author | wenzelm |
Wed, 05 Jan 2000 11:35:18 +0100 | |
changeset 8086 | 78e254305ae6 |
parent 7898 | d7e65a52acf9 |
child 8129 | 29e239c7b8c2 |
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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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) |
|
7636 | 23 |
val strip_shyps_warning : thm -> thm |
1460 | 24 |
val forall_intr_list : cterm list -> thm -> thm |
25 |
val forall_intr_frees : thm -> thm |
|
26 |
val forall_intr_vars : thm -> thm |
|
27 |
val forall_elim_list : cterm list -> thm -> thm |
|
28 |
val forall_elim_var : int -> thm -> thm |
|
29 |
val forall_elim_vars : int -> thm -> thm |
|
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30 |
val freeze_thaw : thm -> thm * (thm -> thm) |
1460 | 31 |
val implies_elim_list : thm -> thm list -> thm |
32 |
val implies_intr_list : cterm list -> thm -> thm |
|
4285 | 33 |
val zero_var_indexes : thm -> thm |
34 |
val standard : thm -> thm |
|
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35 |
val rotate_prems : int -> thm -> thm |
4285 | 36 |
val assume_ax : theory -> string -> thm |
37 |
val RSN : thm * (int * thm) -> thm |
|
38 |
val RS : thm * thm -> thm |
|
39 |
val RLN : thm list * (int * thm list) -> thm list |
|
40 |
val RL : thm list * thm list -> thm list |
|
41 |
val MRS : thm list * thm -> thm |
|
1460 | 42 |
val MRL : thm list list * thm list -> thm list |
4285 | 43 |
val compose : thm * int * thm -> thm list |
44 |
val COMP : thm * thm -> thm |
|
0 | 45 |
val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm |
4285 | 46 |
val read_instantiate : (string*string)list -> thm -> thm |
47 |
val cterm_instantiate : (cterm*cterm)list -> thm -> thm |
|
48 |
val weak_eq_thm : thm * thm -> bool |
|
49 |
val eq_thm_sg : thm * thm -> bool |
|
50 |
val size_of_thm : thm -> int |
|
1460 | 51 |
val reflexive_thm : thm |
4285 | 52 |
val symmetric_thm : thm |
53 |
val transitive_thm : thm |
|
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54 |
val refl_implies : thm |
4679 | 55 |
val symmetric_fun : thm -> thm |
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56 |
val rewrite_rule_aux : (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm |
4713 | 57 |
val rewrite_thm : bool * bool * bool |
58 |
-> (meta_simpset -> thm -> thm option) |
|
59 |
-> meta_simpset -> thm -> thm |
|
5079 | 60 |
val rewrite_cterm : bool * bool * bool |
61 |
-> (meta_simpset -> thm -> thm option) |
|
62 |
-> meta_simpset -> cterm -> thm |
|
4285 | 63 |
val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm |
4713 | 64 |
val rewrite_goal_rule : bool* bool * bool |
65 |
-> (meta_simpset -> thm -> thm option) |
|
66 |
-> meta_simpset -> int -> thm -> thm |
|
4285 | 67 |
val equal_abs_elim : cterm -> thm -> thm |
68 |
val equal_abs_elim_list: cterm list -> thm -> thm |
|
69 |
val flexpair_abs_elim_list: cterm list -> thm -> thm |
|
70 |
val asm_rl : thm |
|
71 |
val cut_rl : thm |
|
72 |
val revcut_rl : thm |
|
73 |
val thin_rl : thm |
|
74 |
val triv_forall_equality: thm |
|
1756 | 75 |
val swap_prems_rl : thm |
4285 | 76 |
val equal_intr_rule : thm |
5903 | 77 |
val instantiate' : ctyp option list -> cterm option list -> thm -> thm |
6435 | 78 |
val incr_indexes : int -> thm -> thm |
79 |
val incr_indexes_wrt : int list -> ctyp list -> cterm list -> thm list -> thm -> thm |
|
5903 | 80 |
end; |
81 |
||
82 |
signature DRULE = |
|
83 |
sig |
|
84 |
include BASIC_DRULE |
|
6946 | 85 |
val compose_single : thm * int * thm -> thm |
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86 |
val triv_goal : thm |
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87 |
val rev_triv_goal : thm |
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88 |
val mk_triv_goal : cterm -> thm |
6995 | 89 |
val mk_cgoal : cterm -> cterm |
90 |
val assume_goal : cterm -> thm |
|
5903 | 91 |
val tvars_of_terms : term list -> (indexname * sort) list |
92 |
val vars_of_terms : term list -> (indexname * typ) list |
|
93 |
val tvars_of : thm -> (indexname * sort) list |
|
94 |
val vars_of : thm -> (indexname * typ) list |
|
5688 | 95 |
val unvarifyT : thm -> thm |
96 |
val unvarify : thm -> thm |
|
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97 |
val rule_attribute : ('a -> thm -> thm) -> 'a attribute |
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98 |
val tag : tag -> 'a attribute |
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99 |
val untag : tag -> 'a attribute |
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100 |
val tag_lemma : 'a attribute |
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101 |
val tag_assumption : 'a attribute |
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102 |
val tag_internal : 'a attribute |
3766 | 103 |
end; |
0 | 104 |
|
5903 | 105 |
structure Drule: DRULE = |
0 | 106 |
struct |
107 |
||
3991 | 108 |
|
708
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109 |
(** some cterm->cterm operations: much faster than calling cterm_of! **) |
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110 |
|
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111 |
(** SAME NAMES as in structure Logic: use compound identifiers! **) |
