author | wenzelm |
Wed, 17 Mar 1999 16:33:00 +0100 | |
changeset 6390 | 5d58c100ca3f |
parent 6086 | 8cd4190e633a |
child 6435 | 154b88d2b62e |
permissions | -rw-r--r-- |
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1 |
(* Title: Pure/drule.ML |
0 | 2 |
ID: $Id$ |
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3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
0 | 4 |
Copyright 1993 University of Cambridge |
5 |
||
3766 | 6 |
Derived rules and other operations on theorems. |
0 | 7 |
*) |
8 |
||
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Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
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9 |
infix 0 RS RSN RL RLN MRS MRL COMP; |
0 | 10 |
|
5903 | 11 |
signature BASIC_DRULE = |
3766 | 12 |
sig |
4285 | 13 |
val dest_implies : cterm -> cterm * cterm |
14 |
val skip_flexpairs : cterm -> cterm |
|
15 |
val strip_imp_prems : cterm -> cterm list |
|
1460 | 16 |
val cprems_of : thm -> cterm list |
4285 | 17 |
val read_insts : |
18 |
Sign.sg -> (indexname -> typ option) * (indexname -> sort option) |
|
19 |
-> (indexname -> typ option) * (indexname -> sort option) |
|
20 |
-> string list -> (string*string)list |
|
21 |
-> (indexname*ctyp)list * (cterm*cterm)list |
|
22 |
val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option) |
|
1460 | 23 |
val forall_intr_list : cterm list -> thm -> thm |
24 |
val forall_intr_frees : thm -> thm |
|
25 |
val forall_intr_vars : thm -> thm |
|
26 |
val forall_elim_list : cterm list -> thm -> thm |
|
27 |
val forall_elim_var : int -> thm -> thm |
|
28 |
val forall_elim_vars : int -> thm -> thm |
|
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Tidying; rotate_prems; moved freeze_thaw from tactic.ML
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29 |
val freeze_thaw : thm -> thm * (thm -> thm) |
1460 | 30 |
val implies_elim_list : thm -> thm list -> thm |
31 |
val implies_intr_list : cterm list -> thm -> thm |
|
4285 | 32 |
val zero_var_indexes : thm -> thm |
33 |
val standard : thm -> thm |
|
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34 |
val rotate_prems : int -> thm -> thm |
4285 | 35 |
val assume_ax : theory -> string -> thm |
36 |
val RSN : thm * (int * thm) -> thm |
|
37 |
val RS : thm * thm -> thm |
|
38 |
val RLN : thm list * (int * thm list) -> thm list |
|
39 |
val RL : thm list * thm list -> thm list |
|
40 |
val MRS : thm list * thm -> thm |
|
1460 | 41 |
val MRL : thm list list * thm list -> thm list |
4285 | 42 |
val compose : thm * int * thm -> thm list |
43 |
val COMP : thm * thm -> thm |
|
0 | 44 |
val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm |
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val read_instantiate : (string*string)list -> thm -> thm |
46 |
val cterm_instantiate : (cterm*cterm)list -> thm -> thm |
|
47 |
val weak_eq_thm : thm * thm -> bool |
|
48 |
val eq_thm_sg : thm * thm -> bool |
|
49 |
val size_of_thm : thm -> int |
|
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val reflexive_thm : thm |
4285 | 51 |
val symmetric_thm : thm |
52 |
val transitive_thm : thm |
|
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val refl_implies : thm |
4679 | 54 |
val symmetric_fun : thm -> thm |
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55 |
val rewrite_rule_aux : (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm |
4713 | 56 |
val rewrite_thm : bool * bool * bool |
57 |
-> (meta_simpset -> thm -> thm option) |
|
58 |
-> meta_simpset -> thm -> thm |
|
5079 | 59 |
val rewrite_cterm : bool * bool * bool |
60 |
-> (meta_simpset -> thm -> thm option) |
|
61 |
-> meta_simpset -> cterm -> thm |
|
4285 | 62 |
val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm |
4713 | 63 |
val rewrite_goal_rule : bool* bool * bool |
64 |
-> (meta_simpset -> thm -> thm option) |
|
65 |
-> meta_simpset -> int -> thm -> thm |
|
4285 | 66 |
val equal_abs_elim : cterm -> thm -> thm |
67 |
val equal_abs_elim_list: cterm list -> thm -> thm |
|
68 |
val flexpair_abs_elim_list: cterm list -> thm -> thm |
|
69 |
val asm_rl : thm |
|
70 |
val cut_rl : thm |
|
71 |
val revcut_rl : thm |
|
72 |
val thin_rl : thm |
|
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val triv_forall_equality: thm |
|
1756 | 74 |
val swap_prems_rl : thm |
4285 | 75 |
val equal_intr_rule : thm |
5903 | 76 |
val instantiate' : ctyp option list -> cterm option list -> thm -> thm |
77 |
end; |
|
78 |
||
79 |
signature DRULE = |
|
80 |
sig |
|
81 |
include BASIC_DRULE |
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val triv_goal : thm |
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val rev_triv_goal : thm |
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84 |
val mk_triv_goal : cterm -> thm |
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val tvars_of_terms : term list -> (indexname * sort) list |
86 |
val vars_of_terms : term list -> (indexname * typ) list |
|
87 |
val tvars_of : thm -> (indexname * sort) list |
|
88 |
val vars_of : thm -> (indexname * typ) list |
|
5688 | 89 |
val unvarifyT : thm -> thm |
90 |
val unvarify : thm -> thm |
|
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91 |
val rule_attribute : ('a -> thm -> thm) -> 'a attribute |
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92 |
val tag : tag -> 'a attribute |
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val untag : tag -> 'a attribute |
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94 |
val tag_lemma : 'a attribute |
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95 |
val tag_assumption : 'a attribute |
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val tag_internal : 'a attribute |
