The Conceptual Calculus For Automatic Program Understanding

The CAN system for automatic understanding of LISP programs is presented. Uhen applied on a LISP program, CAN needs no assertion about what the program is intended to do. CAN's general task is to associate e meaning to a program, from which it is able to diagnose semantlc properties (unused portions of code, undefinitions, underused programs, classes Of data for which evaluation of an expression never terminates), and to exhibit deep semantic properties. CAN's underlying theory is the conceptual calculus, based on the clausal form of predicate logic. It involves two main ideas :-an Induction principle specially adapted to program understanding (as opposed to program verification).-An extension of unificetion to equation solving. 1. INTRODUCTION CAN is an implemented program understanding system. It is fully automatic and detects semantic properties :-unused portions of code, or undefined function applicet ions-classes of data for which a program execution never terminates-programs which are underused in a given task this diagnosis activity is superimposed to CAN's normal activity x assigning a meaning to a program. CAN'S underlying formal theory, the conceptual calculus, is baaed on clausal form of predicate logic. It admits new types of variables (segment variables, typed element variables, index notations) and constructors (sequences, bags, sets) within terms, with associated equation solvers. It uses an Induction rule whose tesk is to Induce properties of data from recursive equations [6], rather then to prove them. The application criteria of this Induction rule is a vicious circle detector. As opposed to program verification, which lies on verification conditions generation (VCG) [3,8] and theorem proving, program understanding lies on meta-evaluation [17,4] and equation solving [5,7,15,163. Meta-eveluetion as defined in [53 is e generalisation of symbolic evaluation [9,18]. 2. FROM VERIFICATION CONDITION GENERATION TO META-EVALUATION Statements subsume implicit structures which they access and modify (tables of identifiers, I/O buffers, stacks, arrays). Symbolic evaluation pays a closer attention to these implicit structures than verification condition generetion. Instead of being hidden in logicaI expressions, they are Individualized as data abstractions. As an example, where assignment is reduced, within VCG, to e mere operation of substitution on a logical expression [8], symbolic evaluation uses an abstract data structure uhich models a table of identifiers. It permits to easily take in account different assignment modes, as they exist in programming languages. But symbolic evaluation, as it is defined in most works, leaves some problems unsolved. A cell to e LISP-defined symbolic …