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112 |
|
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113 |
(*dest_implies for cterms. Note T=prop below*) |
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114 |
fun dest_implies ct = |
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115 |
case term_of ct of |
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116 |
(Const("==>", _) $ _ $ _) => |
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117 |
let val (ct1,ct2) = dest_comb ct |
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118 |
in (#2 (dest_comb ct1), ct2) end |
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119 |
| _ => raise TERM ("dest_implies", [term_of ct]) ; |
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120 |
|
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121 |
|
708
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122 |
(*Discard flexflex pairs; return a cterm*) |
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|
123 |
fun skip_flexpairs ct = |
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124 |
case term_of ct of |
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(Const("==>", _) $ (Const("=?=",_)$_$_) $ _) => |
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126 |
skip_flexpairs (#2 (dest_implies ct)) |
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| _ => ct; |
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128 |
|
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129 |
(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *) |
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130 |
fun strip_imp_prems ct = |
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131 |
let val (cA,cB) = dest_implies ct |
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132 |
in cA :: strip_imp_prems cB end |
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handle TERM _ => []; |
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134 |
|
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135 |
(* A1==>...An==>B goes to B, where B is not an implication *) |
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|
136 |
fun strip_imp_concl ct = |
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137 |
case term_of ct of (Const("==>", _) $ _ $ _) => |
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138 |
strip_imp_concl (#2 (dest_comb ct)) |
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139 |
| _ => ct; |
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140 |
|
708
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141 |
(*The premises of a theorem, as a cterm list*) |
2004
3411fe560611
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142 |
val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of; |
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143 |
|
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144 |
|
229
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Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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|
145 |
(** reading of instantiations **) |
4002c4cd450c
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146 |
|
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147 |
fun absent ixn = |
4002c4cd450c
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148 |
error("No such variable in term: " ^ Syntax.string_of_vname ixn); |
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149 |
|
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150 |
fun inst_failure ixn = |
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|
151 |
error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails"); |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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152 |
|
4281
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Added read_def_cterms for simultaneous reading/typing of terms under
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153 |
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts = |
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154 |
let val {tsig,...} = Sign.rep_sg sign |
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|
155 |
fun split([],tvs,vs) = (tvs,vs) |
4691 | 156 |
| split((sv,st)::l,tvs,vs) = (case Symbol.explode sv of |
157 |
"'"::cs => split(l,(Syntax.indexname cs,st)::tvs,vs) |
|
158 |
| cs => split(l,tvs,(Syntax.indexname cs,st)::vs)); |
|
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159 |
val (tvs,vs) = split(insts,[],[]); |
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160 |
fun readT((a,i),st) = |
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161 |
let val ixn = ("'" ^ a,i); |
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162 |
val S = case rsorts ixn of Some S => S | None => absent ixn; |
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163 |
val T = Sign.read_typ (sign,sorts) st; |
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164 |
in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T) |
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165 |
else inst_failure ixn |
