it as window in... |

12 |
The design of divide and conquer algorithms
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- 1985
(Show Context)
Citation Context ...chemata can be identified [7]. When such a schema is formalised as a theorem in the form of (6), we call the resulting transformation rule a design transformation. Examples include divide and conquer =-=[20]-=-, global search [22] or branch and bound. Recall from Sect. 2.2 that transformation rules are represented by a logical core theorem with an input pattern and an output pattern. Characteristically, des... |

9 | PROSPECTRA: program development by specification and transformation - Hoffmann, Krieg-Brückner - 1993 |

9 |
A Mechanised Theory of Refinement
- Staples
- 1999
(Show Context)
Citation Context ...s example, we will use Zermelo-Fränkel set theory (as encoded in Isabelle/ZF). On top of Isabelle/ZF, Mark Staples has built a substantial theory for imperative program refinement and data refinement =-=[24,25]-=- following the lines of Back’s Refinement Calculus RC [2]. RC is based on a weakest precondition semantics, where predicates and predicate transformers are represented as sets of states and functions ... |

8 |
A program refinement tool
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(Show Context)
Citation Context ...ness. On the other hand, a variety of calculi have been developed which allow formal proof in a transformational way and are proven correct [8–10,28, 11, 2], some even with a graphical user interface =-=[14,6]-=-. However, what has been lacking is a systematic, generic and reusable way to obtain a user-friendly tool implementing transformational reasoning, with an open system architecture capable of coping wi... |

5 |
The Munich Project CIP. The Wide Spectrum Language CIP-L
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(Show Context)
Citation Context ...d to proofs by transformation as in calculus. As a way out of this dilemma, a number of systems have been developed to support transformational development. However, many of these systems such as CIP =-=[3]-=-, KIDS [21] or PROSPECTRA [12] suffered from a lack of proof support and proven correctness. On the other hand, a variety of calculi have been developed which allow formal proof in a transformational ... |

5 | Window inference in isabelle
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- 1995
(Show Context)
Citation Context ...ng and closing subwindows, – applying transformations, – searching for applicable transformations, – and starting and concluding developments.sIn general, our implementation follows Staples’ approach =-=[23]-=-, for example in the use of the transitivity rules to translate the forward chaining of transformation steps into backwards proofs on top of Isabelle’s goal package, or the reflexivity rules to close ... |

3 | Program Development by Speci and Transformation - Homann, Krieg-Bruckner - 1993 |

2 |
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(Show Context)
Citation Context ...ness. On the other hand, a variety of calculi have been developed which allow formal proof in a transformational way and are proven correct [8–10,28, 11, 2], some even with a graphical user interface =-=[14,6]-=-. However, what has been lacking is a systematic, generic and reusable way to obtain a user-friendly tool implementing transformational reasoning, with an open system architecture capable of coping wi... |

2 | Representing wp semantics in isabelle/zf
- Staples
- 1999
(Show Context)
Citation Context ...s example, we will use Zermelo-Fränkel set theory (as encoded in Isabelle/ZF). On top of Isabelle/ZF, Mark Staples has built a substantial theory for imperative program refinement and data refinement =-=[24,25]-=- following the lines of Back’s Refinement Calculus RC [2]. RC is based on a weakest precondition semantics, where predicates and predicate transformers are represented as sets of states and functions ... |

2 |
Extending window inference
- Wright
- 1998
(Show Context)
Citation Context ..., process refinement S ⊑F D P (the process P is more defined and more deterministic than the process S, see Sect. 4), set inclusion (see Sect. 5), or arithmetic orderings for numerical approximations =-=[29]-=-. An example for an infinite family of refinement relations in HOL is the Scott-definedness ordering for higher-order function spaces (where the indexing set I is given by the types): f ⊑(α→β)×(α→β)→B... |

2 | A Mechanised Theory of Re - Staples - 1998 |

1 |
Combining methods for the deadlock analysis of a fault-tolerant system
- Buth, Peleska, et al.
- 1997
(Show Context)
Citation Context ...ects of its behaviour, which can then be validated by a model-checker. For example, deadlock checks using CSP and FDR have been carried out in this manner, where the abstraction has been done manually=-=[4,5, 17]-=-. Thus we believe that TAS represents an important step towards our ultimate goal of a transformation system which is similarly flexible with respect to underlying specification languages and refineme... |

1 | A Program Re Tool. Formal Aspects of Computing - Carrington, Hayes, et al. - 1998 |

1 | Teaching calculation and discrimination: A more eecticulum - Gries - 1991 |