L. C. Paulson: "Isabelle: The Next 700 theorem provers", Logic and Computer Science, pp.361--386,1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a seed of a counter model if the input formula is not provable. So we need an algorithm that constructs a counter Kripke model from this deduction tree. This construction is explained in chapter 5. We prove the correctness and completeness of our algorithm in chapter 6. In other proving systems [2, 7, 8], the process of generating a counter model is completely separated from the process of searching the proof. In chapter 7 and 8, we show an implementation of the algorithm and its user interface through internet. We call the system SKIP. It stands for Simple Kripke model Internet Prover and can be ....

....If the formula is not provable, the result has the (MODEL (model) The car part is a header describing whether the result is a proof or the result is counter Kripke model. 33 Chapter 8 Internet Prover SKIP 8. 1 Internet interface to prover There have been many automated theorem proving systems [13, 7, 8]. But they are standalone systems and require particular computer environment. It means that if a user want to use any of these automated theorem prover, he has to install some programs, e.g. compilers, libraries and even operating system. Even he can build an environment, the most user interface ....

L. C. Paulson: "Isabelle: The Next 700 theorem provers", Logic and Computer Science, pp.361--386,1990.

....tests are minimal, hand tailored axiomatizations) so that these systems show a nonmonotonic characteristic in the sense that they are no longer capable of proving some theorems if further (irrelevant) axioms are added. In interactive systems, structured theories are more commonly used. Isabelle [15, 16], HOL [8] and IMPS [6, 4] for instance use a layered approach to knowledge bases (cf. little theories in IMPS [5] Theories, however, are in a sense atomic, so that for a proof one must either explicitly enter a theory and use its methods solely, or gets the sum of all theories logically ....

Lawrence C. Paulson, `Isabelle: The next 700 theorem provers', Logic and Computer Science, 361--386, (1990).

....satisfying the goal. During the proof, the planvariable Plan is replaced by a plan formula satisfying the specification. The proofs are guided by tactics which can be described in a tactic language [3] provided by the system, an idea which was borrowed from the field of tactical theorem proving [5, 8, 18]. The application domain of phi is the unix mail domain where objects like messages and mailboxes are manipulated by actions like read, delete, and save. The atomic actions available to the planner are the elementary commands of the unix mail system. For example, the axiomatization of the save ....

L. Paulson, `Isabelle: The next 700 theorem provers', in Logic and Computer Science, ed., P. Odifredi, Academic Press, (1990). Planning, Scheduling and Reasoning about Actions 609 J. Koehler

....that allows the user to guide precisely the proof process with the mouse of his workstation. This idea is widely applicable and has been implemented by the authors in userinterfaces for several proof development systems: Amy Felty s Theorem Prover [Felty89] Coq [Coq91] HOL [HOL88] and Isabelle [Isa90]. The paper is organized as follows: first, we give an example of the kind of interaction that results from adopting our principle. Then the second section describes rigorously the principle, its logical foundations and simple consequences. The third section examines potential difficulties ....

....make proofs less cumbersome, we will want to dispose of certain assumptions. In doing so, one must be careful not to sacrifice completeness. 3 Implementation Proof by pointing has been implemented for several proof assistants: Felty s theorem prover [Felty89] Coq [Coq91] HOL[HOL88] and Isabelle [Isa90]. We used the Centaur system [Centaur93] as a toolkit for building interfaces, mostly for the ability to point at a subexpression with the mouse. As a matter of principle, we tried not to modify the proof engines at all. This is easier if the user is allowed to program his own proof tactics. This ....

L.C. Paulson, "Isabelle: The next 700 theorem provers", in Logic and Computer Science, P. Odifreddi, ed., pp. 361--386, Academic Press, 1990.

.... P ) I fPg if E [F] then C fQg [I ] hTime(if E [F] then C)i 3 Matching is currently done by an ad hoc procedure which has the definition of Time built in. A more general approach would use Prolog style metavariables to synthesize running times by unification. Theorem provers such as Isabelle [12] provide built in facilities to support this. A Mechanized Hoare Logic of State Transitions 13 fP Eg C 1 fQg [I ] hTime C 1 i fP :Eg C 2 fQg [I ] hTime C 2 i P ) I fPg if E then C 1 else C 2 fQg [I ] hTime(if E then C 1 else C 2 )i fP Eg C 1 fQg [I ] hTime C 1 i P ) E P ) I ....

