author | paulson |
Sat, 10 Jan 1998 17:59:32 +0100 | |
changeset 4552 | bb8ff763c93d |
parent 4440 | 9ed4098074bc |
child 4588 | 42bf47c1de1f |
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 |
||
11
d0e17c42dbb4
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 |
|
11 |
signature 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 |
|
29 |
val implies_elim_list : thm -> thm list -> thm |
|
30 |
val implies_intr_list : cterm list -> thm -> thm |
|
4285 | 31 |
val zero_var_indexes : thm -> thm |
32 |
val standard : thm -> thm |
|
33 |
val assume_ax : theory -> string -> thm |
|
34 |
val RSN : thm * (int * thm) -> thm |
|
35 |
val RS : thm * thm -> thm |
|
36 |
val RLN : thm list * (int * thm list) -> thm list |
|
37 |
val RL : thm list * thm list -> thm list |
|
38 |
val MRS : thm list * thm -> thm |
|
1460 | 39 |
val MRL : thm list list * thm list -> thm list |
4285 | 40 |
val compose : thm * int * thm -> thm list |
41 |
val COMP : thm * thm -> thm |
|
0 | 42 |
val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm |
4285 | 43 |
val read_instantiate : (string*string)list -> thm -> thm |
44 |
val cterm_instantiate : (cterm*cterm)list -> thm -> thm |
|
45 |
val weak_eq_thm : thm * thm -> bool |
|
46 |
val eq_thm_sg : thm * thm -> bool |
|
47 |
val size_of_thm : thm -> int |
|
1460 | 48 |
val reflexive_thm : thm |
4285 | 49 |
val symmetric_thm : thm |
50 |
val transitive_thm : thm |
|
2004
3411fe560611
New operations on cterms. Now same names as in Logic
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diff
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51 |
val refl_implies : thm |
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
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parents:
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52 |
val rewrite_rule_aux : (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm |
3555 | 53 |
val rewrite_thm : bool * bool -> (meta_simpset -> thm -> thm option) |
54 |
-> meta_simpset -> thm -> thm |
|
4285 | 55 |
val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm |
56 |
val rewrite_goal_rule : bool * bool -> (meta_simpset -> thm -> thm option) |
|
57 |
-> meta_simpset -> int -> thm -> thm |
|
58 |
||
59 |
val equal_abs_elim : cterm -> thm -> thm |
|
60 |
val equal_abs_elim_list: cterm list -> thm -> thm |
|
61 |
val flexpair_abs_elim_list: cterm list -> thm -> thm |
|
62 |
val asm_rl : thm |
|
63 |
val cut_rl : thm |
|
64 |
val revcut_rl : thm |
|
65 |
val thin_rl : thm |
|
66 |
val triv_forall_equality: thm |
|
1756 | 67 |
val swap_prems_rl : thm |
4285 | 68 |
val equal_intr_rule : thm |
69 |
val instantiate': ctyp option list -> cterm option list -> thm -> thm |
|
3766 | 70 |
end; |
0 | 71 |
|
1499 | 72 |
structure Drule : DRULE = |
0 | 73 |
struct |
74 |
||
3991 | 75 |
|
708
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Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
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parents:
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76 |
(** some cterm->cterm operations: much faster than calling cterm_of! **) |
8422e50adce0
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lcp
parents:
668
diff
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|
77 |
|
2004
3411fe560611
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|
78 |
(** SAME NAMES as in structure Logic: use compound identifiers! **) |
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79 |
|
1703
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moved dest_cimplies to drule.ML; added adjust_maxidx
clasohm
parents:
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80 |
(*dest_implies for cterms. Note T=prop below*) |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
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|
81 |
fun dest_implies ct = |
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New operations on cterms. Now same names as in Logic
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parents:
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82 |
case term_of ct of |
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New operations on cterms. Now same names as in Logic
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|
83 |
(Const("==>", _) $ _ $ _) => |
3411fe560611
New operations on cterms. Now same names as in Logic
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changeset
|
84 |
let val (ct1,ct2) = dest_comb ct |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
85 |
in (#2 (dest_comb ct1), ct2) end |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
86 |
| _ => raise TERM ("dest_implies", [term_of ct]) ; |
1703
e22ad43bab5f
moved dest_cimplies to drule.ML; added adjust_maxidx
clasohm
parents:
1596
diff
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|
87 |
|
e22ad43bab5f
moved dest_cimplies to drule.ML; added adjust_maxidx
clasohm
parents:
1596
diff
changeset
|
88 |
|
708
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
89 |
(*Discard flexflex pairs; return a cterm*) |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
90 |
fun skip_flexpairs ct = |
708
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
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|
91 |
case term_of ct of |
1460 | 92 |
(Const("==>", _) $ (Const("=?=",_)$_$_) $ _) => |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
93 |
skip_flexpairs (#2 (dest_implies ct)) |
708
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
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|
94 |
| _ => ct; |
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
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|
95 |
|
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
96 |
(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *) |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
97 |
fun strip_imp_prems ct = |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
98 |
let val (cA,cB) = dest_implies ct |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
99 |
in cA :: strip_imp_prems cB end |
708
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
100 |
handle TERM _ => []; |
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
101 |
|
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
102 |
(* A1==>...An==>B goes to B, where B is not an implication *) |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
103 |
fun strip_imp_concl ct = |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
104 |
case term_of ct of (Const("==>", _) $ _ $ _) => |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
105 |
strip_imp_concl (#2 (dest_comb ct)) |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
106 |
| _ => ct; |
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
107 |
|
708
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
108 |
(*The premises of a theorem, as a cterm list*) |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
109 |
val cprems_of = strip_imp_prems o skip_flexpairs o cprop_of; |
708
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
110 |
|
8422e50adce0
Pure/drule/cprems_of, cskip_flexpairs, cstrip_imp_prems: new cterm operations
lcp
parents:
668
diff
changeset
|
111 |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
112 |
(** reading of instantiations **) |
4002c4cd450c
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diff
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|
113 |
|
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