3766 | 97 |
end; |
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|
5903 | 99 |
structure Drule: DRULE = |
0 | 100 |
struct |
101 |
||
3991 | 102 |
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(** some cterm->cterm operations: much faster than calling cterm_of! **) |
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104 |
|
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105 |
(** SAME NAMES as in structure Logic: use compound identifiers! **) |
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106 |
|
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moved dest_cimplies to drule.ML; added adjust_maxidx
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(*dest_implies for cterms. Note T=prop below*) |
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108 |
fun dest_implies ct = |
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case term_of ct of |
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110 |
(Const("==>", _) $ _ $ _) => |
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111 |
let val (ct1,ct2) = dest_comb ct |
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112 |
in (#2 (dest_comb ct1), ct2) end |
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| _ => raise TERM ("dest_implies", [term_of ct]) ; |
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114 |
|
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115 |
|
708
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116 |
(*Discard flexflex pairs; return a cterm*) |
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117 |
fun skip_flexpairs ct = |
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case term_of ct of |
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(Const("==>", _) $ (Const("=?=",_)$_$_) $ _) => |
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120 |
skip_flexpairs (#2 (dest_implies ct)) |
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| _ => ct; |
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122 |
|
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(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *) |
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fun strip_imp_prems ct = |
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let val (cA,cB) = dest_implies ct |
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126 |
in cA :: strip_imp_prems cB end |
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handle TERM _ => []; |
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128 |
|
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(* A1==>...An==>B goes to B, where B is not an implication *) |
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fun strip_imp_concl ct = |
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case term_of ct of (Const("==>", _) $ _ $ _) => |
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strip_imp_concl (#2 (dest_comb ct)) |
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133 |
| _ => ct; |
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134 |
|
708
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135 |
(*The premises of a theorem, as a cterm list*) |
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3411fe560611
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136 |
val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of; |
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|
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138 |
|
229
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139 |
(** reading of instantiations **) |
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140 |
|
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141 |
fun absent ixn = |
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142 |
error("No such variable in term: " ^ Syntax.string_of_vname ixn); |
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143 |
|
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144 |
fun inst_failure ixn = |
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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145 |
error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails"); |
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146 |
|
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147 |
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts = |
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148 |
let val {tsig,...} = Sign.rep_sg sign |
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149 |
fun split([],tvs,vs) = (tvs,vs) |
4691 | 150 |
| split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of |
151 |
"'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs) |
|
152 |
| cs => split(l,tvs,(Syntax.indexname cs,st)::vs)); |
|
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val (tvs,vs) = split(insts,[],[]); |
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154 |
fun readT((a,i),st) = |
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155 |
let val ixn = ("'" ^ a,i); |
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156 |
val S = case rsorts ixn of Some S => S | None => absent ixn; |
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157 |
val T = Sign.read_typ (sign,sorts) st; |
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158 |
in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T) |
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159 |
else inst_failure ixn |
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160 |
end |
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161 |
val tye = map readT tvs; |
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162 |
