N. Heintze. Set based analysis of arithmetic. Technical Report CS--93--221, School of Computer Science, Carnegie Mellon University, July 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... for the class of negative set constraints, and one [13] for the class of set constraints with projection (which includes all above mentioned classes) Set constraints were studied from the logical and topological point of view [39, 19, 41] and also in domains different from the Herbrand universe [31, 10, 46, 49, 14, 47]. See [1, 35, 51] for overviews on set constraints. 1 2 Please write authorrunninghead Author Name(s) in file Definite set constraints. This was the first class of set constraints for which decidability was shown [32, 34] It was introduced by Heintze and Jaffar and is used for the type ....

N. Heintze. Set based analysis of arithmetic. Technical Report CS--93--221, School of Computer Science, Carnegie Mellon University, July 1993.

....subterms. Besides, as shown in [59] any Mycroft style strictness analysis completely ignores bindings of variables to constants. 6.3 A Set Based Semantics One of the simplest binding analysis techniques for call by value languages is a set based analysis (SBA) technique developed by N. Heintze [30, 29, 28]. The development of a set based analysis for a given natural semantics proceeds through the following stages: A. Develop a set based version of the operational semantics. The standard operational semantics for the language uses an environment, E : Var Val . The set based semantics uses an ....

N. Heintze. Set Based Analysis of Arithmetic. Technical Report CMU-CS-93-221, School of Computer Science, Carnegie Mellon University, 1993.

....assists the programmer in verifying the preconditions of primitive operations. This kind of tool is a static debugger. Recent advances in proof technology have brought static debugging within reach. Methods like abstract interpretation [5] control flow analysis [21, 25, 15] or set based analysis [12, 11] establish invariants about the sets of values that variables and expressions may assume. Thus, if an array index expression does not assume values outside of the appropriate range, an array bound check is superfluous, and an indexing error will never be signaled for this expression. Or, if the ....

....that the resulting tool expedites the production of e#cient programs. We intend to investigate this area in more depth. We adapted set based analysis for use as the underlying proof technology used in MrSpidey. Set based analysis can be extended to produce accurate information on numeric ranges [11]. This information is useful for eliminating array bounds checks and for array data dependence analysis. Other program analyses that produce information similar to setbased analysis but which provide alternative cost accuracy tradeo#s could also be adapted for use in MrSpidey [15, 16, 13, 1] ....

Heintze, N. Set based analysis of arithmetic. Tech. Rep. CMU-CS-93-221, Carnegie Mellon University, December 1993.

....assists the programmer in verifying the preconditions of program operations. This kind of tool is a static debugger. Recent advances in proof technology have brought static debugging within reach. Methods like abstract interpretation [5] control flow analysis [25, 26, 14] or set based analysis [11, 10] establish invariants about the sets of values that variables and expressions may assume. Thus, if an array index expression does not assume values outside of the appropriate range, an array bound check is superfluous, and an indexing error will never be signaled for this expression. Or, if the ....

....that the resulting tool expedites the production of efficient programs. We intend to investigate this area in more depth. We adapted set based analysis for use as the underlying proof technology used in MrSpidey. Set based analysis can be extended to produce accurate information on numeric ranges [10]. This information is useful for eliminating array bounds checks and for array data dependence analysis. Other program analyses that produce information similar to set based analysis but which provide alternative cost accuracy tradeoffs could also be adapted for use in MrSpidey [14, 15, 12, 1] ....

Heintze, N. Set based analysis of arithmetic. Tech. Rep. CMU-CS-93-221, Carnegie Mellon University, December 1993.

.... with projection by Charatonik and Pacholski [20] which settled the open problem for the general class formulated by Heintze and Jaffar [53] Set constraints were also studied from the logical and topological point of view [63,25,65,22] and also in domains different from the Herbrand universe [50,17,71]. Kozen [64] explores the use of set constraints in constraint logic programming. Uribe [92] uses set constaints in order sorted languages. Seynhave, Tommasi and Treinen [85] showed that the 9 8 fragment of the theory of set constraints is undecidable. Charatonik [17,18] studied set ....

N. Heintze. Set based analysis of arithmetic. Draft manuscript, July 1993.

....which given a closed term M as input, computes a non trivial dynamic slice of the term A trivial dynamic slice of a term is its entire set of labels, M ) One of the simplest binding analysis techniques for call by value languages is a set based analysis (SBA) technique developed by N. Heintze [27, 26, 25]. The development of a set based analysis for a given natural semantics proceeds through the following stages: A. Develop a set based version of the operational semantics. The standard operational semantics for the language uses an environment, E : Var Val. The set based semantics uses an ....

N. Heintze. Set Based Analysis of Arithmetic. Technical Report CMU-CS-93-221, School of Computer Science, Carnegie Mellon University, 1993.

.... for the class of negative set constraints, and one [11] for the class of set constraints with projection (which includes all above mentioned classes) Set constraints were studied from the logical and topological point of view [27, 13, 29] and also in domains different from the Herbrand universe [19, 9, 34, 36, 12]. Definite set constraints. This was the first class of set constraints for which decidability was shown [20, 22] It was introduced by Heintze and Jaffar and is used for the type analysis of Prolog programs [21, 18, 23] The satisfiable constraints in this class have a least solution (this fact ....

N. Heintze. Set based analysis of arithmetic. Draft manuscript, July 1993.

....Semantics We now investigate terminating algorithms that compute non trivial sets of subterms which do not make any contribution to the value returned by a program. One of the simplest analysis techniques for call by value languages is a set based analysis (SBA) technique developed by N. Heintze [11, 10, 9]. The development of a set based analysis for a given natural semantics proceeds through the following stages [8] A. Develop a set based version of the operational semantics. The standard operational semantics uses an environment, E : Var Val . The set based semantics uses an environment, E : ....

N. Heintze. Set Based Analysis of Arithmetic. Technical Report CMU-CS-93-221, School of Computer Science, Carnegie Mellon University, 1993.

....terms built from arithmetic operations and integers. For example, the description of computations for a program variable x might be given by X = 0 [ X 1) that is, the set of computations f0; 0 1; 0 1) 1; g. Clearly, the actual values of x are included in the set f0; 1; 2; g. [14] describes how this approach can be applied to the problem of removing array bounds checks, and this requires that the analysis also reason about arithmetic tests. An example of the kinds of descriptions that arise in this context is: X = 0 [ LE 10] X 2) where [LE 10] is a restriction ....

N. Heintze, "Set-Based Analysis of Arithmetic", Carnegie Mellon University technical report CMU-CS-93-221, 20pp., December 1993.

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