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Termination Analysis of Programs with Multiphase Control-Flow

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 Publication date 2021
and research's language is English




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Programs with multiphase control-flow are programs where the execution passes through several (possibly implicit) phases. Proving termination of such programs (or inferring corresponding runtime bounds) is often challenging since it requires reasoning on these phases separately. In this paper we discuss techniques for proving termination of such programs, in particular: (1) using multiphase ranking functions, where we will discuss theoretical aspects of such ranking functions for several kinds of program representations; and (2) using control-flow refinement, in particular partial evaluation of Constrained Horn Clauses, to simplify the control-flow allowing, among other things, to prove termination with simpler ranking functions.



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147 - Raven Beutner , Luke Ong 2021
We study termination of higher-order probabilistic functional programs with recursion, stochastic conditioning and sampling from continuous distributions. Reasoning about the termination probability of programs with continuous distributions is hard, because the enumeration of terminating executions cannot provide any non-trivial bounds. We present a new operational semantics based on traces of intervals, which is sound and complete with respect to the standard sampling-based semantics, in which (countable) enumeration can provide arbitrarily tight lower bounds. Consequently we obtain the first proof that deciding almost-sure termination (AST) for programs with continuous distributions is $Pi^0_2$-complete. We also provide a compositional representation of our semantics in terms of an intersection type system. In the second part, we present a method of proving AST for non-affine programs, i.e., recursive programs that can, during the evaluation of the recursive body, make multiple recursive calls (of a first-order function) from distinct call sites. Unlike in a deterministic language, the number of recursion call sites has direct consequences on the termination probability. Our framework supports a proof system that can verify AST for programs that are well beyond the scope of existing methods. We have constructed prototype implementations of our method of computing lower bounds of termination probability, and AST verification.
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112 - Vincent Nys 2017
We extend a technique called Compiling Control. The technique transforms coroutining logic programs into logic programs that, when executed under the standard left-to-right selection rule (and not using any delay features) have the same computational behavior as the coroutining program. In recent work, we revised Compiling Control and reformulated it as an instance of Abstract Conjunctive Partial Deduction. This work was mostly focused on the program analysis performed in Compiling Control. In the current paper, we focus on the synthesis of the transformed program. Instead of synthesizing a new logic program, we synthesize a CHR(Prolog) program which mimics the coroutining program. The synthesis to CHR yields programs containing only simplification rules, which are particularly amenable to certain static analysis techniques. The programs are also more concise and readable and can be ported to CHR implementations embedded in other languages than Prolog.
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