fun mkty(ixn,st) = (case rtypes ixn of |
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163 |
Some T => (ixn,(st,typ_subst_TVars tye T)) |
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164 |
| None => absent ixn); |
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165 |
val ixnsTs = map mkty vs; |
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166 |
val ixns = map fst ixnsTs |
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167 |
and sTs = map snd ixnsTs |
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168 |
val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs; |
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fun mkcVar(ixn,T) = |
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let val U = typ_subst_TVars tye2 T |
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171 |
in cterm_of sign (Var(ixn,U)) end |
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val ixnTs = ListPair.zip(ixns, map snd sTs) |
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in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye), |
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174 |
ListPair.zip(map mkcVar ixnTs,cts)) |
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175 |
end; |
229
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parents:
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176 |
|
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|
177 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
178 |
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term |
0 | 179 |
Used for establishing default types (of variables) and sorts (of |
180 |
type variables) when reading another term. |
|
181 |
Index -1 indicates that a (T)Free rather than a (T)Var is wanted. |
|
182 |
***) |
|
183 |
||
184 |
fun types_sorts thm = |
|
185 |
let val {prop,hyps,...} = rep_thm thm; |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
186 |
val big = list_comb(prop,hyps); (* bogus term! *) |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
187 |
val vars = map dest_Var (term_vars big); |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
188 |
val frees = map dest_Free (term_frees big); |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
189 |
val tvars = term_tvars big; |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
190 |
val tfrees = term_tfrees big; |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
191 |
fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i)); |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
192 |
fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); |
0 | 193 |
in (typ,sort) end; |
194 |
||
195 |
(** Standardization of rules **) |
|
196 |
||
197 |
(*Generalization over a list of variables, IGNORING bad ones*) |
|
198 |
fun forall_intr_list [] th = th |
|
199 |
| forall_intr_list (y::ys) th = |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
200 |
let val gth = forall_intr_list ys th |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
201 |
in forall_intr y gth handle THM _ => gth end; |
0 | 202 |
|
203 |
(*Generalization over all suitable Free variables*) |
|
204 |
fun forall_intr_frees th = |
|
205 |
let val {prop,sign,...} = rep_thm th |
|
206 |
in forall_intr_list |
|
4440 | 207 |
(map (cterm_of sign) (sort (make_ord atless) (term_frees prop))) |
0 | 208 |
th |
209 |
end; |
|
210 |
||
211 |
(*Replace outermost quantified variable by Var of given index. |
|
212 |
Could clash with Vars already present.*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
213 |
fun forall_elim_var i th = |
0 | 214 |
let val {prop,sign,...} = rep_thm th |
215 |
in case prop of |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
216 |
Const("all",_) $ Abs(a,T,_) => |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
217 |
forall_elim (cterm_of sign (Var((a,i), T))) th |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
218 |
| _ => raise THM("forall_elim_var", i, [th]) |
0 | 219 |
end; |
220 |
||
221 |
(*Repeat forall_elim_var until all outer quantifiers are removed*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
222 |
fun forall_elim_vars i th = |
0 | 223 |
forall_elim_vars i (forall_elim_var i th) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
224 |
handle THM _ => th; |
0 | 225 |
|
226 |
(*Specialization over a list of cterms*) |
|
227 |
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th); |
|
228 |
||
229 |
(* maps [A1,...,An], B to [| A1;...;An |] ==> B *) |
|
230 |
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th); |
|
231 |
||
232 |
(* maps [| A1;...;An |] ==> B and [A1,...,An] to B *) |
|
233 |
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths); |
|
234 |
||
235 |
(*Reset Var indexes to zero, renaming to preserve distinctness*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
236 |
fun zero_var_indexes th = |
0 | 237 |
let val {prop,sign,...} = rep_thm th; |
238 |
val vars = term_vars prop |
|
239 |
val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
240 |
val inrs = add_term_tvars(prop,[]); |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
241 |
val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); |
2266 | 242 |
val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs))) |
243 |
(inrs, nms') |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
244 |
val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye; |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
245 |
fun varpairs([],[]) = [] |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
246 |
| varpairs((var as Var(v,T)) :: vars, b::bs) = |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
247 |
