1(*  Title:    HOL/ex/Conditional_Parametricity_Examples.thy
2    Author:   Jan Gilcher, Andreas Lochbihler, Dmitriy Traytel, ETH Z��rich
3
4Examples for the parametric_constant command
5*)
6
7theory Conditional_Parametricity_Examples
8  imports "HOL-Library.Conditional_Parametricity"
9begin
10
11definition "bar x xs = rev (x # xs)"
12parametric_constant bar_def
13
14definition bar2 where "bar2 = bar"
15parametric_constant bar2_def
16
17parametric_constant bar_thm[transfer_rule]: bar_def
18parametric_constant bar2_thm1: bar2_def
19
20definition "t1 y x = zip x y"
21parametric_constant t1_thm: t1_def
22
23definition "t2 f x = f (rev x)"
24parametric_constant t2_thm: t2_def
25
26definition "t3 xs = rev (rev (xs :: 'b list))"
27parametric_constant t3_thm: t3_def
28
29definition "t4 f x = rev (f x (f x (rev x)))"
30parametric_constant t4_thm: t4_def
31
32definition "t5 x y = zip x (rev y)"
33parametric_constant t5_thm: t5_def
34
35(* Conditional Parametricity*)
36
37definition "t6_1 x y = inf y x"
38parametric_constant t6_1_thm: t6_1_def
39
40definition "t6_2 x y = sup y x"
41parametric_constant t6_2_thm: t6_2_def
42
43definition "t6_3 x z y = sup (inf x y) z"
44parametric_constant t6_3_thm: t6_3_def
45
46definition "t6_4 x xs y = map (sup (inf y x)) xs"
47parametric_constant t6_4_thm: t6_4_def
48
49definition "t7 x y = (y = x)"
50parametric_constant t7_thm: t7_def
51
52definition "t8 x y = ((x=y) \<and> (y=x))"
53parametric_constant t8_thm: t8_def
54
55(* Definition via primrec*)
56primrec delete where
57  "delete _ [] = []"
58| "delete x (y # ys) = (if x = y then ys else y # (delete x ys))"
59parametric_constant delete_thm: delete_def
60
61definition "foo f x y = (if f x = f y then x else sup y x)"
62parametric_constant foo_parametricity: foo_def
63
64end
65