C. Bohm and G. Jacopini. Flow diagrams, turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--371, 1966.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....engineering often use controlflow graphs and data flow graphs to describe certain aspects of programs. Bohm and Jacopini consider the relation of flow diagrams to the fundamental notion of computation in their classic paper Flow Diagrams, Turing Machines and Languages with only Two Formation Rules [8]. Litoiu, Starkey Schmidt consider that there is an analogy between flows and classes (in the object oriented programming sense of the word) when modeling flows with mof [24] From their perspective, the Risk:Assess and Risk:Reassess boxes in Figure 4c represent instances of the flow Risk shown ....

C. Bohm and G. Jacopini. Flow diagrams, turing machines and languages with only two formation rules. CACM, 9(5):366--371, May 1966. Reprinted in [40].

....flow diagrams may be refined a task may be refined to an entire diagram. The hierarchy at the control layer must correspond to the hierarchy at the inference layer, i.e. every task corresponds to an inference action at the inference layer. The diagrams at the control layer have to be structured [BJ66]. Structured diagrams may easily be mapped to the linear notation of KARL for the control layer which provides sequence, loops, and branches. Tests in branches and loops are expressed by necessary conditions in L KARL. 4 The Graphical Representation of L KARL formulae The graphical ....

C. Bhm, G. Jacopini: Flow Diagrams, Turing Machines And Languages With Only Two Formation Rules. In Communications of the ACM, Vol. 9, Nr. 5, Mai 1966, 366-371.

....DFKI, Stuhlsatzenhausweg 3, 66123 Saarbrucken 11, Germany, wuertz dfki.uni sb.de Contents 1 Introduction 3 2 Reduction 4 3 Related Work 7 1 Introduction Recursivity is well known to be a crucial and important concept in programming theory. For imperative languages, Bohm and Jacopini [Boe66] proved that all programming can be done with at most one while loop. In the context of logic programming a simple scheme of recursion is the binary Horn clause P (l 1 ; l n ) P (r 1 ; r n ) such that l 1 ; r 1 ; l n ; r n are finite terms. But is such a scheme really ....

C. Bohm and G. Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Communication of the ACM, 9:366--371, 1966.

....obtained by addition of an interpretation are equivalent for all interpretations. It is well known that the schematic concept of recursion is more powerful than that of iteration [12] that recursion equals iteration stack [2] and that iteration equals while Boolean variables [1]. Unfortunately the question of scheme equivalence is undecidable in the general case [11] The reason is not, as one might expect, the large number of interpretations which one has to apply for deciding scheme equivalence it suffices to consider free interpretations (or Herbrand ....

Corrado Bohm and Giuseppe Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--371, 1966.

.... gotoL1=0; L2: gotoL2=0; a) repeated pattern (b) eliminate goto L1 first (c) eliminate goto L2 first Figure 5. 5: Different orderings of goto elimination for asuite 67 Chapter 6 Related Work One of the first approaches to structuring was given by Bohm and Jacopini [BJ66] Their structuring method was done in the context of normalizing flowgraphs (where the flowgraph represented mappings of a set onto itself) This result is mostly of historical and theoretical interest and does not give a complete algorithm, but rather presents a set of pattern matching rules ....

C. Bohm and G. Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366-- 371, May 1966.

....isolate design decisions, automated restructuring must support changing the interface relationships between modules so that what otherwise would be intermodule changes become intramodule changes. Remodularization requires more than automated removal of gotos or control flow restructuring [Bohm Jacopini 66] Williams Ossher 77] Morgan 84] For example, it requires operations such as adding or removing a function from a module interface, changing a function interface, or hiding exposed representation in a module. And since these restructuring operations are intended to ease future maintenance, the ....

....that goal. These are not examined item by item in each discussed work, but the appropriate points are raised as necessary. 6. 1 Imposing Block Structure A program using gotos can be automatically transformed into a program using only the structured flow graph operators sequence, branch, and loop [Bohm Jacopini 66] The intent is to improve a program s structure to lower the cost of maintenance, a shared motivation with the research of this thesis. Most of the solutions involve simulating gotos with structured operators. One possibility is to use a large case statement inside a loop [Williams Ossher 77] ....

