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(* Title: HOL/ex/Sorting_Algorithms_Examples.thy
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Author: Florian Haftmann, TU Muenchen
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*)
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theory Sorting_Algorithms_Examples
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imports Main "HOL-Library.Sorting_Algorithms"
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begin
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subsection \<open>Evaluation examples\<close>
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definition int_abs_reversed :: "int comparator"
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where "int_abs_reversed = key abs (reversed default)"
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definition example_1 :: "int list"
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where "example_1 = [65, 1705, -2322, 734, 4, (-17::int)]"
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definition example_2 :: "int list"
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where "example_2 = [-3000..3000]"
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ML \<open>
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local
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val term_of_int_list = HOLogic.mk_list \<^typ>\<open>int\<close>
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o map (HOLogic.mk_number \<^typ>\<open>int\<close> o @{code integer_of_int});
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fun raw_sort (ctxt, ct, ks) =
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\<^instantiate>\<open>x = ct and y = \<open>Thm.cterm_of ctxt (term_of_int_list ks)\<close>
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in cterm \<open>x \<equiv> y\<close> for x y :: \<open>int list\<close>\<close>;
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val (_, sort_oracle) = Context.>>> (Context.map_theory_result
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(Thm.add_oracle (\<^binding>\<open>sort\<close>, raw_sort)));
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in
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val sort_int_abs_reversed_conv = @{computation_conv "int list" terms: int_abs_reversed
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"sort :: int comparator \<Rightarrow> _"
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"quicksort :: int comparator \<Rightarrow> _"
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"mergesort :: int comparator \<Rightarrow> _"
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example_1 example_2
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} (fn ctxt => fn ct => fn ks => sort_oracle (ctxt, ks, ct))
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end
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\<close>
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declare [[code_timing]]
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ML_val \<open>sort_int_abs_reversed_conv \<^context>
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\<^cterm>\<open>sort int_abs_reversed example_1\<close>\<close>
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ML_val \<open>sort_int_abs_reversed_conv \<^context>
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\<^cterm>\<open>quicksort int_abs_reversed example_1\<close>\<close>
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ML_val \<open>sort_int_abs_reversed_conv \<^context>
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\<^cterm>\<open>mergesort int_abs_reversed example_1\<close>\<close>
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ML_val \<open>sort_int_abs_reversed_conv \<^context>
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\<^cterm>\<open>sort int_abs_reversed example_2\<close>\<close>
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ML_val \<open>sort_int_abs_reversed_conv \<^context>
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\<^cterm>\<open>quicksort int_abs_reversed example_2\<close>\<close>
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ML_val \<open>sort_int_abs_reversed_conv \<^context>
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\<^cterm>\<open>mergesort int_abs_reversed example_2\<close>\<close>
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end
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