(* Title: HOL/Lifting_Option.thy
Author: Brian Huffman and Ondrej Kuncar
Author: Andreas Lochbihler, Karlsruhe Institute of Technology
*)
header {* Setup for Lifting/Transfer for the option type *}
theory Lifting_Option
imports Lifting Option
begin
subsection {* Relator and predicator properties *}
lemma rel_option_iff:
"rel_option R x y = (case (x, y) of (None, None) \<Rightarrow> True
| (Some x, Some y) \<Rightarrow> R x y
| _ \<Rightarrow> False)"
by (auto split: prod.split option.split)
subsection {* Transfer rules for the Transfer package *}
context
begin
interpretation lifting_syntax .
lemma None_transfer [transfer_rule]: "(rel_option A) None None"
by (rule option.rel_inject)
lemma Some_transfer [transfer_rule]: "(A ===> rel_option A) Some Some"
unfolding rel_fun_def by simp
lemma case_option_transfer [transfer_rule]:
"(B ===> (A ===> B) ===> rel_option A ===> B) case_option case_option"
unfolding rel_fun_def split_option_all by simp
lemma map_option_transfer [transfer_rule]:
"((A ===> B) ===> rel_option A ===> rel_option B) map_option map_option"
unfolding map_option_case[abs_def] by transfer_prover
lemma option_bind_transfer [transfer_rule]:
"(rel_option A ===> (A ===> rel_option B) ===> rel_option B)
Option.bind Option.bind"
unfolding rel_fun_def split_option_all by simp
end
end