R. Burstall. Program proving as hand simulation with a little induction. In Proceedings of IFIP Congress 74, North Holland Publishing Co., Amsterdam, 1974, pages 308--312. 5  Home/Search   Document Not in Database   Summary   Related Articles   Check

....language. A good means for detecting such potential loops is to make a symbolic execution of a program on the abstracted values. This method of abstract reduction has been applied in strictness analysis [Noc93, SSPS95] An early example for executing programs on abstract values is presented in [Bur74]. Finally, to prove termination of programs, one has to show that all potential loops are harmless, i.e. they will only be executed finitely many times in a concrete program execution. The usual means for this test is to find some Noetherian orderings on the argument and variable values. It has ....

R. M. Burstall. Program proving as hand simulation with a little induction. In Information Processing, IFIP, pages 308--312. North-Holland Publishing Company, 1974.

....were introduced by [Fischer and Ladner, 1979] in the context of PDL. The concept of nondeterminism was introduced in the original paper of [Turing, 1936] although he did not develop the idea. Nondeterminism was further developed by [Rabin and Scott, 1959] in the context of finite automata. [Burstall, 1974] suggested using modal logic for reasoning about programs, but it was not until the work of [Pratt, 1976] prompted by a suggestion of R. Moore, that it was actually shown how to extend modal logic in a useful way by considering a separate modality for every program. The first research devoted to ....

R. M. Burstall. Program proving as hand simulation with a little induction. Information Processing, pages 308--312, 1974.

....citations to [Man68] suggest. 32 Rod Burstall has consistently produced seminal contributions and one of his proposals is the idea of intermittent assertions which for some tasks produce clearer proofs than Floyd s assertions which are linked to the ow of control. His invited talk at IFIP 74 [Bur74] additionally broke the mould of using predicate calculus alone by introducing the use of temporal logic (see Section 4.1) 3 Formal development methods A crucial test for program development ideas is whether they scale that is, they can be used to develop large programs without an ....

.... 52 This is developed in [Jon83, St 90] 28 literature has developed on compositional methods and a good overview is given in [dR85] 53 The proof methods discussed so far have nearly all been based on classical logic (First Order Predicate Calculus) As mentioned above, Burstall suggested [Bur74] that some form of Temporal Logic could be used in the development of programs. It would appear that Amir Pnueli (b1941) was the rst person to suggest that Temporal Logic be used in specifying and developing concurrent programs [Pnu77] 54 . Within the temporal logic framework, the issue of ....

R. M. Burstall. Program proving as hand simulation with a little induction. In J. L. Rosenfeld, editor, Information Processing 74, pages 308-312, 1974. Proceedings of IFIP'74.

....lower and lower 1 , and serve to state liveness or inevitable properties. The purpose of the index variables is to provide a mechanism for inductive reasoning here. Our algorithm, by manipulating such constraints, provides a realization of the original concept of proving liveness by Burstall [2]. Define an indexed constraint to be a constraint but where there may be index variables in addition to program variables. For an indexed constraint C we define 2 43 3 to be the union of 2 26 q 3 3 for all instantiations q that map index variables into natural numbers. We also define a ....

.... A p , p q i (we observe that this last statement is equivalent to proving 1 p A 1 assume A p , p , where 1 p A 1 denotes the result of replacing by A 1 in 1 p ) We note now that the hand simulation step informally defined by Burstall [2] is now formally integrated in our algorithm. In the example above, assume A p , p q i is the result of computing the effect of the inevitable property A p at program point p by hand simulation. The following definition of confirmation generalizes these conditions. Definition 4 ....

R.M. Burstall, "Program proving as Hand Simulation with a little Induction", Information Processing Letters, 74, 308-312, 1974.

....about recursive Lisp functions, for instance that the function reverse is its own inverse. Ammarguellat and Harrison [3] use abstract interpretation to recognize recurrence relations in programs for purposes of translating serial programs into programs better suited to parallel execution. Burstall [6] presents a formal discussion on using symbolic interpretation and induction to prove properties of programs. A number of approaches have been taken to the problem of program verification. Manna [17] addresses verification issues within the formalism of predicate calculus. Improving upon the work ....

Burstall, R. M., (August 1974), Program proving as hand simulation with a little induction, Information Processing 1974, North-Holland Publishing Company, Amsterdam, pp. 308-312.

....is not proved simultaneously. The usual approach for termination proofs of such algorithms f is to let the human provide an alternative speci cation g which is not nested or mutually recursive. Then termination and correctness are proved simultaneously by verifying the equivalence of f and g, cf. [6, 8, 18, 23, 25]. Hence, such termination proofs do not work fully automatically. For that reason the handling of nested and mutual recursion is often regarded as one of the main challenge problems in automated termination analysis. In this paper we show that (surprisingly) termination proofs for algorithms with ....

....nest. So in contrast to ack, for nest we have to consider its own semantics in its termination proof. Of course one possibility for nest s termination proof is to prove its termination and its correctness simultaneously. This is the usual approach for proving termination of nested recursion, cf. [6, 8, 18, 23, 25]. If we knew the speci cation nest(x) 0 and if we knew that nest was partially correct with respect to 4 It may also be possible to use a so called measured subset of x as induction variables, cf. 5, 32] 9 this speci cation, then in inequality (14) we could replace nest(x) by 0 and ....

