Y. Bertot, G. Kahn, and L. Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and could probably be reformulated in a uniform way, instead of deriving ad hoc results along the way. A few files contain as well proof texts that were automatically generated by CtCoq 96b] which is an user interface that allows one to perform derivations with the proof by pointing technique [BKT94]. This technique has turned out to be helpful for general theorems, in that the user has facilities to build a proof by controlling its general shape without entering too much into the details at first. For technical lemmas, however, a direct interaction with the Coq system is often more ....

Y. Bertot, G. Kahn, and L. Th'ery. Proof by pointing. In Proceedings of STACS, LNCS, Sendai (Japan), April 1994.

....suggested that window inference could form the basis of a simple graphic user interface to the HOL system. While in Cambridge, Laurent Th ery of INRIA Sophia Antipolis constructed a graphic front end for the window inference interface [Th e93] The front end was constructed using the Centaur tool [BKT94, TBK92] Users of the graphic front end may open subwindows on terms in the focus or context of a window by selecting the desired subterm with the mouse. A variety of transformations, like rewriting, can be applied to a window by selecting them from a menu. Users can write their own ....

Yves Bertot, Gilles Kahn, and Laurent Th'ery. Proof by pointing. In Takayasu Ito, Masami Hagiya, Albert R. Meyer, and John Mitchell, editors, Proceedings of the Symposium on Theoretical Aspects of Computer 193 Science, Tohoku University, Sendai, Japan, 19--21 April 1994. Information Processing Society of Japan.

....proof assistant top level. Bertot, Th ery and Kahn [TBK92] showed that the technology developed around the Centaur system to define programming environments could be used to provide graphical interfaces for interactive proof systems. Doing so, they came up new ideas such as proof by selection [BKT94] or the drag and drop mechanism [Ber97] After various experiments on the systems HOL, Isabelle and Lego, this technology was fully implemented for the Coq system giving rise to the CtCoq (now PCoq) environment used for our work. Some of the ideas developed in the CtCoq system were recently ....

Yves Bertot, Gilles Kahn, and Laurent Th'ery. Proof by Pointing. In International Symposium on Theoretical Aspects of Computer Science, 1994.

....support. Mathspad[3] has very similar intension as we have in RefStep. Their tool supports the notational conventions of Gries and Schneider [7] by a stencil that is comparable to our theories. Mathspad s goal is literate programming and the interfacing to other systems. Proof by Pointing [4] is an interesting possibility of performing proofs under the unique control of the mouse. It is based on logical deduction and has similarities to window inference. CADiZ [15] allows similar to RefStep the direct manipulation of well formed formulae. The subterm selection mechanism as described ....

Yves Bertot, Gilles Kahn, and Laurent Th'ery. Proof by pointing. In STACS'94, number 789 in LNCS, 1994.

....sketches by a human user on different abstraction layers is made possible through a graphical interface which follows the paradigm of direct manipulation. In addition, it provides comprehensive hypertext facilities to access information of the actual specification. In contrast to, for instance [BKT94] the INKA interface is entirely integrated into the theorem prover in order to achieve a close interlocking between users hints and the strategies of the prover. ....

Yves Bertot, Gilles Kahn, and Laurent Th'ery. Proof by pointing. In Symposium on Theoretical Aspects Computer Software, Lecture Notes in Computer Science (LNCS) 789, Sendai, Japan, April 1994. STACS, Springer-Verlag, Berlin, Germany.

....intermediate goals) can be explicitly embedded in a proof script, which also improves the readability of the proof script. It is not necessary to write such subgoals by hand, as they are usually inserted as a result of the local execution of a tactic. The user can also employ proof by pointing [BKT94]. At any position in a proof script, the user can pop up the current goal window (Figure 7) and point to a subterm in the current goal using a mouse. A tactic called a proof by pointing tactic is then generated and inserted into the proof script (Figure 8) Since the result of proof by pointing ....

