src/HOL/Quotient_Examples/Lifting_Code_Dt_Test.thy
author haftmann
Sun Oct 08 22:28:22 2017 +0200 (23 months ago)
changeset 66816 212a3334e7da
parent 61169 4de9ff3ea29a
permissions -rw-r--r--
more fundamental definition of div and mod on int
     1 (*  Title:      HOL/Quotient_Examples/Lifting_Code_Dt_Test.thy
     2     Author:     Ondrej Kuncar, TU Muenchen
     3     Copyright   2015
     4 
     5 Miscellaneous lift_definition(code_dt) definitions (for testing purposes).
     6 *)
     7 
     8 theory Lifting_Code_Dt_Test
     9 imports Main
    10 begin
    11 
    12 (* basic examples *)
    13 
    14 typedef bool2 = "{x. x}" by auto
    15 
    16 setup_lifting type_definition_bool2
    17 
    18 lift_definition(code_dt) f1 :: "bool2 option" is "Some True" by simp
    19 
    20 lift_definition(code_dt) f2 :: "bool2 list" is "[True]" by simp
    21 
    22 lift_definition(code_dt) f3 :: "bool2 \<times> int" is "(True, 42)" by simp
    23 
    24 lift_definition(code_dt) f4 :: "int + bool2" is "Inr True" by simp
    25 
    26 lift_definition(code_dt) f5 :: "'a \<Rightarrow> (bool2 \<times> 'a) option" is "\<lambda>x. Some (True, x)" by simp
    27 
    28 (* ugly (i.e., sensitive to rewriting done in my tactics) definition of T *)
    29 
    30 typedef 'a T = "{ x::'a. \<forall>(y::'a) z::'a. \<exists>(w::'a). (z = z) \<and> eq_onp top y y 
    31   \<or> rel_prod (eq_onp top) (eq_onp top) (x, y) (x, y) \<longrightarrow> pred_prod top top (w, w) }"
    32   by auto
    33 
    34 setup_lifting type_definition_T
    35 
    36 lift_definition(code_dt) f6 :: "bool T option" is "Some True" by simp
    37 
    38 lift_definition(code_dt) f7 :: "(bool T \<times> int) option" is "Some (True, 42)" by simp
    39 
    40 lift_definition(code_dt) f8 :: "bool T \<Rightarrow> int \<Rightarrow> (bool T \<times> int) option" 
    41   is "\<lambda>x y. if x then Some (x, y) else None" by simp
    42 
    43 lift_definition(code_dt) f9 :: "nat \<Rightarrow> ((bool T \<times> int) option) list \<times> nat" 
    44   is "\<lambda>x. ([Some (True, 42)], x)" by simp
    45 
    46 (* complicated nested datatypes *)
    47 
    48 (* stolen from Datatype_Examples *)
    49 datatype 'a tree = Empty | Node 'a "'a tree list"
    50 
    51 datatype 'a ttree = TEmpty | TNode 'a "'a ttree list tree"
    52 
    53 datatype 'a tttree = TEmpty | TNode 'a "'a tttree list ttree list tree"
    54 
    55 lift_definition(code_dt) f10 :: "int \<Rightarrow> int T tree" is "\<lambda>i. Node i [Node i Nil, Empty]" by simp
    56 
    57 lift_definition(code_dt) f11 :: "int \<Rightarrow> int T ttree" 
    58   is "\<lambda>i. ttree.TNode i (Node [ttree.TNode i Empty] [])" by simp
    59 
    60 lift_definition(code_dt) f12 :: "int \<Rightarrow> int T tttree" is "\<lambda>i. tttree.TNode i Empty" by simp
    61 
    62 (* Phantom type variables *)
    63 
    64 datatype 'a phantom = PH1 | PH2 
    65 
    66 datatype ('a, 'b) phantom2 = PH21 'a | PH22 "'a option"
    67 
    68 lift_definition(code_dt) f13 :: "int \<Rightarrow> int T phantom" is "\<lambda>i. PH1" by auto
    69 
    70 lift_definition(code_dt) f14 :: "int \<Rightarrow> (int T, nat T) phantom2" is "\<lambda>i. PH22 (Some i)" by auto
    71 
    72 (* Mutual datatypes *)
    73 
    74 datatype 'a M1 = Empty 'a | CM "'a M2"
    75 and 'a M2 = CM2 "'a M1"
    76 
    77 lift_definition(code_dt) f15 :: "int \<Rightarrow> int T M1" is "\<lambda>i. Empty i" by auto
    78 
    79 (* Codatatypes *)
    80 
    81 codatatype 'a stream = S 'a "'a stream"
    82 
    83 primcorec 
    84   sconst :: "'a \<Rightarrow> 'a stream" where
    85   "sconst a = S a (sconst a)"
    86 
    87 lift_definition(code_dt) f16 :: "int \<Rightarrow> int T stream" is "\<lambda>i. sconst i"  unfolding pred_stream_def
    88 by auto
    89 
    90 (* Sort constraints *)
    91 
    92 datatype ('a::finite, 'b::finite) F = F 'a | F2 'b
    93 
    94 instance T :: (finite) finite by standard (transfer, auto)
    95 
    96 lift_definition(code_dt) f17 :: "bool \<Rightarrow> (bool T, 'b::finite) F" is "\<lambda>b. F b" by auto
    97 
    98 export_code f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 
    99   checking SML OCaml? Haskell? Scala? 
   100 
   101 end