7 fun permute ty = Const (@{const_name permute}, @{typ perm} --> ty --> ty); |
7 fun permute ty = Const (@{const_name permute}, @{typ perm} --> ty --> ty); |
8 val minus_perm = Const (@{const_name minus}, @{typ perm} --> @{typ perm}); |
8 val minus_perm = Const (@{const_name minus}, @{typ perm} --> @{typ perm}); |
9 *} |
9 *} |
10 |
10 |
11 ML {* |
11 ML {* |
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12 fun prove_perm_empty lthy induct perm_def perm_frees = |
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13 let |
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14 val perm_types = map fastype_of perm_frees; |
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15 val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); |
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16 val gl = |
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17 HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
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18 (map (fn ((perm, T), x) => HOLogic.mk_eq |
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19 (perm $ @{term "0 :: perm"} $ Free (x, T), |
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20 Free (x, T))) |
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21 (perm_frees ~~ |
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22 map body_type perm_types ~~ perm_indnames))); |
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23 fun tac _ = |
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24 EVERY [ |
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25 indtac induct perm_indnames 1, |
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26 ALLGOALS (asm_full_simp_tac (HOL_ss addsimps (@{thm permute_zero} :: perm_def))) |
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27 ]; |
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28 in |
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29 split_conj_thm (Goal.prove lthy perm_indnames [] gl tac) |
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30 end; |
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31 *} |
12 |
32 |
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33 ML {* |
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34 fun prove_perm_append lthy induct perm_def perm_frees = |
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35 let |
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36 val add_perm = @{term "op + :: (perm \<Rightarrow> perm \<Rightarrow> perm)"} |
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37 val pi1 = Free ("pi1", @{typ perm}); |
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38 val pi2 = Free ("pi2", @{typ perm}); |
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39 val perm_types = map fastype_of perm_frees |
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40 val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); |
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41 val gl = |
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42 (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
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43 (map (fn ((perm, T), x) => |
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44 let |
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45 val lhs = perm $ (add_perm $ pi1 $ pi2) $ Free (x, T) |
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46 val rhs = perm $ pi1 $ (perm $ pi2 $ Free (x, T)) |
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47 in HOLogic.mk_eq (lhs, rhs) |
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48 end) |
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49 (perm_frees ~~ map body_type perm_types ~~ perm_indnames)))) |
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50 fun tac _ = |
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51 EVERY [ |
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52 indtac induct perm_indnames 1, |
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53 ALLGOALS (asm_full_simp_tac (HOL_ss addsimps (@{thm permute_plus} :: perm_def))) |
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54 ] |
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55 in |
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56 split_conj_thm (Goal.prove lthy ("pi1" :: "pi2" :: perm_indnames) [] gl tac) |
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57 end; |
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58 *} |
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59 |
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60 ML {* |
13 (* TODO: full_name can be obtained from new_type_names with Datatype *) |
61 (* TODO: full_name can be obtained from new_type_names with Datatype *) |
14 fun define_raw_perms new_type_names full_tnames thy = |
62 fun define_raw_perms new_type_names full_tnames thy = |
15 let |
63 let |
16 val {descr, induct, ...} = Datatype.the_info thy (hd full_tnames); |
64 val {descr, induct, ...} = Datatype.the_info thy (hd full_tnames); |
17 (* TODO: [] should be the sorts that we'll take from the specification *) |
65 (* TODO: [] should be the sorts that we'll take from the specification *) |
20 val perm_names' = Datatype_Prop.indexify_names (map (fn (i, _) => |
68 val perm_names' = Datatype_Prop.indexify_names (map (fn (i, _) => |
21 "permute_" ^ name_of_typ (nth_dtyp i)) descr); |
69 "permute_" ^ name_of_typ (nth_dtyp i)) descr); |
22 val perm_types = map (fn (i, _) => |
70 val perm_types = map (fn (i, _) => |
23 let val T = nth_dtyp i |