....it is possible to propagate the change through the script by repeatedly invoking this command. It is also considered as solving the constraint between a CLAIM and a tactic before it. Proving as Editing HOL Tactics 7 Fig. 7. A window of the current goal 3. Proof by pointing Proof by pointing [BKT94] is a very useful interface for interactive theorem proving. Proof by pointing starts with pointing to a subterm in a goal. The goal is repeatedly decomposed by inference rules until the subterm appears at the top level. For example, when the user points to the subterm B in the goal A = B ....

Bertot, Y., Kahn, G. and Thery, L.: Proof by Pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, 1994, pp.141-160.

....ihintj list of theorems, etc. 3.3 The user interface Coq is an interactive proof assistant and not an automatic theorem prover. Therefore it is crucial to provide a good user interface [4] CtCoq is such an interface for Coq. Proof developments with CtCoq are eased thanks to iproof by pointingj [5], terms are pretty printed and pseudo natural language text can be extracted from proof terms [10] 4 4 Microprocessor modeling with Coq Hardware verication seems to be one of the major uses of theorem provers and proof assistants. But this is not the case for Coq since to our knowledge the ....

Y. Bertot, G. Kahn, and L. Th#ry. Proof by pointing. In Theoretical Aspects of Computer Science, volume 789 of Lecture Notes in Computer Science, Sendai, Japan, 1994.

....to accompany the actual on line theorems. Various references are made to Nuprl libraries in the text. In the html version these were hot references (one could click on them to open the referenced files) 2 Type Theory Preliminaries Accounts of Nuprl s type theory can be found in several sources [8, 35, 20, 1, 6]. 2.1 Basic Types The integers Z= f0; Sigma1; Sigma2; g are a primitive type of Nuprl with primitive operations of ; Gamma ; Delta ; Xi ; rem (for remainder) Equality, x = y in Z, and order, x y , are also primitive. The natural numbers N are defined as fi : Zj 0 ig, and the ....

....There is a subtle computational point about these sets, namely a function f from fx : A j P (x)g to B does not have access to a proof that P (x) holds when calculating its value f(x) 5 4 We only need the universe of small types denoted simply U. For a full discussion of universes, see Allen [1] as well as Jackson [20] 5 A discussion of the constructive meaning of these types is beyond the scope of this work, but see [9, 20, 28] A finite type is one which can be put into a 1 1 correspondence with [1 : n] its cardinality is n. We write Fin(T ) to mean that T is finite. This ....

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Y. Bertot, G. Kahn, and L. Th'ery. Proof by pointing. In Theoretical Aspects of Computer Software, Lecture Notes in Computer Science, volume 789, pages 141--160, 1994.

....interface of our system is implemented in Centaur [3] In particular, we build on an existing interface for the theorem prover obtained from the rst order intuitionistic logic speci cation mentioned above. First, we extend the techniques of proof by pointing and point and shoot described in [2] to associate operations to mouse clicks on temporal formulas. Second, we extend techniques for generating textual explanations from proofs. To do so, we de ne a natural deduction inference system which is better suited than the sequent calculus to the generation of readable text. We extend the ....

....proofs for this fragment. 4 Proof Construction Interactive proof construction is most often done in a backward direction. The user sets a goal and then, applying the rules of the logic, tries to reduce it to already known theorems or axioms. The technique of proof by pointing described in [2] provides a means of giving proof directions by selecting subexpressions of goals. It has been proved sound and complete for classical logic. In what follows, we explain how the technique can be extended to our sequent system for S4.3, and we give some examples of proofs of temporal properties. We ....

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Y. Bertot, G. Kahn, and L. Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

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Yves Bertot, Gilles Kahn, and Laurent Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

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Bertot, Y., Kahn, G., & Th'ery, L. (1994). Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141--160.

....proposals around XML: OpenMath and MathML. Manipulating mathematical formulas as structured data, we have been able to instrument the proof development environment with capabilities that increase the bandwidth between the user and the logical engine. An example is that of Proof by pointing [3], where complex commands can be constructed in one click by the user, through an analysis of the mouse position in the formula. Another capability that is instrumental in enhancing the bandwidth between the user and the logical engine is the possibility to layout the mathematical formulas in a ....