C. Bohm and G. Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--71, May 1966.

....be considered as both a review and some of my own personal comments on the material. These comments arise from my experiences teaching beginning (as well as advanced) programmers using a variety of control structures in several different programming languages. 2 Background Bohm and Jacopini [BJ66] demonstrated that any program written with GOTOs could be transformed into an equivalent program which uses only IF and WHILE control structures (actually only WHILE is necessary) The transformation requires the following modifications to the original GOTO program: 1. copying of fragments of the ....

C. Bohm and G. Jacopini. Flow diagrams, Turing Machines and Languages with only two Formation Rules. Communications of the ACM, 9(5):366--371, May 1966.

....For example, we use the name f:g:h(x; y) for a procedure h which was declared within procedure g which was declared within procedure f . module Dhal kernel syntax context free syntax proc Id VarList begin DhalStat end DhalDecl 5.2. 2 Structured Flow of Control A theorem of Bohm and Jacopini [BJ66] states that any program can be expressed using only three structured control constructs: composition, conditional and iteration. All Dhal languages will have exactly these three constructs to denote structured flow of control: Composition A series of Dhal statements is composed from two ....

C. Bohm and G. Jacopini. Flow diagrams, turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--371, 1966.

....statements, and on most benchmarks the effect on execution speed is minimal. Thus, we can exploit structured representations for designing compilers while paying only a minimal penalty due to restructuring. 5 Related ork One of the first approaches to restructuring was given by Bohm and Jacopini [BJ66] Their restructuring method was done in the context of normalizing flow graphs (where the flow graph represented mappings of a set onto itself) This result is mostly of historical and theoretical interest and does not give a complete algorithm, but rather presents a set of pattern matching ....

C. Bohm and G. Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--371, May 1966.

....The effect of this is to detect all of the loops and to eliminate all pathological syntactic constructions that the program contains. Williams and Ossher [47] have proved that such an elimination is necessary and sufficient to obtain a structured form of the program. A theorem of Bohm and Jacopini [13] says that we may transform any program into another one where only the following three control structures are used: ffl Assignment ffl Conditional ffl Iteration However, their theorem is not constructive in that it does not give a method for deriving such a program. The technique presented ....

....its resolution) and x 1 , x 2 , x 3 , and x 4 are the continuations associated with the labels I 1 , I 2 , I 3 , and I 4 respectively. x 0 , x 1 , x 2 x 3 , and x 4 represent the unknowns of the system. The only control structures used in these systems are the three proposed by Bohm and Jacopini [13]. The solution to this system will represent the normalized form of the procedure. In the next section we will present the method we choose to solve this system. 2.4 Gaussian Elimination Like Resolution A straightforward Gaussian elimination like resolution method may be used to solve the system ....

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C. Bohm and G. Jacopini. Flow diagrams, turing machines and languages with only two formation rules. CACM, 9(5), 1966.

....effect on execution speed is minimal. Thus, for the vast majority of programs, we can exploit structured representations for designing compilers while paying only a minimal penalty due to restructuring. 5 Related Work One of the first approaches to restructuring was given by Bohm and Jacopini [6]. Their restructuring method was done in the context of normalizing flow graphs (where the flow graph represented mappings of a set onto itself) This result is mostly of historical and theoretical interest and does not give a complete algorithm, but rather presents a set of pattern matching rules ....

C. Bohm and G. Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Comm. of the ACM, 9(5):366--371, May 1966.

....only by the code generator, and no labels are placed on the graph on the earlier control flow analysis phase. 7 Previous Work Most structuring algorithms have concentrated on the removal of goto statements from control flow graphs at the expense of introduction of new boolean variables [8, 29, 22, 28, 6, 13], code replication [17, 27, 29] the use of multilevel exits [7, 24] or the use of a set of high level structures not available in commonly used languages [25] None of these methods are applicable to a decompiler because: the introduction of new boolean variables modifies the semantics of the ....

C. Bohm and G. Jacopini. Flow diagrams, Turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--371, May 1966.

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C. Bohm and G. Jacopini. Flow diagrams, turing machines and languages with only two formation rules. Communications of the ACM, 9(5):366--371, 1966.

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C. Bohm and G. Jacopini. Flow diagrams, turing machines and languages with only two formation rules. CACM, 9(5):366--371, May 1966. Reprinted in [34].

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