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The Spineless Tag-less G-machine (STG machine) was defined as the target abstract machine for compiling the lazy functional language Haskell. It is at the heart of the Glasgow Haskell Compiler (GHC) which is claimed to be the Haskell compiler that generates the most efficient code. A high-level description of the STG machine can be found in Peyton ). Should the reader be interested in a more detailed view, then the only additional information available is the Haskell code of GHC and the C code of its runtime system.It is hard to prove that this machine correctly implements the lazy semantics of Haskell. Part of the problem lies in the fact that the STG machine executes a bare-bones functional language, called STGL, much lower level than Haskell. Therefore, part of the correctness should be-and it is-established by showing that the translation from Haskell to STGL preserves Haskell's semantics.The other part involves showing that the STG machine correctly implements the lazy semantics of STGL. In this paper we provide a step-by-step formal derivation of the STG machine and of its compilation to C, starting from a natural semantics of STGL. Thus, our starting point is higher level than the descriptions found Peyton

Starting from P. Sestoft semantics for lazy evaluation, we define a new semantics in which normal forms consist of variables pointing to lambdas or constructions. This is in accordance with the more recent changes in the Spineless Tagless G-machine (STG) machine, where constructions only appear in closures (lambdas only appeared in closures already in previous versions). We prove the equivalence between the new semantics and Sestoft's. Then, a sequence of STG machines are derived, formally proving the correctness of each derivation. The last machine consists of a few imperative instructions and its distance to a conventional language is minimal. The paper also discusses the differences between the final machine and the actual STG machine implemented in the Glasgow Haskell Compiler.

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Due to the use of higher-order functions and laziness, debugging lazy functional programs is not a trivial task. Fortunately, several debuggers have appeared during the last years. However, the difficulty of the debugging process is increased when considering parallel extensions of lazy functional languages. Thus, it is necessary not only to develop practical debuggers, but also to provide a clear semantic environment to understand what the debuggers should do. In this paper we present a formal framework for debugging two different parallel extensions of the lazy functional language Haskell. In order to do that, we define an operational semantics model which allows us to deal with side-effects and parallelism. By doing so, we provide a formalization of a parallel debugger we have already implemented by extending the sequential debugger Hood.

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