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166 |
end |
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|
167 |
val tye = map readT tvs; |
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168 |
fun mkty(ixn,st) = (case rtypes ixn of |
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169 |
Some T => (ixn,(st,typ_subst_TVars tye T)) |
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| None => absent ixn); |
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171 |
val ixnsTs = map mkty vs; |
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172 |
val ixns = map fst ixnsTs |
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173 |
and sTs = map snd ixnsTs |
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174 |
val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs; |
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175 |
fun mkcVar(ixn,T) = |
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176 |
let val U = typ_subst_TVars tye2 T |
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177 |
in cterm_of sign (Var(ixn,U)) end |
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val ixnTs = ListPair.zip(ixns, map snd sTs) |
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179 |
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye), |
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180 |
ListPair.zip(map mkcVar ixnTs,cts)) |
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
diff
changeset
|
181 |
end; |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
182 |
|
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
183 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
184 |
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term |
0 | 185 |
Used for establishing default types (of variables) and sorts (of |
186 |
type variables) when reading another term. |
|
187 |
Index -1 indicates that a (T)Free rather than a (T)Var is wanted. |
|
188 |
***) |
|
189 |
||
190 |
fun types_sorts thm = |
|
191 |
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
|
192 |
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
|
193 |
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
|
194 |
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
|
195 |
val tvars = term_tvars big; |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
196 |
val tfrees = term_tfrees big; |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
197 |
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
|
198 |
fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); |
0 | 199 |
in (typ,sort) end; |
200 |
||
7636 | 201 |
|
0 | 202 |
(** Standardization of rules **) |
203 |
||
7636 | 204 |
(*Strip extraneous shyps as far as possible*) |
205 |
fun strip_shyps_warning thm = |
|
206 |
let |
|
207 |
val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm); |
|
208 |
val thm' = Thm.strip_shyps thm; |
|
209 |
val xshyps = Thm.extra_shyps thm'; |
|
210 |
in |
|
211 |
if null xshyps then () |
|
212 |
else warning ("Pending sort hypotheses: " ^ commas (map str_of_sort xshyps)); |
|
213 |
thm' |
|
214 |
end; |
|
215 |
||
0 | 216 |
(*Generalization over a list of variables, IGNORING bad ones*) |
217 |
fun forall_intr_list [] th = th |
|
218 |
| forall_intr_list (y::ys) th = |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
219 |
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
|
220 |
in forall_intr y gth handle THM _ => gth end; |
0 | 221 |
|
222 |
(*Generalization over all suitable Free variables*) |
|
223 |
fun forall_intr_frees th = |
|
224 |
let val {prop,sign,...} = rep_thm th |
|
225 |
in forall_intr_list |
|
4440 | 226 |
(map (cterm_of sign) (sort (make_ord atless) (term_frees prop))) |
0 | 227 |
th |
228 |
end; |
|
229 |
||
7898 | 230 |
val forall_elim_var = PureThy.forall_elim_var; |
231 |
val forall_elim_vars = PureThy.forall_elim_vars; |
|
0 | 232 |
|
233 |
(*Specialization over a list of cterms*) |
|
234 |
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th); |
|
235 |
||
236 |
(* maps [A1,...,An], B to [| A1;...;An |] ==> B *) |
|
237 |
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th); |
|
238 |
||
239 |
(* maps [| A1;...;An |] ==> B and [A1,...,An] to B *) |
|
240 |
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths); |
|
241 |
||
242 |
(*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
|
243 |
fun zero_var_indexes th = |
0 | 244 |
let val {prop,sign,...} = rep_thm th; |
245 |
val vars = term_vars prop |
|
246 |
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
|
247 |
val inrs = add_term_tvars(prop,[]); |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
248 |
val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); |
2266 | 249 |
val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs))) |
250 |
(inrs, nms') |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
251 |
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
|
252 |
fun varpairs([],[]) = [] |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
253 |
| 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
|
254 |
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
|
255 |