....that can be manipulated using the mouse. This can be used for constructing proof commands: since we know how to display proofs that are not yet nished, this interaction can be used to complete proofs. In our experiment, we combine textual proof presentation with proof bypointing as described in [3]. It is instrumental that logical formulas appearing in the text are displayed as structured data exactly in the same manner as they are when using plain goal directed proof. We must also take into account the fact that several goals may occur at the same time in the proof text. Each sentence of ....

Yves Bertot, Gilles Kahn, and Laurent Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

....are much more powerful than the STSRs presented here. However, the STSRs avoid to confront a user with proofs in higher order logic. Moreover, the direct combination with the interaction makes the STSRs di erent. Other concepts on proving by mouse click have been presented: proof by pointing [BKT94] and proof by drag and drop [Ber97] are two very interesting techniques. The aim of proof by pointing is to bring subformulas to the surface, however, it does not focus on theory speci c knowledge. The aim of proof by drag and drop is to select term rewriting steps by what Bertot calls a gesture. ....

Y. Bertot, G. Kahn, and L. Thery. Proof by pointing. In M. Hagiya and J. C. Mitchell, editors, Theoretical Aspects of Computer Software (TACS '94), number 789 in LNCS. Springer, 1994.

.... 88] Over the years, CtCoq has been used to perform larger and larger proof developments [BF95, Th#98, Ber98] and to experiment with new interaction ideas. For instance, we have proposed new techniques to guide the proof process using the mouse, with proof by pointing for predicate calculus [BKT94] and drag and drop for algebraic manipulations [Ber97a] We have also described tools to help undo selectively past commands [Pon97] and, more generally use dependencies between commands or mathematical objects [PBR98] We have accumulated a wealth of experience regarding the integration of a ....

....of CtCoq revolve around its capability to let the user guide proofs using the mouse in a very eOEcient way. Of course, one could consider providing menus with all the Coq commands, but this would be much less eOEcient than usual text interaction. Instead, we have implemented proof by pointing [BKT94, BT98] and drag anddrop [Ber97a] The rst facility interprets clicking actions as a language to perform proofs in predicate calculus. For instance, let us consider the following goal: 8x : nat: 9y : nat: x = 2 Theta y) even(x) If the user simply clicks on the second x and chooses the ....

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Yves Bertot, Gilles Kahn, and Laurent Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

....possible to provide more elaborate notations and to give more help to the editor, in the form of menus which indicate the constructs that are allowed in the current context. On the other hand, structure editing puts constraints on the editing process, which some users may nd unwieldy. The paper [2] introduces a man machine interaction technique called proof by pointing, which makes it possible to perform entire proofs in propositional logic using only the mouse to convey the intentions of the human user in a very eOEcient way. The intuitive idea of this technique is that the proof system ....

....the goals in a graphical window, and the user can guide the proof process by simply indicating the sub expressions of these goals that are important. The proof system then executes commands that bring these sub expressions to ithe foregroundj and applies trivial reasoning gures. The authors of [2] insist that the technique relies on a need for the editing component to be aware of the structure of logical formulas and they explain that their use of an environment based on structure editing makes this constraint easy to cope with. This paper completes the work on proof by pointing by ....

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Yves Bertot, Gilles Kahn, and Laurent Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141 160, 1994.

....environments, with control and composition operators. Recent studies in the user interface of theorem proving tools [22] have shown that the characteristics of modern computer workstations could be used eOEciently to improve the usage of proof environments. With features like Proofby pointing [2], it is possible to interpret simple tokens of information, like the position of the mouse with respect to a logical formula, to produce complex 2 tactics. In this paradigm, mouse interaction is considered a high level language, compiled into the tactics language, considered as a low level ....

