Abstract Interpretation Using Typed Decision Graphs

This article presents a way of implementing abstract interpretations that can be very efficient. The improvement lies in the use of a symbolic representation of boolean functions called typed decision graphs (TDGs), a refinement of binary decision diagrams. A general procedure for using this representation in abstract interpretation is given; we examine in particular the possibility of encoding higher-order functions into TDGs. Moreover, this representation is used to design a widening operator based on the size of the objects represented, so that abstract interpretations will not fail due to insufficient memory. This approach is illustrated on strictness analysis of higher-order functions, showing a great increase in efficiency.

[1]  Patrick Cousot,et al.  Abstract Interpretation Frameworks , 1992, J. Log. Comput..

[2]  Olivier Coudert,et al.  New ideas on symbolic manipulations of finite state machines , 1990, Proceedings., 1990 IEEE International Conference on Computer Design: VLSI in Computers and Processors.

[3]  Chris Hankin,et al.  Strictness Analysis for Higher-Order Functions , 1986, Sci. Comput. Program..

[4]  P. Cousot,et al.  Constructive versions of tarski's fixed point theorems , 1979 .

[5]  Paul Hudak,et al.  Higher-order strictness analysis in untyped lambda calculus , 1986, POPL '86.

[6]  Christophe Ratel.  Définition et réalisation d'un outil de vérification formelle de programmes LUSTRE : le système LESAR , 1992 .

[7]  Patrick Cousot,et al.  Galois Connection Based Abstract Interpretations for Strictness Analysis (Invited Paper) , 1993, Formal Methods in Programming and Their Applications.

[8]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[9]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[10]  Patrick Cousot,et al.  Static Determination of Dynamic Properties of Recursive Procedures , 1977, Formal Description of Programming Concepts.

[11]  Thomas Filkorn,et al.  Generating BDDs for Symbolic Model Checking in CCS , 1991, CAV.

[12]  Pascal Van Hentenryck,et al.  Evaluation of the Domain Prop , 1995, J. Log. Program..

[13]  Alan Mycroft,et al.  The Theory and Practice of Transforming Call-by-need into Call-by-value , 1980, Symposium on Programming.

[14]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[15]  Robert K. Brayton,et al.  Extracting local don't cares for network optimization , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[16]  Pascal Van Hentenryck,et al.  Groundness analysis for Prolog: implementation and evaluation of domain prop , 1993, PEPM '93.

[17]  Jean Christophe Madre,et al.  Proving circuit correctness using formal comparison between expected and extracted behaviour , 1988, 25th ACM/IEEE, Design Automation Conference.Proceedings 1988..

[18]  Antoine Rauzy,et al.  Efficient Bottom-up Abstract Interpretation of Prolog by Means of Constraint Solving over Symbolic Finite Domains , 1993, PLILP.

[19]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[20]  Gebreselassie Baraki.  Abstract interpretation of polymorphic higher-order functions , 1993 .

[21]  A. Richard Newton,et al.  Don't care minimization of multi-level sequential logic networks , 1990, 1990 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  Claude E. Shannon,et al.  A symbolic analysis of relay and switching circuits , 1938, Transactions of the American Institute of Electrical Engineers.

[24]  Alex Ferguson,et al.  Fast Abstract Interpretation Using Sequential Algorithms , 1993, WSA.