On Graph Rewriting, Reduction and Evaluation

Abstract

machine Danvy and Nielsen’s refocusing inlining Ohori and Sasano’s lightweight fusion transition compression Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 24 / 33 Introduction Formalization Derivation Conclusion Result: an abstract machine This abstract machine coincides with Turner’s reduction machine. Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 25 / 33 Introduction Formalization Derivation Conclusion Rewriting system to reduction machine Summary Side effects are restricted to axioms Driving machinery is functional Syntactic correspondence applies Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 26 / 33 Introduction Formalization Derivation Conclusion Overview Formalization of a reduction machine Formalization of a graph rewriting system Derivation Towards graph evaluation Conclusion Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 27 / 33 Introduction Formalization Derivation Conclusion Towards graph evaluation Background: Reynolds’s functional correspondence. Evaluator · · Abstract machine closure conversion CPS transformation defunctionalizationmachine closure conversion CPS transformation defunctionalization Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 28 / 33 Introduction Formalization Derivation Conclusion The functional correspondence Danvy and students: abstract machines oo functional correspondence // evaluators CEK oo // KAM oo // SECD oo // oo // monadic evaluator Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 29 / 33 Introduction Formalization Derivation Conclusion Towards graph evaluation To defunctionalized form: stack marking to list of stack frames Refunctionalization Direct-style transformation Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 30 / 33 Introduction Formalization Derivation Conclusion Towards graph evaluation Result: A graph evaluator Resembles the one of Okasaki, Lee and Tarditi Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 31 / 33 Introduction Formalization Derivation Conclusion Overview Formalization of a reduction machine Formalization of a graph rewriting system Derivation Towards graph evaluation Conclusion Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 32 / 33 Introduction Formalization Derivation Conclusion Conclusion Danvy et al.’s syntactic correspondence terms // graphs Barendregt et al. and Turner’s graph reduction graph rewriting oo // reduction machines Reynolds’s functional correspondence reduction machines oo // graph evaluators Thank you Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 33 / 33 Introduction Formalization Derivation Conclusion Conclusion Danvy et al.’s syntactic correspondence terms // graphs Barendregt et al. and Turner’s graph reduction graph rewriting oo // reduction machines Reynolds’s functional correspondence reduction machines oo // graph evaluators Thank you Ian Zerny (zerny@cs.au.dk) On Graph Rewriting, Reduction and Evaluation TFP ’09 33 / 33