The problem of probabilistic modeling and inference, at a high-level, can be viewed as constructing a ( model , query , inference ) tuple, where an inference algorithm implements a query on a model . Notably, the derivation of inference algorithms can be a difficult and error-prone task. Hence, researchers have explored how ideas from probabilistic programming can be applied. In the context of constructing these tuples, probabilistic programming can be seen as taking a language-based approach to probabilistic modeling and inference. For instance, by using (1) appropriate languages for expressing models and queries and (2) devising inference techniques that operate on encodings of models (and queries) as program expressions, the task of inference can be automated. In this paper, we describe a compiler that transforms a probabilistic model written in a restricted modeling language and a query for posterior samples given observed data into a Markov Chain Monte Carlo (MCMC) inference algorithm that implements the query. The compiler uses a sequence of intermediate languages (ILs) that guide it in gradually and successively refining a declarative specification of a probabilistic model and the query into an executable MCMC inference algorithm. The compilation strategy produces composable MCMC algorithms for execution on a CPU or GPU.
Software pipelining is a loop optimization that overlaps the execution of several iterations of a loop to expose more instruction-level parallelism. It can result in first-class performance characteristics, but at the cost of significant obfuscation of the code, making this optimization difficult to test and debug. In this paper, we present a translation validation algorithm that uses symbolic evaluation to detect semantics discrepancies between a loop and its pipelined version. Our algorithm can be implemented simply and efficiently, is provably sound, and appears to be complete with respect to most modulo scheduling algorithms. A conclusion of this case study is that it is possible and effective to use symbolic evaluation to reason about loop transformations.
Translation validation establishes a posteriori the correctness of a run of a compilation pass or other program transformation. In this paper, we develop an efficient translation validation algorithm for the Lazy Code Motion (LCM) optimization. LCM is an interesting challenge for validation because it is a global optimization that moves code across loops. Consequently, care must be taken not to move computations that may fail before loops that may not terminate. Our validator includes a specific check for anticipability to rule out such incorrect moves. We present a mechanicallychecked proof of correctness of the validation algorithm, using the Coq proof assistant. Combining our validator with an unverified implementation of LCM, we obtain a LCM pass that is provably semantics-preserving and was integrated in the CompCert formally verified compiler.
Translation validation consists of transforming a program and a posteriori validating it in order to detect a modification of itssemantics. This approach can be used in a verified compiler, provided that validation is formally proved to be correct. We present two such validators and their Coq proofs of correctness. The validators are designed for two instruction scheduling optimizations: list scheduling and trace scheduling.
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