let val T' = typ_subst_TVars tye T |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
248 |
in (cterm_of sign (Var(v,T')), |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
249 |
cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs) |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
250 |
end |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
251 |
| varpairs _ = raise TERM("varpairs", []); |
0 | 252 |
in instantiate (ctye, varpairs(vars,rev bs)) th end; |
253 |
||
254 |
||
255 |
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers; |
|
256 |
all generality expressed by Vars having index 0.*) |
|
257 |
fun standard th = |
|
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
258 |
let val {maxidx,...} = rep_thm th |
1237 | 259 |
in |
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
260 |
th |> implies_intr_hyps |
1412 | 261 |
|> forall_intr_frees |> forall_elim_vars (maxidx + 1) |
1439 | 262 |
|> Thm.strip_shyps |> Thm.implies_intr_shyps |
1412 | 263 |
|> zero_var_indexes |> Thm.varifyT |> Thm.compress |
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
264 |
end; |
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
265 |
|
0 | 266 |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
267 |
(*Convert all Vars in a theorem to Frees. Also return a function for |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
268 |
reversing that operation. DOES NOT WORK FOR TYPE VARIABLES. |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
269 |
Similar code in type/freeze_thaw*) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
270 |
fun freeze_thaw th = |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
271 |
let val fth = freezeT th |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
272 |
val {prop,sign,...} = rep_thm fth |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
273 |
val used = add_term_names (prop, []) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
274 |
and vars = term_vars prop |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
275 |
fun newName (Var(ix,_), (pairs,used)) = |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
276 |
let val v = variant used (string_of_indexname ix) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
277 |
in ((ix,v)::pairs, v::used) end; |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
278 |
val (alist, _) = foldr newName (vars, ([], used)) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
279 |
fun mk_inst (Var(v,T)) = |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
280 |
(cterm_of sign (Var(v,T)), |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
281 |
cterm_of sign (Free(the (assoc(alist,v)), T))) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
282 |
val insts = map mk_inst vars |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
283 |
fun thaw th' = |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
284 |
th' |> forall_intr_list (map #2 insts) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
285 |
|> forall_elim_list (map #1 insts) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
286 |
in (instantiate ([],insts) fth, thaw) end; |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
287 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
288 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
289 |
(*Rotates a rule's premises to the left by k. Does nothing if k=0 or |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
290 |
if k equals the number of premises. Useful, for instance, with etac. |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
291 |
Similar to tactic/defer_tac*) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
292 |
fun rotate_prems k rl = |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
293 |
let val (rl',thaw) = freeze_thaw rl |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
294 |
val hyps = strip_imp_prems (adjust_maxidx (cprop_of rl')) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
295 |
val hyps' = List.drop(hyps, k) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
296 |
in implies_elim_list rl' (map assume hyps) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
297 |
|> implies_intr_list (hyps' @ List.take(hyps, k)) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
298 |
|> thaw |> varifyT |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
299 |
end; |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
300 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
301 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
302 |
(*Assume a new formula, read following the same conventions as axioms. |
0 | 303 |
Generalizes over Free variables, |
304 |
creates the assumption, and then strips quantifiers. |
|
305 |
Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |] |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
306 |
[ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ] *) |
0 | 307 |
fun assume_ax thy sP = |
6390 | 308 |
let val sign = Theory.sign_of thy |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
309 |
val prop = Logic.close_form (term_of (read_cterm sign (sP, propT))) |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
310 |
in forall_elim_vars 0 (assume (cterm_of sign prop)) end; |
0 | 311 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
312 |
(*Resolution: exactly one resolvent must be produced.*) |
0 | 313 |
fun tha RSN (i,thb) = |
4270 | 314 |
case Seq.chop (2, biresolution false [(false,tha)] i thb) of |
0 | 315 |
([th],_) => th |
316 |
| ([],_) => raise THM("RSN: no unifiers", i, [tha,thb]) |
|
317 |
| _ => raise THM("RSN: multiple unifiers", i, [tha,thb]); |
|
318 |
||
319 |
