(* Title: HOL/Library/Conditional_Parametricity.thy
Author: Jan Gilcher, Andreas Lochbihler, Dmitriy Traytel, ETH Zürich
A conditional parametricity prover
*)
theory Conditional_Parametricity
imports Main
keywords "parametric_constant" :: thy_decl
begin
context includes lifting_syntax begin
qualified definition Rel_match :: "('a \<Rightarrow> 'b \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> bool" where
"Rel_match R x y = R x y"
named_theorems parametricity_preprocess
lemma bi_unique_Rel_match [parametricity_preprocess]:
"bi_unique A = Rel_match (A ===> A ===> (=)) (=) (=)"
unfolding bi_unique_alt_def2 Rel_match_def ..
lemma bi_total_Rel_match [parametricity_preprocess]:
"bi_total A = Rel_match ((A ===> (=)) ===> (=)) All All"
unfolding bi_total_alt_def2 Rel_match_def ..
lemma is_equality_Rel: "is_equality A \<Longrightarrow> Transfer.Rel A t t"
by (fact transfer_raw)
lemma Rel_Rel_match: "Transfer.Rel R x y \<Longrightarrow> Rel_match R x y"
unfolding Rel_match_def Rel_def .
lemma Rel_match_Rel: "Rel_match R x y \<Longrightarrow> Transfer.Rel R x y"
unfolding Rel_match_def Rel_def .
lemma Rel_Rel_match_eq: "Transfer.Rel R x y = Rel_match R x y"
using Rel_Rel_match Rel_match_Rel by fast
lemma Rel_match_app:
assumes "Rel_match (A ===> B) f g" and "Transfer.Rel A x y"
shows "Rel_match B (f x) (g y)"
using assms Rel_match_Rel Rel_app Rel_Rel_match by fast
end
ML_file \<open>conditional_parametricity.ML\<close>
end