in (cterm_of sign (Var(v,T')), |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
256 |
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
|
257 |
end |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
258 |
| varpairs _ = raise TERM("varpairs", []); |
0 | 259 |
in instantiate (ctye, varpairs(vars,rev bs)) th end; |
260 |
||
261 |
||
262 |
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers; |
|
263 |
all generality expressed by Vars having index 0.*) |
|
264 |
fun standard th = |
|
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
265 |
let val {maxidx,...} = rep_thm th |
1237 | 266 |
in |
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
267 |
th |> implies_intr_hyps |
1412 | 268 |
|> forall_intr_frees |> forall_elim_vars (maxidx + 1) |
7636 | 269 |
|> strip_shyps_warning |
1412 | 270 |
|> zero_var_indexes |> Thm.varifyT |> Thm.compress |
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
271 |
end; |
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
272 |
|
0 | 273 |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
274 |
(*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
|
275 |
reversing that operation. DOES NOT WORK FOR TYPE VARIABLES. |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
276 |
Similar code in type/freeze_thaw*) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
277 |
fun freeze_thaw th = |
7248
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
278 |
let val fth = freezeT th |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
279 |
val {prop,sign,...} = rep_thm fth |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
280 |
in |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
281 |
case term_vars prop of |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
282 |
[] => (fth, fn x => x) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
283 |
| vars => |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
284 |
let fun newName (Var(ix,_), (pairs,used)) = |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
285 |
let val v = variant used (string_of_indexname ix) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
286 |
in ((ix,v)::pairs, v::used) end; |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
287 |
val (alist, _) = foldr newName |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
288 |
(vars, ([], add_term_names (prop, []))) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
289 |
fun mk_inst (Var(v,T)) = |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
290 |
(cterm_of sign (Var(v,T)), |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
291 |
cterm_of sign (Free(the (assoc(alist,v)), T))) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
292 |
val insts = map mk_inst vars |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
293 |
fun thaw th' = |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
294 |
th' |> forall_intr_list (map #2 insts) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
295 |
|> forall_elim_list (map #1 insts) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
296 |
in (instantiate ([],insts) fth, thaw) end |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
297 |
end; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
298 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
299 |
|
7248
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
300 |
(*Rotates a rule's premises to the left by k*) |
322151fe6f02
new primitive rule permute_prems to underlie defer_tac and rotate_prems
paulson
parents:
6995
diff
changeset
|
301 |
val rotate_prems = permute_prems 0; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
302 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
303 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
304 |
(*Assume a new formula, read following the same conventions as axioms. |
0 | 305 |
Generalizes over Free variables, |
306 |
creates the assumption, and then strips quantifiers. |
|
307 |
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
|
308 |
[ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ] *) |
0 | 309 |
fun assume_ax thy sP = |
6390 | 310 |
let val sign = Theory.sign_of thy |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
311 |
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
|
312 |
in forall_elim_vars 0 (assume (cterm_of sign prop)) end; |
0 | 313 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
314 |
(*Resolution: exactly one resolvent must be produced.*) |
0 | 315 |
fun tha RSN (i,thb) = |
4270 | 316 |
case Seq.chop (2, biresolution false [(false,tha)] i thb) of |
0 | 317 |
([th],_) => th |
318 |
| ([],_) => raise THM("RSN: no unifiers", i, [tha,thb]) |
|
319 |
| _ => raise THM("RSN: multiple unifiers", i, [tha,thb]); |
|
320 |
||
321 |
(*resolution: P==>Q, Q==>R gives P==>R. *) |
|
322 |
fun tha RS thb = tha RSN (1,thb); |
|
323 |
||
324 |
(*For joining lists of rules*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
325 |
fun thas RLN (i,thbs) = |
0 | 326 |
let val resolve = biresolution false (map (pair false) thas) i |
4270 | 327 |
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
|
328 |
in List.concat (map resb thbs) end; |
0 | 329 |
|
330 |
fun thas RL thbs = thas RLN (1,thbs); |