(*resolution: P==>Q, Q==>R gives P==>R. *) |
|
320 |
fun tha RS thb = tha RSN (1,thb); |
|
321 |
||
322 |
(*For joining lists of rules*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
323 |
fun thas RLN (i,thbs) = |
0 | 324 |
let val resolve = biresolution false (map (pair false) thas) i |
4270 | 325 |
fun resb thb = Seq.list_of (resolve thb) handle THM _ => [] |
2672
85d7e800d754
Replaced "flat" by the Basis Library function List.concat
paulson
parents:
2266
diff
changeset
|
326 |
in List.concat (map resb thbs) end; |
0 | 327 |
|
328 |
fun thas RL thbs = thas RLN (1,thbs); |
|
329 |
||
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
330 |
(*Resolve a list of rules against bottom_rl from right to left; |
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
331 |
makes proof trees*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
332 |
fun rls MRS bottom_rl = |
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
333 |
let fun rs_aux i [] = bottom_rl |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
334 |
| rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls) |
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
335 |
in rs_aux 1 rls end; |
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
336 |
|
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
337 |
(*As above, but for rule lists*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
338 |
fun rlss MRL bottom_rls = |
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
339 |
let fun rs_aux i [] = bottom_rls |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
340 |
| rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss) |
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
341 |
in rs_aux 1 rlss end; |
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
342 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
343 |
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R |
0 | 344 |
with no lifting or renaming! Q may contain ==> or meta-quants |
345 |
ALWAYS deletes premise i *) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
346 |
fun compose(tha,i,thb) = |
4270 | 347 |
Seq.list_of (bicompose false (false,tha,0) i thb); |
0 | 348 |
|
349 |
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*) |
|
350 |
fun tha COMP thb = |
|
351 |
case compose(tha,1,thb) of |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
352 |
[th] => th |
0 | 353 |
| _ => raise THM("COMP", 1, [tha,thb]); |
354 |
||
355 |
(*Instantiate theorem th, reading instantiations under signature sg*) |
|
356 |
fun read_instantiate_sg sg sinsts th = |
|
357 |
let val ts = types_sorts th; |
|
952
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
358 |
val used = add_term_tvarnames(#prop(rep_thm th),[]); |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
359 |
in instantiate (read_insts sg ts ts used sinsts) th end; |
0 | 360 |
|
361 |
(*Instantiate theorem th, reading instantiations under theory of th*) |
|
362 |
fun read_instantiate sinsts th = |
|
363 |
read_instantiate_sg (#sign (rep_thm th)) sinsts th; |
|
364 |
||
365 |
||
366 |
(*Left-to-right replacements: tpairs = [...,(vi,ti),...]. |
|
367 |
Instantiates distinct Vars by terms, inferring type instantiations. *) |
|
368 |
local |
|
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
369 |
fun add_types ((ct,cu), (sign,tye,maxidx)) = |
2152 | 370 |
let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct |
371 |
and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu; |
|
372 |
val maxi = Int.max(maxidx, Int.max(maxt, maxu)); |
|
0 | 373 |
val sign' = Sign.merge(sign, Sign.merge(signt, signu)) |
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
374 |
val (tye',maxi') = Type.unify (#tsig(Sign.rep_sg sign')) maxi tye (T,U) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
375 |
handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u]) |
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
376 |
in (sign', tye', maxi') end; |
0 | 377 |
in |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
378 |
fun cterm_instantiate ctpairs0 th = |
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
379 |
let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th),[],0)) |
0 | 380 |
val tsig = #tsig(Sign.rep_sg sign); |
381 |
fun instT(ct,cu) = let val inst = subst_TVars tye |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
382 |
in (cterm_fun inst ct, cterm_fun inst cu) end |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
383 |
fun ctyp2 (ix,T) = (ix, ctyp_of sign T) |
0 | 384 |
in instantiate (map ctyp2 tye, map instT ctpairs0) th end |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
385 |
handle TERM _ => |
0 | 386 |
raise THM("cterm_instantiate: incompatible signatures",0,[th]) |
4057 | 387 |
| TYPE (msg, _, _) => raise THM("cterm_instantiate: " ^ msg, 0, [th]) |
0 | 388 |
end; |
389 |
||
390 |
||
4016 | 391 |
(** theorem equality **) |
0 | 392 |
|
393 |
(*Do the two theorems have the same signature?*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
394 |
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); |
0 | 395 |
|
396 |
(*Useful "distance" function for BEST_FIRST*) |
|
397 |
val size_of_thm = size_of_term o #prop o rep_thm; |
|
398 |
||
399 |
||
1194
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
400 |
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
401 |
(some) type variable renaming **) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
402 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
403 |
(* Can't use term_vars, because it sorts the resulting list of variable names. |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
404 |
