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The optimization phase of a compiler is responsible for transforming an intermediate representation (IR) of a program into a more efficient form. Modern optimizers, such as that used in the GraalVM compiler, use an IR consisting of a sophisticated graph data structure that combines data flow and control flow into the one structure. As part of a wider project on the verification of optimization passes of GraalVM, this paper describes a semantics for its IR within Isabelle/HOL. The semantics consists of a big-step operational semantics for data nodes (which are represented in a graph-based static single assignment (SSA) form) and a small-step operational semantics for handling control flow including heap-based reads and writes, exceptions, and method calls. We have proved a suite of canonicalization optimizations and conditional elimination optimizations with respect to the semantics.
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an abstract one an
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we define a new
We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of emph{mixed-sign unbounded} random variables after execution of a probabilistic program. The semantics of a while-loop is well-defined as th
Designing software that controls industrial equipment is challenging, especially due to its inherent concurrent nature. Testing this kind of event driven control software is difficult and, due to the large number of possible execution scenarios only
Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melli`es (2018) suggested that such categories of games and strategies may be obtained