71 let val T = nth_dtyp i |
24 in @{typ perm} --> T --> T end) descr; |
72 in @{typ perm} --> T --> T end) descr; |
25 val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); |
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26 val perm_names_types' = perm_names' ~~ perm_types; |
73 val perm_names_types' = perm_names' ~~ perm_types; |
27 val pi = Free ("pi", @{typ perm}); |
74 val pi = Free ("pi", @{typ perm}); |
28 fun perm_eq_constr i (cname, dts) = |
75 fun perm_eq_constr i (cname, dts) = |
29 let |
76 let |
30 val Ts = map (typ_of_dtyp descr sorts) dts; |
77 val Ts = map (typ_of_dtyp descr sorts) dts; |
58 val ((_, perm_ldef), lthy') = |
105 val ((_, perm_ldef), lthy') = |
59 Primrec.add_primrec |
106 Primrec.add_primrec |
60 (map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs lthy; |
107 (map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs lthy; |
61 val perm_frees = |
108 val perm_frees = |
62 (distinct (op =)) (map (fst o strip_comb o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) perm_ldef); |
109 (distinct (op =)) (map (fst o strip_comb o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) perm_ldef); |
63 val perm_empty_thms = |
110 val perm_empty_thms = List.take (prove_perm_empty lthy' induct perm_ldef perm_frees, length new_type_names); |
64 let |
111 val perm_append_thms = List.take (prove_perm_append lthy' induct perm_ldef perm_frees, length new_type_names) |
65 val gl = |
112 val perms_name = space_implode "_" perm_names' |
66 HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
113 val perms_zero_bind = Binding.name (perms_name ^ "_zero") |
67 (map (fn ((perm, T), x) => HOLogic.mk_eq |
114 val perms_append_bind = Binding.name (perms_name ^ "_append") |
68 (perm $ @{term "0 :: perm"} $ Free (x, T), |
115 fun tac _ perm_thms = |
69 Free (x, T))) |
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70 (perm_frees ~~ |
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71 map body_type perm_types ~~ perm_indnames))); |
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72 fun tac {context = ctxt, ...} = |
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73 EVERY [ |
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74 indtac induct perm_indnames 1, |
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75 ALLGOALS (asm_full_simp_tac (@{simpset} addsimps perm_ldef)) |
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76 ]; |
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77 in |
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78 (List.take (split_conj_thm (Goal.prove lthy' perm_indnames [] gl tac), length new_type_names)) |
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79 end; |
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80 val add_perm = @{term "op + :: (perm \<Rightarrow> perm \<Rightarrow> perm)"} |
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81 val pi1 = Free ("pi1", @{typ perm}); |
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82 val pi2 = Free ("pi2", @{typ perm}); |
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83 val perm_append_thms = |
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84 List.take ((split_conj_thm |
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85 (Goal.prove lthy' ("pi1" :: "pi2" :: perm_indnames) [] |
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86 (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
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87 (map (fn ((perm, T), x) => |
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88 let |
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89 val lhs = perm $ (add_perm $ pi1 $ pi2) $ Free (x, T) |
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90 val rhs = perm $ pi1 $ (perm $ pi2 $ Free (x, T)) |
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91 in HOLogic.mk_eq (lhs, rhs) |
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92 end) |
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93 (perm_frees ~~ |
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94 map body_type perm_types ~~ perm_indnames)))) |
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95 (fn _ => EVERY [indtac induct perm_indnames 1, |
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96 ALLGOALS (asm_full_simp_tac (@{simpset} addsimps perm_ldef))]))), |
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97 length new_type_names); |
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98 fun tac ctxt perm_thms = |
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99 (Class.intro_classes_tac []) THEN (ALLGOALS ( |
116 (Class.intro_classes_tac []) THEN (ALLGOALS ( |
100 simp_tac (@{simpset} addsimps perm_thms |
117 simp_tac (HOL_ss addsimps perm_thms |
101 ))); |
118 ))); |
102 fun morphism phi = map (Morphism.thm phi); |
119 fun morphism phi = map (Morphism.thm phi); |
103 in |
120 in |
104 Class_Target.prove_instantiation_exit_result morphism tac (perm_empty_thms @ perm_append_thms) lthy' |
121 lthy' |
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122 |> snd o (Local_Theory.note ((perms_zero_bind, []), perm_empty_thms)) |
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123 |> snd o (Local_Theory.note ((perms_append_bind, []), perm_append_thms)) |
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124 |> Class_Target.prove_instantiation_exit_result morphism tac (perm_empty_thms @ perm_append_thms) |
105 end |
125 end |
106 |
126 |
107 *} |
127 *} |
108 |
128 |
109 (* Test |
129 (* Test |