We instead need the unique list noramlised by the order of appearance |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
405 |
in the term. *) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
406 |
fun term_vars' (t as Var(v,T)) = [t] |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
407 |
| term_vars' (Abs(_,_,b)) = term_vars' b |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
408 |
| term_vars' (f$a) = (term_vars' f) @ (term_vars' a) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
409 |
| term_vars' _ = []; |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
410 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
411 |
fun forall_intr_vars th = |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
412 |
let val {prop,sign,...} = rep_thm th; |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
413 |
val vars = distinct (term_vars' prop); |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
414 |
in forall_intr_list (map (cterm_of sign) vars) th end; |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
415 |
|
1237 | 416 |
fun weak_eq_thm (tha,thb) = |
1194
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
417 |
eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb)); |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
418 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
419 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
420 |
|
0 | 421 |
(*** Meta-Rewriting Rules ***) |
422 |
||
6390 | 423 |
val proto_sign = Theory.sign_of ProtoPure.thy; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
424 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
425 |
fun read_prop s = read_cterm proto_sign (s, propT); |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
426 |
|
4016 | 427 |
fun store_thm name thm = PureThy.smart_store_thm (name, standard thm); |
428 |
||
0 | 429 |
val reflexive_thm = |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
430 |
let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS))) |
4016 | 431 |
in store_thm "reflexive" (Thm.reflexive cx) end; |
0 | 432 |
|
433 |
val symmetric_thm = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
434 |
let val xy = read_prop "x::'a::logic == y" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
435 |
in store_thm "symmetric" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
436 |
(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
437 |
end; |
0 | 438 |
|
439 |
val transitive_thm = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
440 |
let val xy = read_prop "x::'a::logic == y" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
441 |
val yz = read_prop "y::'a::logic == z" |
0 | 442 |
val xythm = Thm.assume xy and yzthm = Thm.assume yz |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
443 |
in store_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
444 |
end; |
0 | 445 |
|
4679 | 446 |
fun symmetric_fun thm = thm RS symmetric_thm; |
447 |
||
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
448 |
(** Below, a "conversion" has type cterm -> thm **) |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
449 |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
450 |
val refl_implies = reflexive (cterm_of proto_sign implies); |
0 | 451 |
|
452 |
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*) |
|
214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
453 |
(*Do not rewrite flex-flex pairs*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
454 |
fun goals_conv pred cv = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
455 |
let fun gconv i ct = |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
456 |
let val (A,B) = dest_implies ct |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
457 |
val (thA,j) = case term_of A of |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
458 |
Const("=?=",_)$_$_ => (reflexive A, i) |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
459 |
| _ => (if pred i then cv A else reflexive A, i+1) |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
460 |
in combination (combination refl_implies thA) (gconv j B) end |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
461 |
handle TERM _ => reflexive ct |
0 | 462 |
in gconv 1 end; |
463 |
||
464 |
(*Use a conversion to transform a theorem*) |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
465 |
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th; |
0 | 466 |
|
467 |
(*rewriting conversion*) |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
468 |
fun rew_conv mode prover mss = rewrite_cterm mode mss prover; |
0 | 469 |
|
470 |
(*Rewrite a theorem*) |
|
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
471 |
fun rewrite_rule_aux _ [] th = th |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
472 |
| rewrite_rule_aux prover thms th = |
4713 | 473 |
fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th; |
0 | 474 |
|
3555 | 475 |
fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss); |
5079 | 476 |
fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover; |
3555 | 477 |
|
0 | 478 |
(*Rewrite the subgoals of a proof state (represented by a theorem) *) |
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
479 |
fun rewrite_goals_rule_aux _ [] th = th |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
480 |
| rewrite_goals_rule_aux prover thms th = |
4713 | 481 |
fconv_rule (goals_conv (K true) (rew_conv (true, true, false) prover |
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
482 |
(Thm.mss_of thms))) th; |
0 | 483 |
|
484 |
(*Rewrite the subgoal of a proof state (represented by a theorem) *) |
|
214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
