|
1 (* Title: HOLCF/Tools/pcpodef.ML |
|
2 Author: Brian Huffman |
|
3 |
|
4 Primitive domain definitions for HOLCF, similar to Gordon/HOL-style |
|
5 typedef (see also ~~/src/HOL/Tools/typedef.ML). |
|
6 *) |
|
7 |
|
8 signature PCPODEF = |
|
9 sig |
|
10 val pcpodef_proof: (bool * binding) * (binding * string list * mixfix) * term |
|
11 * (binding * binding) option -> theory -> Proof.state |
|
12 val pcpodef_proof_cmd: (bool * binding) * (binding * string list * mixfix) * string |
|
13 * (binding * binding) option -> theory -> Proof.state |
|
14 val cpodef_proof: (bool * binding) * (binding * string list * mixfix) * term |
|
15 * (binding * binding) option -> theory -> Proof.state |
|
16 val cpodef_proof_cmd: (bool * binding) * (binding * string list * mixfix) * string |
|
17 * (binding * binding) option -> theory -> Proof.state |
|
18 end; |
|
19 |
|
20 structure Pcpodef :> PCPODEF = |
|
21 struct |
|
22 |
|
23 (** type definitions **) |
|
24 |
|
25 (* prepare_cpodef *) |
|
26 |
|
27 fun declare_type_name a = Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS))); |
|
28 |
|
29 fun adm_const T = Const (@{const_name adm}, (T --> HOLogic.boolT) --> HOLogic.boolT); |
|
30 fun mk_adm (x, T, P) = adm_const T $ absfree (x, T, P); |
|
31 |
|
32 fun prepare_pcpodef prep_term pcpo def name (t, vs, mx) raw_set opt_morphs thy = |
|
33 let |
|
34 val _ = Theory.requires thy "Pcpodef" "pcpodefs"; |
|
35 val ctxt = ProofContext.init thy; |
|
36 |
|
37 val full = Sign.full_name thy; |
|
38 val full_name = full name; |
|
39 val bname = Binding.name_of name; |
|
40 |
|
41 (*rhs*) |
|
42 val set = prep_term (ctxt |> fold declare_type_name vs) raw_set; |
|
43 val setT = Term.fastype_of set; |
|
44 val rhs_tfrees = Term.add_tfrees set []; |
|
45 val oldT = HOLogic.dest_setT setT handle TYPE _ => |
|
46 error ("Not a set type: " ^ quote (Syntax.string_of_typ ctxt setT)); |
|
47 |
|
48 (*goal*) |
|
49 val goal_UU_mem = HOLogic.mk_Trueprop (HOLogic.mk_mem (Const (@{const_name UU}, oldT), set)); |
|
50 val goal_nonempty = |
|
51 HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), set))); |
|
52 val goal_admissible = |
|
53 HOLogic.mk_Trueprop (mk_adm ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), set))); |
|
54 |
|
55 (*lhs*) |
|
56 val defS = Sign.defaultS thy; |
|
57 val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs; |
|
58 val lhs_sorts = map snd lhs_tfrees; |
|
59 |
|
60 val tname = Binding.map_name (Syntax.type_name mx) t; |
|
61 val full_tname = full tname; |
|
62 val newT = Type (full_tname, map TFree lhs_tfrees); |
|
63 |
|
64 val (Rep_name, Abs_name) = |
|
65 (case opt_morphs of |
|
66 NONE => (Binding.prefix_name "Rep_" name, Binding.prefix_name "Abs_" name) |
|
67 | SOME morphs => morphs); |
|
68 val RepC = Const (full Rep_name, newT --> oldT); |
|
69 fun belowC T = Const (@{const_name below}, T --> T --> HOLogic.boolT); |
|
70 val below_def = Logic.mk_equals (belowC newT, |
|
71 Abs ("x", newT, Abs ("y", newT, belowC oldT $ (RepC $ Bound 1) $ (RepC $ Bound 0)))); |
