Dag Representation And Optimization of Rewriting
Dag Representation And Optimization of Rewriting
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S remains a redex after rewriting of /. n Theorem 1 In dag rewriting, for a lef. -linear and variable-more TBS. Given any term, any derivation for that term is oplimal. Proof: Suppose D and D' are two derivations for term t and \D'\ < \D\. Suppose D[l. I] = D'[l. I] and D[i + l] # D'[, + l]. D[, + I] rewrites.^ and D'[i + l] rewrites . S'. By lemma 1. . *; remains a redex until it is rewritten in the subsequent derivation of D'. Suppose i! is rewritten in D' by rule r at step D'[j]{i < j). All function syml^ols 12 (and constants, if there are) in 5 matched with function symbols in the left side of r are called the critical part of, s. Note that those subterms in . S matched with variables of r are not in the critical ])arr. Suppose j = i + A" [i- j defined above). Let /, +, be the term after step D'[i + p] in D' {0 < p < k — 1). Root-rewrite . <; in t, by rule r. T, Ijecoming /q. Consider applying D'[i + l]. D'[i + 2] D'[i + k - I] to t'^. Let t[, be the term after rewriting step D'[i +p](0 < p < k - 1).
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To quickly assess the difficulty of the text, read a short excerpt:
S remains a redex after rewriting of /. n Theorem 1 In dag rewriting, for a lef. -linear and variable-more TBS. Given any term, any derivation for that term is oplimal. Proof: Suppose D and D' are two derivations for term t and \D'\ < \D\. Suppose D[l. I] = D'[l. I] and D[i + l] # D'[, + l]. D[, + I] rewrites.^ and D'[i + l] rewrites . S'. By lemma 1. . *; remains a redex until it is rewritten in the subsequent derivation of D'. Suppose i! is rewritten in D' by rule r at step D'[j]{i < j). All function syml^ols 12 (and constants, if there are) in 5 matched with function symbols in the left side of r are called the critical part of, s. Note that those subterms in . S matched with variables of r are not in the critical ])arr. Suppose j = i + A" [i- j defined above). Let /, +, be the term after step D'[i + p] in D' {0 < p < k — 1). Root-rewrite . <; in t, by rule r. T, Ijecoming /q. Consider applying D'[i + l]. D'[i + 2] D'[i + k - I] to t'^. Let t[, be the term after rewriting step D'[i +p](0 < p < k - 1).
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