485 |
fun rewrite_goal_rule mode prover mss i thm = |
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
486 |
if 0 < i andalso i <= nprems_of thm |
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
487 |
then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm |
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
488 |
else raise THM("rewrite_goal_rule",i,[thm]); |
0 | 489 |
|
490 |
||
491 |
(** Derived rules mainly for METAHYPS **) |
|
492 |
||
493 |
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*) |
|
494 |
fun equal_abs_elim ca eqth = |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
495 |
let val {sign=signa, t=a, ...} = rep_cterm ca |
0 | 496 |
and combth = combination eqth (reflexive ca) |
497 |
val {sign,prop,...} = rep_thm eqth |
|
498 |
val (abst,absu) = Logic.dest_equals prop |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
499 |
val cterm = cterm_of (Sign.merge (sign,signa)) |
0 | 500 |
in transitive (symmetric (beta_conversion (cterm (abst$a)))) |
501 |
(transitive combth (beta_conversion (cterm (absu$a)))) |
|
502 |
end |
|
503 |
handle THM _ => raise THM("equal_abs_elim", 0, [eqth]); |
|
504 |
||
505 |
(*Calling equal_abs_elim with multiple terms*) |
|
506 |
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th); |
|
507 |
||
508 |
local |
|
509 |
val alpha = TVar(("'a",0), []) (* type ?'a::{} *) |
|
510 |
fun err th = raise THM("flexpair_inst: ", 0, [th]) |
|
511 |
fun flexpair_inst def th = |
|
512 |
let val {prop = Const _ $ t $ u, sign,...} = rep_thm th |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
513 |
val cterm = cterm_of sign |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
514 |
fun cvar a = cterm(Var((a,0),alpha)) |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
515 |
val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)] |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
516 |
def |
0 | 517 |
in equal_elim def' th |
518 |
end |
|
519 |
handle THM _ => err th | bind => err th |
|
520 |
in |
|
3991 | 521 |
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def) |
522 |
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def |
|
0 | 523 |
end; |
524 |
||
525 |
(*Version for flexflex pairs -- this supports lifting.*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
526 |
fun flexpair_abs_elim_list cts = |
0 | 527 |
flexpair_intr o equal_abs_elim_list cts o flexpair_elim; |
528 |
||
529 |
||
530 |
(*** Some useful meta-theorems ***) |
|
531 |
||
532 |
(*The rule V/V, obtains assumption solving for eresolve_tac*) |
|
4016 | 533 |
val asm_rl = |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
534 |
store_thm "asm_rl" (trivial(read_prop "PROP ?psi")); |
0 | 535 |
|
536 |
(*Meta-level cut rule: [| V==>W; V |] ==> W *) |
|
4016 | 537 |
val cut_rl = |
538 |
store_thm "cut_rl" |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
539 |
(trivial(read_prop "PROP ?psi ==> PROP ?theta")); |
0 | 540 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
541 |
(*Generalized elim rule for one conclusion; cut_rl with reversed premises: |
0 | 542 |
[| PROP V; PROP V ==> PROP W |] ==> PROP W *) |
543 |
val revcut_rl = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
544 |
let val V = read_prop "PROP V" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
545 |
and VW = read_prop "PROP V ==> PROP W"; |
4016 | 546 |
in |
547 |
store_thm "revcut_rl" |
|
548 |
(implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V)))) |
|
0 | 549 |
end; |
550 |
||
668 | 551 |
(*for deleting an unwanted assumption*) |
552 |
val thin_rl = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
553 |
let val V = read_prop "PROP V" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
554 |
and W = read_prop "PROP W"; |
4016 | 555 |
in store_thm "thin_rl" (implies_intr V (implies_intr W (assume W))) |
668 | 556 |
end; |
557 |
||
0 | 558 |
(* (!!x. PROP ?V) == PROP ?V Allows removal of redundant parameters*) |
559 |
val triv_forall_equality = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
560 |
let val V = read_prop "PROP V" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
561 |
and QV = read_prop "!!x::'a. PROP V" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
562 |
and x = read_cterm proto_sign ("x", TFree("'a",logicS)); |
4016 | 563 |
in |
564 |
store_thm "triv_forall_equality" |
|
565 |
(equal_intr (implies_intr QV (forall_elim x (assume QV))) |
|
566 |
(implies_intr V (forall_intr x (assume V)))) |
|
0 | 567 |
end; |
568 |
||
1756 | 569 |
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==> |
570 |
(PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi) |
|
571 |
`thm COMP swap_prems_rl' swaps the first two premises of `thm' |
|
572 |
*) |
|
573 |
val swap_prems_rl = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
574 |
let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi"; |
1756 | 575 |
val major = assume cmajor; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
576 |
val cminor1 = read_prop "PROP PhiA"; |
1756 | 577 |
val minor1 = assume cminor1; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
578 |
val cminor2 = read_prop "PROP PhiB"; |
1756 | 579 |
val minor2 = assume cminor2; |
4016 | 580 |
in store_thm "swap_prems_rl" |
1756 | 581 |
(implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1 |
582 |
(implies_elim (implies_elim major minor1) minor2)))) |
|
583 |
end; |
|
584 |
||
3653 | 585 |
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |] |
586 |
==> PROP ?phi == PROP ?psi |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
587 |
Introduction rule for == as a meta-theorem. |
3653 | 588 |
*) |
589 |