|
72 |
|
73 fun make_po tac thy1 = |
|
74 let |
|
75 val ((_, {type_definition, set_def, ...}), thy2) = thy1 |
|
76 |> Typedef.add_typedef def (SOME name) (t, vs, mx) set opt_morphs tac; |
|
77 val lthy3 = thy2 |
|
78 |> TheoryTarget.instantiation ([full_tname], lhs_tfrees, @{sort po}); |
|
79 val below_def' = Syntax.check_term lthy3 below_def; |
|
80 val ((_, (_, below_definition')), lthy4) = lthy3 |
|
81 |> Specification.definition (NONE, |
|
82 ((Binding.prefix_name "below_" (Binding.suffix_name "_def" name), []), below_def')); |
|
83 val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy4); |
|
84 val below_definition = singleton (ProofContext.export lthy4 ctxt_thy) below_definition'; |
|
85 val thy5 = lthy4 |
|
86 |> Class.prove_instantiation_instance |
|
87 (K (Tactic.rtac (@{thm typedef_po} OF [type_definition, below_definition]) 1)) |
|
88 |> LocalTheory.exit_global; |
|
89 in ((type_definition, below_definition, set_def), thy5) end; |
|
90 |
|
91 fun make_cpo admissible (type_def, below_def, set_def) theory = |
|
92 let |
|
93 val admissible' = fold_rule (the_list set_def) admissible; |
|
94 val cpo_thms = map (Thm.transfer theory) [type_def, below_def, admissible']; |
|
95 val theory' = theory |
|
96 |> AxClass.prove_arity (full_tname, lhs_sorts, @{sort cpo}) |
|
97 (Tactic.rtac (@{thm typedef_cpo} OF cpo_thms) 1); |
|
98 val cpo_thms' = map (Thm.transfer theory') cpo_thms; |
|
99 in |
|
100 theory' |
|
101 |> Sign.add_path (Binding.name_of name) |
|
102 |> PureThy.add_thms |
|
103 ([((Binding.prefix_name "adm_" name, admissible'), []), |
|
104 ((Binding.prefix_name "cont_" Rep_name, @{thm typedef_cont_Rep} OF cpo_thms'), []), |
|
105 ((Binding.prefix_name "cont_" Abs_name, @{thm typedef_cont_Abs} OF cpo_thms'), []), |
|
106 ((Binding.prefix_name "lub_" name, @{thm typedef_lub} OF cpo_thms'), []), |
|
107 ((Binding.prefix_name "thelub_" name, @{thm typedef_thelub} OF cpo_thms'), []), |
|
108 ((Binding.prefix_name "compact_" name, @{thm typedef_compact} OF cpo_thms'), [])]) |
|
109 |> snd |
|
110 |> Sign.parent_path |
|
111 end; |
|
112 |
|
113 fun make_pcpo UU_mem (type_def, below_def, set_def) theory = |
|
114 let |
|
115 val UU_mem' = fold_rule (the_list set_def) UU_mem; |
|
116 val pcpo_thms = map (Thm.transfer theory) [type_def, below_def, UU_mem']; |
|
117 val theory' = theory |
|
118 |> AxClass.prove_arity (full_tname, lhs_sorts, @{sort pcpo}) |
|
119 (Tactic.rtac (@{thm typedef_pcpo} OF pcpo_thms) 1); |
|
120 val pcpo_thms' = map (Thm.transfer theory') pcpo_thms; |
|
121 in |
|
122 theory' |
|
123 |> Sign.add_path (Binding.name_of name) |
|
124 |> PureThy.add_thms |
|
125 ([((Binding.suffix_name "_strict" Rep_name, @{thm typedef_Rep_strict} OF pcpo_thms'), []), |
|
126 ((Binding.suffix_name "_strict" Abs_name, @{thm typedef_Abs_strict} OF pcpo_thms'), []), |
|
127 ((Binding.suffix_name "_strict_iff" Rep_name, @{thm typedef_Rep_strict_iff} OF pcpo_thms'), []), |
|