|
331 |
||
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
332 |
(*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
|
333 |
makes proof trees*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
334 |
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
|
335 |
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
|
336 |
| 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
|
337 |
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
|
338 |
|
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
339 |
(*As above, but for rule lists*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
340 |
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
|
341 |
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
|
342 |
| 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
|
343 |
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
|
344 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
345 |
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R |
0 | 346 |
with no lifting or renaming! Q may contain ==> or meta-quants |
347 |
ALWAYS deletes premise i *) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
348 |
fun compose(tha,i,thb) = |
4270 | 349 |
Seq.list_of (bicompose false (false,tha,0) i thb); |
0 | 350 |
|
6946 | 351 |
fun compose_single (tha,i,thb) = |
352 |
(case compose (tha,i,thb) of |
|
353 |
[th] => th |
|
354 |
| _ => raise THM ("compose: unique result expected", i, [tha,thb])); |
|
355 |
||
0 | 356 |
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*) |
357 |
fun tha COMP thb = |
|
358 |
case compose(tha,1,thb) of |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
359 |
[th] => th |
0 | 360 |
| _ => raise THM("COMP", 1, [tha,thb]); |
361 |
||
362 |
(*Instantiate theorem th, reading instantiations under signature sg*) |
|
363 |
fun read_instantiate_sg sg sinsts th = |
|
364 |
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
|
365 |
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
|
366 |
in instantiate (read_insts sg ts ts used sinsts) th end; |
0 | 367 |
|
368 |
(*Instantiate theorem th, reading instantiations under theory of th*) |
|
369 |
fun read_instantiate sinsts th = |
|
370 |
read_instantiate_sg (#sign (rep_thm th)) sinsts th; |
|
371 |
||
372 |
||
373 |
(*Left-to-right replacements: tpairs = [...,(vi,ti),...]. |
|
374 |
Instantiates distinct Vars by terms, inferring type instantiations. *) |
|
375 |
local |
|
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
376 |
fun add_types ((ct,cu), (sign,tye,maxidx)) = |
2152 | 377 |
let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct |
378 |
and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu; |
|
379 |
val maxi = Int.max(maxidx, Int.max(maxt, maxu)); |
|
0 | 380 |
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
|
381 |
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
|
382 |
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
|
383 |
in (sign', tye', maxi') end; |
0 | 384 |
in |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
385 |
fun cterm_instantiate ctpairs0 th = |
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
386 |
let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th),[],0)) |
0 | 387 |
val tsig = #tsig(Sign.rep_sg sign); |
388 |
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
|
389 |
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
|
390 |
fun ctyp2 (ix,T) = (ix, ctyp_of sign T) |
0 | 391 |
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
|
392 |
handle TERM _ => |
0 | 393 |
raise THM("cterm_instantiate: incompatible signatures",0,[th]) |
6930 | 394 |
| TYPE (msg, _, _) => raise THM(msg, 0, [th]) |
0 | 395 |
end; |
396 |
||
397 |
||
4016 | 398 |
(** theorem equality **) |
0 | 399 |
|
400 |
(*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
|
401 |
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); |
0 | 402 |
|
403 |
(*Useful "distance" function for BEST_FIRST*) |
|
404 |
val size_of_thm = size_of_term o #prop o rep_thm; |
|
405 |
||
406 |
||
1194
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
407 |
(** 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
|
408 |
(some) type variable renaming **) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
409 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
410 |
(* 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
|
411 |
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
|
412 |
in the term. *) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
413 |
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
|
414 |
| 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
|
415 |
| 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
|
416 |
| term_vars' _ = []; |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
417 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
418 |
fun forall_intr_vars th = |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
419 |
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
|
420 |
val vars = distinct (term_vars' prop); |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
421 |
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
|
422 |
|
1237 | 423 |
