• Corpus ID: 214793472


  author={Vaughan R. Pratt},
  booktitle={FOCS 1976},
  • V. Pratt
  • Published in FOCS 1 September 1976
  • Computer Science, Philosophy
This paper deals with logics of programs. The objective is to formalize a notion of program description and to give both plausible (semantic) and effective (syntactic) criteria for the notion of truth of a description. A novel feature of this treatment is the development of the mathematics underlying Floyd-Hoare axiom systems independently of such systems. Other directions that such research might take are also considered. This paper grew out of, and is intended to be usable as, class notes for… 

Computability and completeness in logics of programs (Preliminary Report)

Borders on the validity problem for the formulae of dynamic logic are given, including a &Pgr;02-completeness result for the partial correctness theories of uninterpreted flowchart programs and the completeness of an axiomatization of dynamic Logic relative to arithmetic are demonstrated.

Hoare Logic: From First-Order to Propositional Formalism

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Nondeterminism in logics of programs

The principles underlying reasoning about nondeterministic programs are investigated, and a logic to support this kind of reasoning is presented, providing in passing, a critical evaluation of the widely used "predicate transformer" approach to the definition of programming constructs.

Effective Axiomatizations of Hoare Logics

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On the theory of programming logics

This paper proves the completeness and decidability of the monadic (iterative) programming logic, and discusses the polyadic logic and the programming language briefly, and considers general models for the iterative programming logic.

A generic complete dynamic logic for reasoning about purity and effects

This work introduces a dynamic logic whose logical formulae are pure programs in a strong sense, and develops a relaxed notion of purity which allows for observationally neutral effects such writing on newly allocated memory.

Matching Explicit and Modal Reasoning about Programs: A Proof Theoretic Delineation of Dynamic Logic

  • D. Leivant
  • Computer Science
    21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
  • 2006
It is shown that Pratt-Segerberg's first-order dynamic logic DL proves precisely program properties that are provable in second-order logic with set-existence restricted to a natural class of formulas, well-known to be related to computation theory.

Logics of Programs

  • D. KozenJ. Tiuryn
  • Philosophy
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990

The characterization problem for Hoare logics

Questions are discussed that suggest that good axioms for total correctness may exist for a wider spectrum of languages than is the case for partial correctness and others which still need to be addressed before the characterization problem can be considered solved.

Mechanizing Programming Logics in Higher Order Logic 1

An attempt to get the advantages of both approaches to formal reasoning about computer programs is described, and a way of mechanizing Hoare logic theory in a way that makes certain practical details work out smoothly is proposed.



Toward a mathematical semantics for computer languages

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Structured Programming With and Without go to Statements

  • C. C. Elgot
  • Computer Science
    IEEE Transactions on Software Engineering
  • 1976
The analogous multiexit composition binary alternation-conditional iteration (CACI) schemes introduced below, which are virtually as simple and perspicuous as Dijkstra schemes, describe exactly the same computational processes as flow-chart schemes (without the aid of additional variables).

Theory of Recursive Functions and Effective Computability

Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.

The Design and Analysis of Computer Algorithms

This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.

A Program Verifier

  • J. King
  • Computer Science
    IFIP Congress
  • 1971

On the Optimality of Some Set Algorithms

The es tab l i shment of lower bounds on the number of comparisons necessary to solve various combinator problems is considered and the maximum of a set of n real numbers cannot be computed in fewer than n 1 comparisons if comparisons of only l inear funct ions of the numbers are permitted.