128 ((Binding.suffix_name "_strict_iff" Abs_name, @{thm typedef_Abs_strict_iff} OF pcpo_thms'), []), |
|
129 ((Binding.suffix_name "_defined" Rep_name, @{thm typedef_Rep_defined} OF pcpo_thms'), []), |
|
130 ((Binding.suffix_name "_defined" Abs_name, @{thm typedef_Abs_defined} OF pcpo_thms'), [])]) |
|
131 |> snd |
|
132 |> Sign.parent_path |
|
133 end; |
|
134 |
|
135 fun pcpodef_result UU_mem admissible = |
|
136 make_po (Tactic.rtac exI 1 THEN Tactic.rtac UU_mem 1) |
|
137 #-> (fn defs => make_cpo admissible defs #> make_pcpo UU_mem defs); |
|
138 |
|
139 fun cpodef_result nonempty admissible = |
|
140 make_po (Tactic.rtac nonempty 1) |
|
141 #-> make_cpo admissible; |
|
142 in |
|
143 if pcpo |
|
144 then (goal_UU_mem, goal_admissible, pcpodef_result) |
|
145 else (goal_nonempty, goal_admissible, cpodef_result) |
|
146 end |
|
147 handle ERROR msg => |
|
148 cat_error msg ("The error(s) above occurred in cpodef " ^ quote (Binding.str_of name)); |
|
149 |
|
150 |
|
151 (* proof interface *) |
|
152 |
|
153 local |
|
154 |
|
155 fun gen_pcpodef_proof prep_term pcpo ((def, name), typ, set, opt_morphs) thy = |
|
156 let |
|
157 val (goal1, goal2, make_result) = |
|
158 prepare_pcpodef prep_term pcpo def name typ set opt_morphs thy; |
|
159 fun after_qed [[th1, th2]] = ProofContext.theory (make_result th1 th2); |
|
160 in Proof.theorem_i NONE after_qed [[(goal1, []), (goal2, [])]] (ProofContext.init thy) end; |
|
161 |
|
162 in |
|
163 |
|
164 fun pcpodef_proof x = gen_pcpodef_proof Syntax.check_term true x; |
|
165 fun pcpodef_proof_cmd x = gen_pcpodef_proof Syntax.read_term true x; |
|
166 |
|
167 fun cpodef_proof x = gen_pcpodef_proof Syntax.check_term false x; |
|
168 fun cpodef_proof_cmd x = gen_pcpodef_proof Syntax.read_term false x; |
|
169 |
|
170 end; |
|
171 |
|
172 |
|
173 |
|
174 (** outer syntax **) |
|
175 |
|
176 local structure P = OuterParse and K = OuterKeyword in |
|
177 |
|
178 val typedef_proof_decl = |
|
179 Scan.optional (P.$$$ "(" |-- |
|
180 ((P.$$$ "open" >> K false) -- Scan.option P.binding || P.binding >> (fn s => (true, SOME s))) |
|
181 --| P.$$$ ")") (true, NONE) -- |
|
182 (P.type_args -- P.binding) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- |
|
183 Scan.option (P.$$$ "morphisms" |-- P.!!! (P.binding -- P.binding)); |
|
184 |
|
185 fun mk_pcpodef_proof pcpo ((((((def, opt_name), (vs, t)), mx), A), morphs)) = |
|
186 (if pcpo then pcpodef_proof_cmd else cpodef_proof_cmd) |
|
187 ((def, the_default (Binding.map_name (Syntax.type_name mx) t) opt_name), (t, vs, mx), A, morphs); |
|
188 |
|
189 val _ = |
|
190 OuterSyntax.command "pcpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal |
|
191 (typedef_proof_decl >> |
|
192 (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof true))); |
|
193 |
|
194 val _ = |
|
195 OuterSyntax.command "cpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal |
|
196 (typedef_proof_decl >> |
|
197 (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof false))); |
|
198 |
|
199 end; |
|
200 |
|
201 end; |