Paulson, L.C., `Isabelle: The Next 700 Theorem Provers', in Odifreddi, P. (Ed) Logic and Computer Science, pp. 361--386, Academic Press, 1990.

....and natural. In fact it is not difficult to derive a program which transform the graph of a circuit into a term. Reasoning about circuits using this representation is not more difficult than using logic, and the formal work could be supported by modern interactive theorem provers like Isabelle (Paulson, 1990). The mechanical support that is needed is given by higher order logic and fixpoint theory. Most of the modern provers are equipped with theories and tools to use these mathematical instruments in a quite effective way. An important observation that we can do about functional method versus the ....

Paulson, Lawrence C. (1990). Isabelle: The next 700 theorem provers. Pages 361--386 of: Odifreddi, P. (ed), Logic and computer science. Academic Press.

.... does the prover allow an implementation of the desired protocol The analysis presented in this paper is based on experiments pursued with three fairly different, publicly available systems: Felty s prover[Felty89] implemented in Prolog, HOL[HOL88] implemented in ML and Lisp, and Isabelle[Isa90], implemented in SML. All three of them have a programmable top level, so that it is possible to implement the prover s side of the protocol with the same insight in the prover s internals as a regular user. The experimental user interfaces were created using the Centaur system [Centaur92] as a ....

L.C. Paulson, "Isabelle: The next 700 theorem provers", in Logic and Computer Science, P. Odifreddi, ed., pp. 361--386, Academic Press, 1990.

.... does the prover allow an implementation of the desired protocol The analysis presented in this paper is based on experiments pursued with three fairly different, publicly available systems: Felty s prover[Felty89] implemented in Prolog, HOL[HOL88] implemented in ML and Lisp, and Isabelle[Isa90], implemented in SML. All three of them have a programmable top level, so that it is possible to implement the prover s side of the protocol while remaining a conventional system s user. The experimental user interfaces were created using the Centaur system [Centaur92] as a toolkit. While the core ....

L.C. Paulson, "Isabelle: The next 700 theorem provers", in Logic and Computer Science, P. Odifreddi, ed., pp. 361--386, Academic Press, 1990.

....of success is possible. Once the theory is complete, we intend to test it on a realistic application. It would also be interesting to compare the practical utility of the HOL mechanization with a proof system for the calculus implemented using a more general logical framework, such as Isabelle [20] or the Edinburgh Logical Framework [10] The research most closely related to the theory described in this paper is Monica Nesi s work on a theory of CCS in HOL [19] This work parallels ours; essentially the same techniques are used to define the syntax and transitional semantics of CCS and to ....

L. C. Paulson, `Isabelle: The Next 700 Theorem Provers', in Logic and Computer Science, edited by P. Odifreddi (Academic Press, 1990), pp. 361--386.

....logic programming languages. For example, first order and higher order versions of hereditary Harrop formulas (formulas with no positive occurrences of disjunctions or existential quantifiers) have been used both as specification languages for proof systems (Felty, 1993; Felty and Miller, 1988; Paulson, 1990; Pfenning, 1988) and as the basis of logic programming languages (Gabbay and Reyle, 1984; Hallnas and Schroeder Heister, 1990; McCarty, 1988; Miller, 1990; Miller, Nadathur, Pfenning, and Scedrov, 1991) Part of the expressiveness of such systems derives from This paper appeared in a special ....

....as the proof is developed from the bottom up. Such monotonicity is problematic in numerous settings. ffl When using an intuitionistic meta logic to design theorem provers it is natural to use the meta logic s context to manage object level hypotheses and eigen variables (Felty and Miller, 1988; Paulson, 1990). With such an approach, however, there is no logical way to specify any variations of the contraction rule for the object logic: arbitrary contraction on all hypotheses is imposed by the meta logic. ffl A proposed technique for parsing relative clauses is to first assume the existence of a noun ....

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Paulson, L. C. (1990). Isabelle: The Next 700 Theorem Provers. In Odifreddi, P. (Ed.), Logic and Computer Science, pp. 361 -- 386. Academic Press.

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L. C. Paulson, "Isabelle: The Next 700 Theorem Provers," in Logic and Computer Science #31, P. Odifreddi, ed., APIC Studies in Data Processing, Academic Press, New York, NY, 1990, 361--386.

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