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(* Title: HOL/ex/Conditional_Parametricity_Examples.thy
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Author: Jan Gilcher, Andreas Lochbihler, Dmitriy Traytel, ETH Zürich
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Examples for the parametric_constant command
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*)
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theory Conditional_Parametricity_Examples
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imports "HOL-Library.Conditional_Parametricity"
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begin
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definition "bar x xs = rev (x # xs)"
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parametric_constant bar_def
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definition bar2 where "bar2 = bar"
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parametric_constant bar2_def
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parametric_constant bar_thm[transfer_rule]: bar_def
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parametric_constant bar2_thm1: bar2_def
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definition "t1 y x = zip x y"
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parametric_constant t1_thm: t1_def
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definition "t2 f x = f (rev x)"
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parametric_constant t2_thm: t2_def
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definition "t3 xs = rev (rev (xs :: 'b list))"
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parametric_constant t3_thm: t3_def
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definition "t4 f x = rev (f x (f x (rev x)))"
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parametric_constant t4_thm: t4_def
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definition "t5 x y = zip x (rev y)"
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parametric_constant t5_thm: t5_def
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(* Conditional Parametricity*)
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definition "t6_1 x y = inf y x"
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parametric_constant t6_1_thm: t6_1_def
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definition "t6_2 x y = sup y x"
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parametric_constant t6_2_thm: t6_2_def
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definition "t6_3 x z y = sup (inf x y) z"
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parametric_constant t6_3_thm: t6_3_def
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definition "t6_4 x xs y = map (sup (inf y x)) xs"
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parametric_constant t6_4_thm: t6_4_def
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definition "t7 x y = (y = x)"
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parametric_constant t7_thm: t7_def
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definition "t8 x y = ((x=y) \<and> (y=x))"
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parametric_constant t8_thm: t8_def
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(* Definition via primrec*)
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primrec delete where
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"delete _ [] = []"
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| "delete x (y # ys) = (if x = y then ys else y # (delete x ys))"
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parametric_constant delete_thm: delete_def
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definition "foo f x y = (if f x = f y then x else sup y x)"
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parametric_constant foo_parametricity: foo_def
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end |