src/HOL/ex/Conditional_Parametricity_Examples.thy
author traytel
Mon Dec 18 16:58:13 2017 +0100 (2017-12-18)
changeset 67224 341fbce5b26d
child 67399 eab6ce8368fa
permissions -rw-r--r--
a conditional paramitrecity prover
     1 (*  Title:    HOL/ex/Conditional_Parametricity_Examples.thy
     2     Author:   Jan Gilcher, Andreas Lochbihler, Dmitriy Traytel, ETH Z├╝rich
     3 
     4 Examples for the parametric_constant command
     5 *)
     6 
     7 theory Conditional_Parametricity_Examples
     8   imports "HOL-Library.Conditional_Parametricity"
     9 begin
    10 
    11 definition "bar x xs = rev (x # xs)"
    12 parametric_constant bar_def
    13 
    14 definition bar2 where "bar2 = bar"
    15 parametric_constant bar2_def
    16 
    17 parametric_constant bar_thm[transfer_rule]: bar_def
    18 parametric_constant bar2_thm1: bar2_def
    19 
    20 definition "t1 y x = zip x y"
    21 parametric_constant t1_thm: t1_def
    22 
    23 definition "t2 f x = f (rev x)"
    24 parametric_constant t2_thm: t2_def
    25 
    26 definition "t3 xs = rev (rev (xs :: 'b list))"
    27 parametric_constant t3_thm: t3_def
    28 
    29 definition "t4 f x = rev (f x (f x (rev x)))"
    30 parametric_constant t4_thm: t4_def
    31 
    32 definition "t5 x y = zip x (rev y)"
    33 parametric_constant t5_thm: t5_def
    34 
    35 (* Conditional Parametricity*)
    36 
    37 definition "t6_1 x y = inf y x"
    38 parametric_constant t6_1_thm: t6_1_def
    39 
    40 definition "t6_2 x y = sup y x"
    41 parametric_constant t6_2_thm: t6_2_def
    42 
    43 definition "t6_3 x z y = sup (inf x y) z"
    44 parametric_constant t6_3_thm: t6_3_def
    45 
    46 definition "t6_4 x xs y = map (sup (inf y x)) xs"
    47 parametric_constant t6_4_thm: t6_4_def
    48 
    49 definition "t7 x y = (y = x)"
    50 parametric_constant t7_thm: t7_def
    51 
    52 definition "t8 x y = ((x=y) \<and> (y=x))"
    53 parametric_constant t8_thm: t8_def
    54 
    55 (* Definition via primrec*)
    56 primrec delete where
    57   "delete _ [] = []"
    58 | "delete x (y # ys) = (if x = y then ys else y # (delete x ys))"
    59 parametric_constant delete_thm: delete_def
    60 
    61 definition "foo f x y = (if f x = f y then x else sup y x)"
    62 parametric_constant foo_parametricity: foo_def
    63 
    64 end