val equal_intr_rule = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
590 |
let val PQ = read_prop "PROP phi ==> PROP psi" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
591 |
and QP = read_prop "PROP psi ==> PROP phi" |
4016 | 592 |
in |
593 |
store_thm "equal_intr_rule" |
|
594 |
(implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP)))) |
|
3653 | 595 |
end; |
596 |
||
4285 | 597 |
|
4789 | 598 |
(* GOAL (PROP A) <==> PROP A *) |
599 |
||
600 |
local |
|
601 |
val A = read_prop "PROP A"; |
|
602 |
val G = read_prop "GOAL (PROP A)"; |
|
603 |
val (G_def, _) = freeze_thaw ProtoPure.Goal_def; |
|
604 |
in |
|
605 |
val triv_goal = store_thm "triv_goal" (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A)); |
|
606 |
val rev_triv_goal = store_thm "rev_triv_goal" (Thm.equal_elim G_def (Thm.assume G)); |
|
607 |
end; |
|
608 |
||
609 |
||
4285 | 610 |
|
5688 | 611 |
(** variations on instantiate **) |
4285 | 612 |
|
613 |
(* collect vars *) |
|
614 |
||
615 |
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs); |
|
616 |
val add_tvars = foldl_types add_tvarsT; |
|
617 |
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs); |
|
618 |
||
5903 | 619 |
fun tvars_of_terms ts = rev (foldl add_tvars ([], ts)); |
620 |
fun vars_of_terms ts = rev (foldl add_vars ([], ts)); |
|
621 |
||
622 |
fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)]; |
|
623 |
fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)]; |
|
4285 | 624 |
|
625 |
||
626 |
(* instantiate by left-to-right occurrence of variables *) |
|
627 |
||
628 |
fun instantiate' cTs cts thm = |
|
629 |
let |
|
630 |
fun err msg = |
|
631 |
raise TYPE ("instantiate': " ^ msg, |
|
632 |
mapfilter (apsome Thm.typ_of) cTs, |
|
633 |
mapfilter (apsome Thm.term_of) cts); |
|
634 |
||
635 |
fun inst_of (v, ct) = |
|
636 |
(Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct) |
|
637 |
handle TYPE (msg, _, _) => err msg; |
|
638 |
||
639 |
fun zip_vars _ [] = [] |
|
640 |
| zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts |
|
641 |
| zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts |
|
642 |
| zip_vars [] _ = err "more instantiations than variables in thm"; |
|
643 |
||
644 |
(*instantiate types first!*) |
|
645 |
val thm' = |
|
646 |
if forall is_none cTs then thm |
|
647 |
else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm; |
|
648 |
in |
|
649 |
if forall is_none cts then thm' |
|
650 |
else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm' |
|
651 |
end; |
|
652 |
||
653 |
||
5688 | 654 |
(* unvarify(T) *) |
655 |
||
656 |
(*assume thm in standard form, i.e. no frees, 0 var indexes*) |
|
657 |
||
658 |
fun unvarifyT thm = |
|
659 |
let |
|
660 |
val cT = Thm.ctyp_of (Thm.sign_of_thm thm); |
|
661 |
val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm); |
|
662 |
in instantiate' tfrees [] thm end; |
|
663 |
||
664 |
fun unvarify raw_thm = |
|
665 |
let |
|
666 |
val thm = unvarifyT raw_thm; |
|
667 |
val ct = Thm.cterm_of (Thm.sign_of_thm thm); |
|
668 |
val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm); |
|
669 |
in instantiate' [] frees thm end; |
|
670 |
||
671 |
||
672 |
(* mk_triv_goal *) |
|
673 |
||
674 |
(*make an initial proof state, "PROP A ==> (PROP A)" *) |
|
5311
f3f71669878e
Rule mk_triv_goal for making instances of triv_goal
paulson
parents:
5079
diff
changeset
|
675 |
fun mk_triv_goal ct = instantiate' [] [Some ct] triv_goal; |
f3f71669878e
Rule mk_triv_goal for making instances of triv_goal
paulson
parents:
5079
diff
changeset
|
676 |
|
5688 | 677 |
|
6086
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
678 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
679 |
(** basic attributes **) |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
680 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
681 |
(* dependent rules *) |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
682 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
683 |
fun rule_attribute f (x, thm) = (x, (f x thm)); |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
684 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
685 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
686 |
(* add / delete tags *) |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
687 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
688 |
fun map_tags f thm = |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
689 |
Thm.put_name_tags (Thm.name_of_thm thm, f (#2 (Thm.get_name_tags thm))) thm; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
690 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
691 |
fun tag tg x = rule_attribute (K (map_tags (fn tgs => if tg mem tgs then tgs else tgs @ [tg]))) x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
692 |
fun untag tg x = rule_attribute (K (map_tags (fn tgs => tgs \ tg))) x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
693 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
694 |
fun simple_tag name x = tag (name, []) x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
695 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
696 |
fun tag_lemma x = simple_tag "lemma" x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
697 |
fun tag_assumption x = simple_tag "assumption" x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
698 |
fun tag_internal x = simple_tag "internal" x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
699 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
700 |
|
0 | 701 |
end; |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
702 |
|
5903 | 703 |
|
704 |
structure BasicDrule: BASIC_DRULE = Drule; |
|
705 |
open BasicDrule; |