物件導向軟體之架構(Object-Oriented Software Construction)探討

ly, this program guesses nondeterministically the correct permutation via permutation(Xs,Ys), and ordered checks that the permutation is actually ordered. Operationally, the behavior is as follows. A query involving sort is reduced to a query involving permutation and ordered. A failure-driven loop ensues. A permutation of the list is generated by permutation and tested by ordered. If the permuted list is not ordered, the execution backtracks to the permutation goal, which generates another permutation to be tested. Eventually an ordered permutation is generated and the computation terminates. Permutation sort is a highly inefficient sorting algorithm, requiring time super-exponential in the size of the list to be sorted. Pushing the tester into the generator, however, leads to a reasonable algorithm. The generator for permutation sort, permutation, selects an arbitrary element and recursively permutes the rest of the list. The tester, ordered, verifies that the first two elements of the permutation are in order, then recursively checks the rest. If we view the combined recursive permutation and ordered goals as a recursive sorting process, we have the basis for insertion sort, Program 3.21. To sort a list, sort the tail of the list and insert the head of the list into its correct place in the order. The arbitrary selection of an element has been replaced by choosing the first element. Another example of the advantage of intertwining generating and testing can be seen with programs solving the N queens problem. The N queens problem requires the placement of N pieces on an Nby-N rectangular board so that no two pieces are on the same line: horizontal, vertical, or diagonal. The original formulation called for 8 queens to be placed on a chessboard, and the criterion of not being on the same line corresponds to two queens not attacking each other under the rules of chess. Hence the problem's name. 253 Nondeterministic Programming

The art of Prolog

We identify a useful class of logic programs with negation, called stratified programs, that disallow certain combinations of recursion and negation. Programs in this class have a simple declarative and procedural meaning based, respectively, on model theory and a back-chaining interpreter. The standard model of a stratified program, which gives the program a declarative meaning and is independent of the stratification, is characterized in two ways. One is based on a fixed point theory of nonmonotonic operators and the other on an abstract declarative characterization. The back-chaining interpreter also determines the standard model. Finally, we prove the consistency of Clark's completion for stratified programs and attempt to clarify the sources of some previously reported difficulties with negation in logic programming.

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Towards a theory of declarative knowledge

This article surveys various complexity and expressiveness results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming.

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Complexity and expressive power of logic programming

The notion that computation = controlled deduction was first proposed by Pay Hayes [19] and more recently by Bibel [2] and Vaughn-Pratt [31]. A similar thesis that database systems should be regarded as consisting of a relational component, which defines the logic of the data, and a control component, which stores and retrieves it, has been successfully argued by Codd [10]. Hewitt's argument [20] for the programming language PLANNER, though generally regarded as an argument against logic, can also be regarded as an argument for the thesis that algorithms be regarded as consisting of both logic and control components. In this paper we shall explore some of the useful consequences of that thesis.

Algorithm = logic + control

A First Order Theory of Data and Programs.

It is proved that a Turing computable functionf is computable in binary Horn clauses, which are a subset of first order logic. Moreover, it is proved that the binary Horn clauses do not need more than one function symbol. The proofs comprise computable relations that can be run efficiently as logic programs on a computer.

Horn clause computability

We present the notion of steadfastness that at once embodies modularity, reusability, and formal correctness. A steadfast program is an open program with parameters, which is parametrically correct ...

Steadfast logic programs

We shall lay down a programming calculus in which we develop a methodology for reasoning about data and programs. Our language, L, is ordinary first order predicate logic. A subset of this language, Lp, is our programming language that can be run efficiently in PROLOG. The calculus consists of a natural deduction system that is used for deducing programs and a system for efficient computation of programs. The axioms of the calculus characterize the data structures. Definitions are used for program specifications and mappings between data structures. The programs are deduced from the axioms and the definitions. Examples of deduced programs are a LISP-program and a program that Burstall and Darlington could not obtain in their transformation system.

A natural programming calculus

Deductive synthesis methods derive programs in an incremental manner, and therefore pose a halting problem { when can synthesis stop with a correct program? We give a characterisation of this problem and state a halting principle as a solution. Another characteristic of deductive synthesis is that it may derive several correct programs, giving rise to another question { which correct programs are desirable? We show that the answer is related to the halting problem, via the notion of steadfast , or reusable, programs as desirable programs. Our work also reveals that Clark's idea of the completion of a program is central to deductive synthesis, since it is the basis of our halting principle and our notion of steadfast programs.

Sten-Åke Tärnlund

Papers

A First Order Theory of Data and Programs.

Horn clause computability

Steadfast logic programs

A natural programming calculus

The halting problem for deductive synthesis of logic programs