R. Milner. The use of machines to assist in rigorous proof. In C.A.R. Hoare and J.C. Shepherdson, editors, Mathematical Logic and Programming Languages, International Series in Computer Science, pages 77--87. Prentice Hall, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....not the name of a rule but an arbitrary function from theorems to a theorem. Likewise the tactic may use an arbitrary function from the goal to the subgoals. Subgoal construction and proof construction are completely separate. Relating these operations are the concepts of achievement and validity [Milner 1985]. Each goal defines some set of theorems that achieve it. If the goal is false then this set is empty. A tactic is valid provided: whenever it reduces goal G to subgoals G 1 , G n and proof P , and theorems T 1 , T n achieve G 1 , G n , then theorem P [T 1 , T n ] achieves G. In ....

Robin Milner. The use of machines to assist in rigorous proof. In C. A. R. Hoare and J. C. Shepherdson, editors. Mathematical Logic and Programming Languages. Prentice-Hall International, pages 77--88.

....challenged every year by something new. Scott s Logic of Computable Functions appeared in 1969 and attracted the interest of Robin Milner. Milner built a proof checker but found it impossibly tedious for proofs of any length. He later developed Edinburgh lcf, a proof checker that was programmable [26]. Edinburgh lcf s meta language (ml) does not merely execute obvious command sequences. ml gives a general representation of logic. Terms and formulae are computable data, as are theorems. Each inference rule is a function from theorems to theorems. A theorem can be built only by applying rules to ....

R. Milner, The use of machines to assist in rigorous proof, in: Hoare and Shepherdson [17], pages 77--88.

....using the notion of tactics, and record derivation histories as an execution trace of the application of tactics. One key idea is that tactics are compositional: higher level tactics are constructed from more rudimentary using defined control primitives. This is similar to the approach used in LCF[12, 18] and NuPRL[1, 8] ffl An approach to the correspondence problem is described [21, 20] The correspondence problem addresses how during replay a correspondence between program parts of the original and modified program is established Our approach uses a combination of name association, structural ....

....from code. In [2] he emphasizes the existence of semantic clues in documentation and variable names that will aid in design recovery. We have adopted in our use of name correspondence this idea. Examples of work on design recovery can be found in [35, 33, 16] Our tactic language is similar to [34, 18]. A richer more theoretical approach is being pursued by [29, 15] using the Deva language. Closer to the spirit of the work reported here is work done at Rutgers University. Their work is couched in a transformational framework. Two domains are addressed: circuit designs [22] and heuristic search ....

Milner, R. The use of machines to assist in rigorous proof. In Mathematical Logic and Programming Languages, C. A. R. Hoare and J. C. Shepherdson, Eds., Prentice-Hall, Englewood Cliffs, NJ, 1985, pp. 77--87.

....the goal is the instances of the anti symmetry of . Instances of the trichotomy of also frequently furnish two symmetrical cases (the strict inequalities) as well as the nonsymmetrical, and frequently quite easy, case with the equality. 6 Comparison with Tactics Tactic based theorem proving [8] has been a major area of research in automated reasoning since the development of Edinburgh lcf [6] In fact, the ml programming language was invented for writing lcf tactics. Today tactics are used in several major theorem proving systems, including hol [7] Isabelle [9] and Nuprl [1] Tactics ....

R. Milner. The use of machines to assist in rigorous proof. In C. A. R. Hoare and J. C. Shepherdson, editors, Mathematical Logic and Programming Languages, pages 77-88. Prentice/Hall International, 1985.

....which are compositions of proof rules. As a result, the safe datatype is that of proofs, not (as here) that of tactics; tactics are valid if they are able to be validated by compositions of primitive rules. Strongly valid tactics are related to our functionally correct ones. 1 Milner [Mil84] generalizes the ideas from LCF somewhat, observing how the notions present in tactic programming (goal, strategy, achievement, and failure) stand together in a far more general setting than merely in the area of machine assisted proof. An independent semantics for LCF s tactics is found in ....

R. Milner. The use of machines to assist in rigorous proof. Philosophical Transactions of the Royal Society, London. Series A, 312:411--422, 1984. Also in [HS85].

....have a short discussion on utilizing logic programming techniques in proof; then we describe useful proof management facilities; and we conclude with a discussion of efficiency issues. 2. 1 Proof style Backwards, or goal oriented, proof is succesfully supported by Milner s seminal idea of tactic[Mil85] Almost all interactive verification systems use some flavour of tactics, and some logics are even expressed wholly in terms of backwards proof[CAB 86] One of the reasons for the success of tactics is that they almost never require complicated programming: tacticals make it simple for ....

Robin Milner. The use of machines to assist in rigorous proof. In C.A.R. Hoare and J.C. Shepherdson, editors, Mathematical Logic and Programming Languages, International Series in Computer Science, pages 77--87. PrenticeHall, 1985.

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R. Milner. The use of machines to assist in rigorous proof. In C.A.R. Hoare and J.C. Shepherdson, editors, Mathematical Logic and Programming Languages, International Series in Computer Science, pages 77--87. Prentice Hall, 1985.

No context found.

R. Milner. The use of machines to assist in rigorous proof. Philosophical Transactions of the Royal Society, London. Series A, 312:411--422, 1984. Also in [HS85].

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