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
|
424 |
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
|
425 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
426 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
427 |
|
0 | 428 |
(*** Meta-Rewriting Rules ***) |
429 |
||
6390 | 430 |
val proto_sign = Theory.sign_of ProtoPure.thy; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
431 |
|
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
432 |
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
|
433 |
|
7404 | 434 |
fun store_thm name thm = hd (PureThy.smart_store_thms (name, [standard thm])); |
4016 | 435 |
|
0 | 436 |
val reflexive_thm = |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
437 |
let val cx = cterm_of proto_sign (Var(("x",0),TVar(("'a",0),logicS))) |
4016 | 438 |
in store_thm "reflexive" (Thm.reflexive cx) end; |
0 | 439 |
|
440 |
val symmetric_thm = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
441 |
let val xy = read_prop "x::'a::logic == y" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
442 |
in store_thm "symmetric" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
443 |
(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
444 |
end; |
0 | 445 |
|
446 |
val transitive_thm = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
447 |
let val xy = read_prop "x::'a::logic == y" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
448 |
val yz = read_prop "y::'a::logic == z" |
0 | 449 |
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
|
450 |
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
|
451 |
end; |
0 | 452 |
|
4679 | 453 |
fun symmetric_fun thm = thm RS symmetric_thm; |
454 |
||
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
455 |
(** 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
|
456 |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
457 |
val refl_implies = reflexive (cterm_of proto_sign implies); |
0 | 458 |
|
459 |
(*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
|
460 |
(*Do not rewrite flex-flex pairs*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
461 |
fun goals_conv pred cv = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
462 |
let fun gconv i ct = |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
463 |
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
|
464 |
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
|
465 |
Const("=?=",_)$_$_ => (reflexive A, i) |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
466 |
| _ => (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
|
467 |
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
|
468 |
handle TERM _ => reflexive ct |
0 | 469 |
in gconv 1 end; |
470 |
||
471 |
(*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
|
472 |
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th; |
0 | 473 |
|
474 |
(*rewriting conversion*) |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
475 |
fun rew_conv mode prover mss = rewrite_cterm mode mss prover; |
0 | 476 |
|
477 |
(*Rewrite a theorem*) |
|
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
478 |
fun rewrite_rule_aux _ [] th = th |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
479 |
| rewrite_rule_aux prover thms th = |
4713 | 480 |
fconv_rule (rew_conv (true,false,false) prover (Thm.mss_of thms)) th; |
0 | 481 |
|
3555 | 482 |
fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss); |
5079 | 483 |
fun rewrite_cterm mode prover mss = Thm.rewrite_cterm mode mss prover; |
3555 | 484 |
|
0 | 485 |
(*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
|
486 |
fun rewrite_goals_rule_aux _ [] th = th |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
487 |
| rewrite_goals_rule_aux prover thms th = |
4713 | 488 |
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
|
489 |
(Thm.mss_of thms))) th; |
0 | 490 |
|
491 |
(*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
|
492 |
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
|
493 |
if 0 < i andalso i <= nprems_of thm |
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
494 |
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
|
495 |
else raise THM("rewrite_goal_rule",i,[thm]); |
0 | 496 |
|
497 |
||
498 |
(** Derived rules mainly for METAHYPS **) |
|
499 |
||
500 |
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*) |
|
501 |
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
|
502 |
let val {sign=signa, t=a, ...} = rep_cterm ca |
0 | 503 |
and combth = combination eqth (reflexive ca) |
504 |
val {sign,prop,...} = rep_thm eqth |
|
505 |
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
|
506 |
val cterm = cterm_of (Sign.merge (sign,signa)) |
0 | 507 |
in transitive (symmetric (beta_conversion (cterm (abst$a)))) |
508 |
(transitive combth (beta_conversion (cterm (absu$a)))) |
|
509 |
end |
|
510 |
handle THM _ => raise THM("equal_abs_elim", 0, [eqth]); |
|
511 |
||
512 |
(*Calling equal_abs_elim with multiple terms*) |
|
513 |
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th); |
|
514 |
||
515 |
local |
|
516 |
val alpha = TVar(("'a",0), []) (* type ?'a::{} *) |
|
517 |
fun err th = raise THM("flexpair_inst: ", 0, [th]) |
