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The substitution vanishes
 In Algebraic Methodology and Software Technology, Proceedings, volume 4019 of LNCS
, 2006
"... Abstract. Accumulation techniques were invented to transform functional programs, which intensively use append functions (like inefficient list reversal), into more efficient programs, which use accumulating parameters instead (like efficient list reversal). In this paper we present a generalized an ..."
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Abstract. Accumulation techniques were invented to transform functional programs, which intensively use append functions (like inefficient list reversal), into more efficient programs, which use accumulating parameters instead (like efficient list reversal). In this paper we present a generalized and automatic accumulation technique that also handles programs operating with unary functions on arbitrary tree structures and employing substitution functions on trees which may replace different designated symbols by different trees. We show that this transformation does not deteriorate the efficiency with respect to callbyneed reduction. 1
Deaccumulation Techniques for Improving Provability ⋆,⋆⋆
"... Several induction theorem provers were developed to verify functional programs mechanically. Unfortunately, automatic verification often fails for functions with accumulating arguments. Using concepts from the theory of tree transducers and extending on earlier work, the paper develops automatic tra ..."
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Several induction theorem provers were developed to verify functional programs mechanically. Unfortunately, automatic verification often fails for functions with accumulating arguments. Using concepts from the theory of tree transducers and extending on earlier work, the paper develops automatic transformations from accumulative functional programs into nonaccumulative ones, which are much better suited for mechanized verification. The overall goal is to reduce the need for generalizing induction hypotheses in (semi)automatic provers. Via the correspondence between imperative programs and tailrecursive functions, the presented approach can also help to reduce the need for inventing loop invariants in the verification of imperative programs. Key words: tree transducers, induction theorem proving, tail recursion, program transformation, program verification ⋆ This work extends the research reported by the same authors in [24]. ⋆⋆This is the author’s version of a work that was accepted for publication in Journal of Logic and Algebraic Programming. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was
Incomparability Results for Classes of Polynomial Tree Series Transformations
, 2003
"... We consider (subclasses of) polynomial bottomup and topdown tree series transducers over a partially ordered semiring A = (A, ⊕, ⊙, 0, 1, ≼), and we compare the classes of treetotreeseries and otreetotreeseries transformations computed by such transducers. Our main result states the followi ..."
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We consider (subclasses of) polynomial bottomup and topdown tree series transducers over a partially ordered semiring A = (A, ⊕, ⊙, 0, 1, ≼), and we compare the classes of treetotreeseries and otreetotreeseries transformations computed by such transducers. Our main result states the following. If, for some a ∈ A with 1 ≼ a, the semiring A is a weak agrowth semiring and either (i) the semiring A is additively idempotent and x, y ∈ {polynomial, deterministic, total, deterministic and total, homomorphism}, or (ii) 1 ≺ 1 ⊕ 1 and x, y ∈ {deterministic, deterministic and total, homomorphism}, then the statements x BOT(A) ⋊ ⋉ y BOT o (A) and x BOT(A) ⋊ ⋉ y TOP(A) hold. Therein x BOT mod (A) for mod ∈ {ε, o} denotes the class of modtreetotreeseries transformations computed by bottomup tree series transducers, which have property x, over the semiring A (the class y TOP(A) is de ned similarly for topdown tree series transducers). Besides, ⋊ ⋉ denotes incomparability with respect to set inclusion.