Burstall, R. M., `Program Proving as Hand Simulation with a little Induction ', in Proc. IFIP Congress 74, Stockholm, Sweden, North-Holland (1974).

....logic was first conducted under the name of tense logic by symbolic logicians and philosophers for reasoning about ordering of events in time without mentioning time explicitly. In the last decade, temporal logic has become a convenient formalism used, among other things, in program verification [7, 32], in artificial intelligence and cognitive science [20, 19, 23] in specification and verification of concurrent computations [3, 26] in verification of network protocols and sequential circuits [28] and in verification of software requirements specifications [2] A complete survey of classical ....

Burstall, R. M. Program proving as hand simulation with a little induction. Information Processing 74 (1974), 308--312.

....are defined in section 6.3. 6 Temporal Semantics Long before temporal logic was used to reason about programs, there was substantial work on temporal logic in philosophy for reasoning about time, e.g. 19, 20] The application of temporal logic in computer science was first introduced in [6]. A logic framework for reasoning about properties of concurrent programs was later developed by Pnueli [18] Although that framework provided very powerful specification and verification tools for global programs, it did not provide much support for decomposition and composition of components. In ....

R.M. Burstall. Program Proving as Hand Simulation with a Little Induction. In Information Processing 74, Pages 308-312, North-Holland Pub. Co., 1974.

....logic was first conducted under the name of tense logic by symbolic logicians and philosophers for reasoning about ordering of events in time without mentioning time explicitly. In the last decade, temporal logic has become a convenient formalism used, among other things, in program verification [6, 23], in artificial intelligence and cognitive science [14, 13, 16] in specification and verification 2 The concept of time implied by the term temporal is not duration but rather the relative ordering of events in a sequence. of concurrent computations [2, 17] and in verification of network ....

R. M. Burstall. Program proving as hand simulation with a little induction. Information Processing, 74:308--312, 1974.

....Possible applications of F (and O) are discussed: in particular, its incrementality is used to define a parallel execution model for clp s based on asynchronous processors assigned to the nodes of the program graph. Moreover, O is used to formalize the Intermittent Assertion Method of Burstall [Bur74] for constraint logic programs. 1 Introduction In this paper a dataflow semantics for constraint logic programs (clp s for short) is introduced. The importance of dataflow semantics is well known: they specify the functionality of the program; and hence can be used to transform a program into a ....

....applications. In particular, the incrementality of F is used to define an or parallel execution model for clp s based on asynchronous processors assigned to the nodes of the program graph. Moreover, the intermediate semantics O is used to formalize the Intermittent Assertion Method of Burstall [Bur74] for clp s. This latter application solves at the same time a problem addressed by the Cousots in [CC93] on how to formalize the Intermittent Assertion Method for clp s. The rest of the paper is organized as follows. The next section contains the terminology and the concepts used in the sequel. ....

[Article contains additional citation context not shown here]

R.M. Burstall. Program proving as hand simulation with a little induction. Information Processing, 74:308--312, 1974.

....language. A good means for detecting such potential loops is to make a symbolic execution of a program on the abstracted values. This method of abstract reduction has been applied in strictness analysis [Noc93, SSPS95] An early example for executing programs on abstract values is presented in [Bur74]. Finally, to prove termination of programs, one has to show that all potential loops are harmless, i.e. they will only be executed finitely many times in a concrete program execution. The usual means for this test is to find some Noetherian orderings on the argument and variable values. It has ....

R. M. Burstall. Program proving as hand simulation with a little induction. In Information Processing, IFIP, pages 308--312. North-Holland Publishing Company, 1974.

No context found.

R. Burstall. Program proving as hand simulation with a little induction. In Proceedings of IFIP Congress 74, North Holland Publishing Co., Amsterdam, 1974, pages 308--312. 5

No context found.

Burstall M. [1974], Program proving as hand simulation with a little induction, in `Proc. IFIP Congress, Stockholm', North Holland, pp. 308-312.

No context found.

R.M. Burstall. Program proving as hand simulation with a little induction. Information Processing, 74:308--312, 1974.

No context found.

Burstall, R.M.: Program proving as hand simulation with a little induction. In Rosenfeld, J.L., ed.: Information Processing 74, Proceedings of IFIP Congress 74. (1974) 201--210

No context found.

Rodney M. Burstall. Program proving as hand simulation with a little induction. Information Processing '74, pages 308 - 312, 1974.

No context found.

R. M. Burstall. Program proving as hand simulation with a little induction. In J. L. Rosenfeld, editor, Information Processing 74, pages 308--312, 1974. Proceedings of IFIP'74.

No context found.

Burstall, R.M.: Program proving as hand simulation with a little induction. In Rosenfeld, J.L., ed.: Information Processing 74, Proceedings of IFIP Congress 74. (1974) 201--210

No context found.

Burstall, R. M. Program proving as hand simulation with a little induction. Information Processing 74 (1974), 308--312.

No context found.

R.M. Burstall. Program proving as hand simulation with a little induction. In IFIP 74, pages 308--312. Norh Holland, 1974.

No context found.

R. M. Burstall. Program proving as hand simulation with a little induction. In J. L. Rosenfeld, editor, Information Processing 74, pages 308--312, 1974. Proceedings of IFIP'74.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC