adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
theory Predicate_Compile_Alternative_Defs
imports "../Predicate_Compile"
begin
section {* Common constants *}
declare HOL.if_bool_eq_disj[code_pred_inline]
setup {* Predicate_Compile_Data.ignore_consts [@{const_name Let}] *}
section {* Pairs *}
setup {* Predicate_Compile_Data.ignore_consts [@{const_name fst}, @{const_name snd}, @{const_name split}] *}
section {* Bounded quantifiers *}
declare Ball_def[code_pred_inline]
declare Bex_def[code_pred_inline]
section {* Set operations *}
declare Collect_def[code_pred_inline]
declare mem_def[code_pred_inline]
declare eq_reflection[OF empty_def, code_pred_inline]
declare insert_code[code_pred_def]
declare subset_iff[code_pred_inline]
declare Int_def[code_pred_inline]
declare eq_reflection[OF Un_def, code_pred_inline]
declare eq_reflection[OF UNION_def, code_pred_inline]
lemma Diff[code_pred_inline]:
"(A - B) = (%x. A x \<and> \<not> B x)"
by (auto simp add: mem_def)
lemma set_equality[code_pred_inline]:
"(A = B) = ((\<forall>x. A x \<longrightarrow> B x) \<and> (\<forall>x. B x \<longrightarrow> A x))"
by (fastsimp simp add: mem_def)
section {* Setup for Numerals *}
setup {* Predicate_Compile_Data.ignore_consts [@{const_name number_of}] *}
setup {* Predicate_Compile_Data.keep_functions [@{const_name number_of}] *}
setup {* Predicate_Compile_Data.ignore_consts [@{const_name div}, @{const_name mod}, @{const_name times}] *}
section {* Alternative list definitions *}
text {* size simps are not yet added to the Spec_Rules interface. So they are just added manually here! *}
lemma [code_pred_def]:
"length [] = 0"
"length (x # xs) = Suc (length xs)"
by auto
subsection {* Alternative rules for set *}
lemma set_ConsI1 [code_pred_intro]:
"set (x # xs) x"
unfolding mem_def[symmetric, of _ x]
by auto
lemma set_ConsI2 [code_pred_intro]:
"set xs x ==> set (x' # xs) x"
unfolding mem_def[symmetric, of _ x]
by auto
code_pred [skip_proof] set
proof -
case set
from this show thesis
apply (case_tac xb)
apply auto
unfolding mem_def[symmetric, of _ xc]
apply auto
unfolding mem_def
apply fastsimp
done
qed
subsection {* Alternative rules for list_all2 *}
lemma list_all2_NilI [code_pred_intro]: "list_all2 P [] []"
by auto
lemma list_all2_ConsI [code_pred_intro]: "list_all2 P xs ys ==> P x y ==> list_all2 P (x#xs) (y#ys)"
by auto
code_pred [skip_proof] list_all2
proof -
case list_all2
from this show thesis
apply -
apply (case_tac xa)
apply (case_tac xb)
apply auto
apply (case_tac xb)
apply auto
done
qed
end