....and has led to many implementations of proof systems [1315,7] Work on proof by pointing is the initial incentive for this work on tactic optimisation. Proof by pointing, where commands are generated from an inter 3 pretation of locations selected by the user, has been formally described in [2] and [4] It has been implemented in several experiments of proof environments, based on a variety of proof systems: Isabelle [20] HOL [21] a theorem prover developped in prolog [8] and Coq [13] all using a structure editor [22,5] to facilitate the input of mouse location information. ....

[Article contains additional citation context not shown here]

Yves Bertot, Gilles Kahn, and Laurent Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

....to observe formal proofs that makes it easier to introduce proof systems to mathematicians. These advanced functionalities rely extensively on the basic components described previously and justify our technological choices. 3.1. Proof by pointing In the functionality we call proof by pointing in Bertot et al. 1994), the goals output by the proof system after each proof step are used to generate new commands. While the menus presented in section 2.4.1 use a very limited notion of context, restricted to the sort of the current selection in the main window, the guidance provided by proof by pointing is more ....

.... B Gamma A oe B 8 left : A[xne] 8x A; Gamma C 8x A ; Gamma C 8 right : Gamma A[xnc] Gamma 8x A 9 left : A[xnc] 9x A; Gamma C 9x A ; Gamma C 9 right : Gamma A[xne] Gamma 9x A Figure 8. Rules of proof by pointing removes assumptions from the context. In Bertot et al. 1994), we propose a ilinearj form of the algorithm that destroys assumptions that are used during the development of the algorithm. This linear algorithm is an overkill: some proofs are no longer possible because assumptions that would have been used twice are destroyed at the rst occasion. The ....

[Article contains additional citation context not shown here]

Bertot, Y., Kahn, G., & Th#ry, L. (1994). Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160.

....used as a complement to other tools that enable rewriting. For instance, the cHOL system [5] provides a tool that selects all the rewrite theorems that apply to a given pattern. In the user interface we use as a test bed [1] mouse interaction is already provided in the form of proof by pointing [2] and point and shoot extensions [3] Other paradigms that use the mouse to limit the scope of operations include window inference [4] 3 Implementation and mode of operation 3.1 Basic data structures Our implementation uses a direct representation of mathematical formulae as trees, with a ....

Yves Bertot, Gilles Kahn, and Laurent Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

....to generate the theorem A A. The main interest in producing such a theorem is when the selection is on an assumption. This allows assumptions to be used as standard theorems. Providing a tactic The generation of a tactic from a selection follows the method of proof by pointing developed in [1]. The basic idea is to give a semantics to the selection in term of elimination of logical connectives. For example, let us consider the case of a disjunction with the following goal: Gamma A B where Gamma is a list of assumptions and A, B arbitrary formulas. A possible way of proving this ....

Y. Bertot, G. Kahn, L. Th'ery, "Proof by Pointing", to be published.

....subgoals. Some of the commands have a very elaborate behavior, while others perform very simple logical bookkeeping. Proof by pointing is a method to ensure that the bookkeeping commands can be very easily triggered and composed, to make their use less tedious. The idea of proof by pointing [1] is that selecting a position in a goal formula can be interpreted as a command to bring the selected sub formula to the surface of the goal. In practice, the behavior of proof by pointing relies heavily on the ability of the graphical interface to construct graphical representations of logical ....

Y. Bertot, G. Kahn, and L. Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

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Y. Bertot, G. Kahn, and L. Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

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Yves Bertot, Gilles Kahn, and L. Th'ery. Proof by Pointing. In Proceedings of TACS '94, Tohoku University, Sendai, Japan, April 1994.

No context found.

Y. Bertot, G. Kahn, and L. Th#ry. Proof by pointing. In Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 141160, 1994.

No context found.

Y. Bertot, G. Kahn, and L. Thery. Proof by pointing. In Theoretical Aspects of Computer Science (TACS), 1994.

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Yves Bertot, Gilles Kahn, and Laurent Thery. Proof by pointing. In M. Hagiya and J. C. Mitchell, editors, Proc. Intl. Symp. on Theoretical Aspects of Computer Software, LNCS 789, pages 141--160. Springer, 1994.

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