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