This paper proposes a lightweight fusion method for general recursive function definitions. Compared with existing proposals, our method has several significant practical features: it works for general recursive functions on general algebraic data types; it does not produce extra runtime overhea (except for possible code size increase due to the success of fusion); and it is readily incorporated in standard inlining optimization. This is achieved by extending the ordinary inlining process with a new fusion law that transforms a term of the form f o (fix g λx. E ) to a new fixed point term fix h λx. E ′ by promoting the function f through the fixed point operator. This is a sound syntactic transformation rule that is not sensitive to the types of f and g . This property makes our method applicable to wide range of functions including those with multi-parameters in both curried and uncurried forms. Although this method does not guarantee any form of completeness, it fuses typical examples discussed in the literature and others that involve accumulating parameters, either in the tt foldl-like specific forms or in general recursive forms, without any additional machinery. In order to substantiate our claim, we have implemented our method in a compiler. Although it is preliminary, it demonstrates practical feasibility of this method.

This paper proposes a lightweight fusion method for general recursive function definitions. Compared with existing proposals, our method has several significant practical features: it works for general recursive functions on general algebraic data types; it does not produce extra runtime overhead (except for possible code size increase due to the success of fusion); and it is readily incorporated in standard inlining optimization. This is achieved by extending the ordinary inlining process with a new fusion law that transforms a term of the form f • (fix g.λx.E) to a new fixed point term fix h.λx.E by promoting the function f through the fixed point operator. This is a sound syntactic transformation rule that is not sensitive to the types of f and g. This property makes our method applicable to wide range of functions including those with multi-parameters in both curried and uncurried forms. Although this method does not guarantee any form of completeness, it fuses typical examples discussed in the literature and others that involve accumulating parameters, either in the foldl-like specific forms or in general recursive forms, without any additional machinery. In order to substantiate our claim, we have implemented our method in a compiler. Although it is preliminary, it demonstrates practical feasibility of this method.

Abstract. Buneman et al. proposed a graph algebra called UnCAL (Unstructured CALculus) for compositional graph transformations based on structural recursion, and we have recently applied to model transformations. The compositional nature of the algebra greatly enhances the modularity of transformations. However, intermediate results generated between composed transformations cause overhead. Buneman et al. proposed fusion rules that eliminate the intermediate results, but auxiliary rewriting rules that enable the actual application of the fusion rules are not apparent so far. UnCAL graph model includes the concept of markers, which correspond to recursive function call in the structural recursion. We have found that there are many optimization opportunities at rewriting level based on static analysis, especially focusing on markers. The analysis can safely eliminate redundant function calls. Performance evaluation shows its practical effectiveness for non-trivial examples in model transformations.

Abstract. ATL is a language for describing model transformations currently in uni-direction. In our previous work we have shown that transformations of graph structures given in some form can be bidirectionalized and have implemented a system called GRoundTram system for bidirectional graph transformations. We say a transformation t is bidirectionalized when we obtain a backward transformation t ′ so that the pair (t, t ′ ) of transformations satisfies certain wellbehavedness properties. Bidirectional model transformation is used to reflect the changes in the target model back to the source model, and vice versa. In this paper, as a first step toward realizing practical bidirectional model transformations, we present bidirectionalization of core part of the ATL by encoding it in the UnQL language, which is used as a transformation language in the GRoundTram system. We give the algorithm for the encoding, based on which we have implemented the system for bidirectionalizing the core ATL in OCaml language.

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