|
518 |
fun flexpair_inst def th = |
|
519 |
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
|
520 |
val cterm = cterm_of sign |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
521 |
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
|
522 |
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
|
523 |
def |
0 | 524 |
in equal_elim def' th |
525 |
end |
|
7467 | 526 |
handle THM _ => err th | Bind => err th |
0 | 527 |
in |
3991 | 528 |
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def) |
529 |
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def |
|
0 | 530 |
end; |
531 |
||
532 |
(*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
|
533 |
fun flexpair_abs_elim_list cts = |
0 | 534 |
flexpair_intr o equal_abs_elim_list cts o flexpair_elim; |
535 |
||
536 |
||
537 |
(*** Some useful meta-theorems ***) |
|
538 |
||
539 |
(*The rule V/V, obtains assumption solving for eresolve_tac*) |
|
7380 | 540 |
val asm_rl = store_thm "asm_rl" (trivial(read_prop "PROP ?psi")); |
541 |
val _ = store_thm "_" asm_rl; |
|
0 | 542 |
|
543 |
(*Meta-level cut rule: [| V==>W; V |] ==> W *) |
|
4016 | 544 |
val cut_rl = |
545 |
store_thm "cut_rl" |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
546 |
(trivial(read_prop "PROP ?psi ==> PROP ?theta")); |
0 | 547 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
548 |
(*Generalized elim rule for one conclusion; cut_rl with reversed premises: |
0 | 549 |
[| PROP V; PROP V ==> PROP W |] ==> PROP W *) |
550 |
val revcut_rl = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
551 |
let val V = read_prop "PROP V" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
552 |
and VW = read_prop "PROP V ==> PROP W"; |
4016 | 553 |
in |
554 |
store_thm "revcut_rl" |
|
555 |
(implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V)))) |
|
0 | 556 |
end; |
557 |
||
668 | 558 |
(*for deleting an unwanted assumption*) |
559 |
val thin_rl = |
|
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 W = read_prop "PROP W"; |
4016 | 562 |
in store_thm "thin_rl" (implies_intr V (implies_intr W (assume W))) |
668 | 563 |
end; |
564 |
||
0 | 565 |
(* (!!x. PROP ?V) == PROP ?V Allows removal of redundant parameters*) |
566 |
val triv_forall_equality = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
567 |
let val V = read_prop "PROP V" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
568 |
and QV = read_prop "!!x::'a. PROP V" |
8086 | 569 |
and x = read_cterm proto_sign ("x", TypeInfer.logicT); |
4016 | 570 |
in |
571 |
store_thm "triv_forall_equality" |
|
572 |
(equal_intr (implies_intr QV (forall_elim x (assume QV))) |
|
573 |
(implies_intr V (forall_intr x (assume V)))) |
|
0 | 574 |
end; |
575 |
||
1756 | 576 |
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==> |
577 |
(PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi) |
|
578 |
`thm COMP swap_prems_rl' swaps the first two premises of `thm' |
|
579 |
*) |
|
580 |
val swap_prems_rl = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
581 |
let val cmajor = read_prop "PROP PhiA ==> PROP PhiB ==> PROP Psi"; |
1756 | 582 |
val major = assume cmajor; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
583 |
val cminor1 = read_prop "PROP PhiA"; |
1756 | 584 |
val minor1 = assume cminor1; |
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
585 |
val cminor2 = read_prop "PROP PhiB"; |
1756 | 586 |
val minor2 = assume cminor2; |
4016 | 587 |
in store_thm "swap_prems_rl" |
1756 | 588 |
(implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1 |
589 |
(implies_elim (implies_elim major minor1) minor2)))) |
|
590 |
end; |
|
591 |
||
3653 | 592 |
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |] |
593 |
==> PROP ?phi == PROP ?psi |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
594 |
Introduction rule for == as a meta-theorem. |
3653 | 595 |
*) |
596 |
val equal_intr_rule = |
|
4610
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
597 |
let val PQ = read_prop "PROP phi ==> PROP psi" |
b1322be47244
Tidying; rotate_prems; moved freeze_thaw from tactic.ML
paulson
parents:
4588
diff
changeset
|
598 |
and QP = read_prop "PROP psi ==> PROP phi" |
4016 | 599 |
in |
600 |
store_thm "equal_intr_rule" |
|
601 |
(implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP)))) |
|
3653 | 602 |
end; |
603 |
||
4285 | 604 |
|
4789 | 605 |
(* GOAL (PROP A) <==> PROP A *) |
606 |
||
607 |
local |
|
608 |
val A = read_prop "PROP A"; |
|
609 |
val G = read_prop "GOAL (PROP A)"; |
|
610 |
val (G_def, _) = freeze_thaw ProtoPure.Goal_def; |
|
611 |
in |
|
612 |
val triv_goal = store_thm "triv_goal" (Thm.equal_elim (Thm.symmetric G_def) (Thm.assume A)); |
|
613 |
val rev_triv_goal = store_thm "rev_triv_goal" (Thm.equal_elim G_def (Thm.assume G)); |
|
614 |
end; |
|
615 |
||
6995 | 616 |
val mk_cgoal = Thm.capply (Thm.cterm_of proto_sign (Const ("Goal", propT --> propT))); |
617 |
fun assume_goal ct = Thm.assume (mk_cgoal ct) RS rev_triv_goal; |
|
618 |
||
4789 | 619 |
|
4285 | 620 |
|
5688 | 621 |
(** variations on instantiate **) |
4285 | 622 |
|
623 |
(* collect vars *) |
|
624 |
||
625 |
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs); |
