Dynamic Tables
نویسنده
چکیده
This article formalizes the amortized analysis of dynamic tables parameterized with their minimal and maximal load factors and the expansion and contraction factors. A full description is found in a companion paper [1]. theory Tables-real imports ../Amortized-Complexity/Amor begin fun Ψ :: bool ⇒ real ⇒ real ⇒ real ⇒ real ⇒ nat ⇒ real where Ψ b i d x 1 x 2 n = (if n ≥ x 2 then i∗(n − x 2) else if n ≤ x 1 ∧ b then d∗(x 1 − n) else 0 ) declare real-of-nat-Suc[simp] real-of-nat-diff [simp] An automatic proof: lemma Psi-diff-Ins: 0 < i =⇒ 0 < d =⇒ Ψ b i d x 1 x 2 (Suc n) − Ψ b i d x 1 x 2 n ≤ i 〈proof 〉 lemma assumes [arith]: 0 < i 0 ≤ d shows Ψ b i d x 1 x 2 (n+1 ) − Ψ b i d x 1 x 2 n ≤ i (is ?D ≤ -) 〈proof 〉 lemma Psi-diff-Del : assumes [arith]: 0 < i 0 ≤ d n 6=0 and x 1 ≤ x 2 shows Ψ b i d x 1 x 2 (n−Suc 0 ) − Ψ b i d x 1 x 2 (n) ≤ d (is ?D ≤ -) 〈proof 〉 locale Table0 = fixes f1 f2 f1 ′ f2 ′ e c :: real assumes e1 [arith]: e > 1 assumes c1 [arith]: c > 1 assumes f1 [arith]: f1 > 0 assumes f1cf2 : f1∗c < f2 assumes f1f2e: f1 < f2/e
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