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Register a new userOn Transforming Functions Accessing Global Variables into Logically Constrained Term Rewriting Systems
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EPTCS
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Authors
Yoshiaki Kanazawa
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In this paper, we show a new approach to transformations of an imperative program with function calls and global variables into a logically constrained term rewriting system. The resulting system represents transitions of the whole execution environment with a call stack. More precisely, we prepare a function symbol for the whole environment, which stores values for global variables and a call stack as its arguments. For a function call, we prepare rewrite rules to push the frame to the stack and to pop it after the execution. Any running frame is located at the top of the stack, and statements accessing global variables are represented by rewrite rules for the environment symbol. We show a precise transformation based on the approach and prove its correctness.
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We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property fails by an example of a weakly orthogonal TRS with two collapsing rules. By translating this example, we show that this property also fails for the infinitary lambda-beta-eta-calculus. As positive results we obtain the following: Infinitary confluence, and hence the infinitary unique normal forms property, holds for weakly orthogonal TRSs that do not contain collapsing rules. To this end we refine the compression lemma. Furthermore, we establish the triangle and diamond properties for infinitary multi-steps (complete developments) in weakly orthogonal TRSs, by refining an earlier cluster-analysis for the finite case.
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