|
626 |
val add_tvars = foldl_types add_tvarsT; |
|
627 |
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs); |
|
628 |
||
5903 | 629 |
fun tvars_of_terms ts = rev (foldl add_tvars ([], ts)); |
630 |
fun vars_of_terms ts = rev (foldl add_vars ([], ts)); |
|
631 |
||
632 |
fun tvars_of thm = tvars_of_terms [#prop (Thm.rep_thm thm)]; |
|
633 |
fun vars_of thm = vars_of_terms [#prop (Thm.rep_thm thm)]; |
|
4285 | 634 |
|
635 |
||
636 |
(* instantiate by left-to-right occurrence of variables *) |
|
637 |
||
638 |
fun instantiate' cTs cts thm = |
|
639 |
let |
|
640 |
fun err msg = |
|
641 |
raise TYPE ("instantiate': " ^ msg, |
|
642 |
mapfilter (apsome Thm.typ_of) cTs, |
|
643 |
mapfilter (apsome Thm.term_of) cts); |
|
644 |
||
645 |
fun inst_of (v, ct) = |
|
646 |
(Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct) |
|
647 |
handle TYPE (msg, _, _) => err msg; |
|
648 |
||
649 |
fun zip_vars _ [] = [] |
|
650 |
| zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts |
|
651 |
| zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts |
|
652 |
| zip_vars [] _ = err "more instantiations than variables in thm"; |
|
653 |
||
654 |
(*instantiate types first!*) |
|
655 |
val thm' = |
|
656 |
if forall is_none cTs then thm |
|
657 |
else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm; |
|
658 |
in |
|
659 |
if forall is_none cts then thm' |
|
660 |
else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm' |
|
661 |
end; |
|
662 |
||
663 |
||
5688 | 664 |
(* unvarify(T) *) |
665 |
||
666 |
(*assume thm in standard form, i.e. no frees, 0 var indexes*) |
|
667 |
||
668 |
fun unvarifyT thm = |
|
669 |
let |
|
670 |
val cT = Thm.ctyp_of (Thm.sign_of_thm thm); |
|
671 |
val tfrees = map (fn ((x, _), S) => Some (cT (TFree (x, S)))) (tvars_of thm); |
|
672 |
in instantiate' tfrees [] thm end; |
|
673 |
||
674 |
fun unvarify raw_thm = |
|
675 |
let |
|
676 |
val thm = unvarifyT raw_thm; |
|
677 |
val ct = Thm.cterm_of (Thm.sign_of_thm thm); |
|
678 |
val frees = map (fn ((x, _), T) => Some (ct (Free (x, T)))) (vars_of thm); |
|
679 |
in instantiate' [] frees thm end; |
|
680 |
||
681 |
||
6435 | 682 |
(* increment var indexes *) |
683 |
||
684 |
fun incr_indexes 0 thm = thm |
|
685 |
| incr_indexes inc thm = |
|
686 |
let |
|
687 |
val sign = Thm.sign_of_thm thm; |
|
688 |
||
689 |
fun inc_tvar ((x, i), S) = Some (Thm.ctyp_of sign (TVar ((x, i + inc), S))); |
|
690 |
fun inc_var ((x, i), T) = Some (Thm.cterm_of sign (Var ((x, i + inc), T))); |
|
6930 | 691 |
val thm' = instantiate' (map inc_tvar (tvars_of thm)) [] thm; |
692 |
val thm'' = instantiate' [] (map inc_var (vars_of thm')) thm'; |
|
693 |
in thm'' end; |
|
6435 | 694 |
|
695 |
fun incr_indexes_wrt is cTs cts thms = |
|
696 |
let |
|
697 |
val maxidx = |
|
698 |
foldl Int.max (~1, is @ |
|
699 |
map (maxidx_of_typ o #T o Thm.rep_ctyp) cTs @ |
|
700 |
map (#maxidx o Thm.rep_cterm) cts @ |
|
701 |
map (#maxidx o Thm.rep_thm) thms); |
|
702 |
in incr_indexes (maxidx + 1) end; |
|
703 |
||
704 |
||
5688 | 705 |
(* mk_triv_goal *) |
706 |
||
707 |
(*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
|
708 |
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
|
709 |
|
5688 | 710 |
|
6086
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
711 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
712 |
(** basic attributes **) |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
713 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
714 |
(* dependent rules *) |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
715 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
716 |
fun rule_attribute f (x, thm) = (x, (f x thm)); |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
717 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
718 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
719 |
(* add / delete tags *) |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
720 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
721 |
fun map_tags f thm = |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
722 |
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
|
723 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
724 |
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
|
725 |
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
|
726 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
727 |
fun simple_tag name x = tag (name, []) x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
728 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
729 |
fun tag_lemma x = simple_tag "lemma" x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
730 |
fun tag_assumption x = simple_tag "assumption" x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
731 |
fun tag_internal x = simple_tag "internal" x; |
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
732 |
|
8cd4190e633a
added rule_attribute: ('a -> thm -> thm) -> 'a attribute;
wenzelm
parents:
5903
diff
changeset
|
733 |
|
0 | 734 |
end; |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
735 |
|
5903 | 736 |
|
737 |
structure BasicDrule: BASIC_DRULE = Drule; |
|
738 |
open BasicDrule; |