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LFCS Seminar: James Brotherston

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Cyclic Abduction of Inductive Safety & Termination Preconditions

What
  • LFCS Seminar
When May 08, 2013
from 04:00 PM to 05:00 PM
Where IF 4.02
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Whether a given program ever encounters a memory fault, or indeed ever terminates, are natural (and undecidable) problems in program analysis. Usually, we are interested in establishing such safety and termination properties under a given "precondition" in logic that expresses some known initial conditions about the program.

However, in this talk, I will go a step further and consider the problem of *inferring* a reasonable precondition under which a given program is memory-safe and/or terminates. When one considers heap-manipulating programs, this problem typically involves inventing the inductive definitions of data structures. For example, a program that traverses a list will:

- terminate safely, given an acyclic list as input;
- run safely but not terminate, given a cyclic list as input;
- encounter a memory fault and crash, given something that is in no way a list as input.

Here I demonstrate a new method, called *cyclic abduction*, for
automatically inferring the inductive definitions of safety and termination preconditions for heap-manipulating programs. That is, given a program, this method attempts to invent the definition of an inductively defined predicate in separation logic under which the program is guaranteed safe and/or terminating. Cyclic abduction
essentially works by searching for a *cyclic proof* of safety / termination, abducing definitional clauses of the precondition as necessary to advance the proof search process.

Our cyclic abduction method has been implemented in the Cyclist theorem
prover, and tested on a suite of small programs. The abduced predicates may define segmented, cyclic, nested, and/or mutually defined data structures.

This is joint work with Nikos Gorogiannis (also at UCL).

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