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parents:
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|
114 |
fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
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|
115 |
| _ => error("Lexical error in variable name " ^ quote (implode cs)); |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
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diff
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|
116 |
|
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
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diff
changeset
|
117 |
fun absent ixn = |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
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diff
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|
118 |
error("No such variable in term: " ^ Syntax.string_of_vname ixn); |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
119 |
|
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
120 |
fun inst_failure ixn = |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
121 |
error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails"); |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
122 |
|
952
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
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|
123 |
(* this code is a bit of a mess. add_cterm could be simplified greatly if |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
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|
124 |
simultaneous instantiations were read or at least type checked |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
125 |
simultaneously rather than one after the other. This would make the tricky |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
126 |
composition of implicit type instantiations (parameter tye) superfluous. |
4281
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
diff
changeset
|
127 |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
128 |
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
129 |
let val {tsig,...} = Sign.rep_sg sign |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
130 |
fun split([],tvs,vs) = (tvs,vs) |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
131 |
| split((sv,st)::l,tvs,vs) = (case explode sv of |
4002c4cd450c
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lcp
parents:
214
diff
changeset
|
132 |
"'"::cs => split(l,(indexname cs,st)::tvs,vs) |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
133 |
| cs => split(l,tvs,(indexname cs,st)::vs)); |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
134 |
val (tvs,vs) = split(insts,[],[]); |
4002c4cd450c
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lcp
parents:
214
diff
changeset
|
135 |
fun readT((a,i),st) = |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
136 |
let val ixn = ("'" ^ a,i); |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
137 |
val S = case rsorts ixn of Some S => S | None => absent ixn; |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
138 |
val T = Sign.read_typ (sign,sorts) st; |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
139 |
in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T) |
4002c4cd450c
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lcp
parents:
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diff
changeset
|
140 |
else inst_failure ixn |
4002c4cd450c
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lcp
parents:
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diff
changeset
|
141 |
end |
4002c4cd450c
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lcp
parents:
214
diff
changeset
|
142 |
val tye = map readT tvs; |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
143 |
fun add_cterm ((cts,tye,used), (ixn,st)) = |
229
4002c4cd450c
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lcp
parents:
214
diff
changeset
|
144 |
let val T = case rtypes ixn of |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
145 |
Some T => typ_subst_TVars tye T |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
146 |
| None => absent ixn; |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
147 |
val (ct,tye2) = read_def_cterm(sign,types,sorts) used false (st,T); |
952
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
148 |
val cts' = (ixn,T,ct)::cts |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
149 |
fun inst(ixn,T,ct) = (ixn,typ_subst_TVars tye2 T,ct) |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
150 |
val used' = add_term_tvarnames(term_of ct,used); |
952
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
151 |
in (map inst cts',tye2 @ tye,used') end |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
922
diff
changeset
|
152 |
val (cterms,tye',_) = foldl add_cterm (([],tye,used), vs); |
952
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
153 |
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
nipkow
parents:
949
diff
changeset
|
154 |
map (fn (ixn,T,ct) => (cterm_of sign (Var(ixn,T)), ct)) cterms) |
9e10962866b0
Removed an old bug which made some simultaneous instantiations fail if they
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parents:
949
diff
changeset
|
155 |
end; |
4281
6c6073b13600
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nipkow
parents:
4270
diff
changeset
|
156 |
*) |
6c6073b13600
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parents:
4270
diff
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|
157 |
|
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
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changeset
|
158 |
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts = |
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
diff
changeset
|
159 |
let val {tsig,...} = Sign.rep_sg sign |
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
diff
changeset
|
160 |
fun split([],tvs,vs) = (tvs,vs) |
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
diff
changeset
|
161 |
| split((sv,st)::l,tvs,vs) = (case explode sv of |
6c6073b13600
Added read_def_cterms for simultaneous reading/typing of terms under
nipkow
parents:
4270
diff
changeset
|
162 |
"'"::cs => split(l,(indexname cs,st)::tvs,vs) |
6c6073b13600
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|
163 |
| cs => split(l,tvs,(indexname cs,st)::vs)); |
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|
164 |
val (tvs,vs) = split(insts,[],[]); |
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|
165 |
fun readT((a,i),st) = |
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|
166 |
let val ixn = ("'" ^ a,i); |
6c6073b13600
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|
167 |
val S = case rsorts ixn of Some S => S | None => absent ixn; |
6c6073b13600
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|
168 |
val T = Sign.read_typ (sign,sorts) st; |
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|
169 |
in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T) |
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|
170 |
else inst_failure ixn |
6c6073b13600
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|
171 |
end |
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|
172 |
val tye = map readT tvs; |
6c6073b13600
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|
173 |
fun mkty(ixn,st) = (case rtypes ixn of |
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|
174 |
Some T => (ixn,(st,typ_subst_TVars tye T)) |
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|
175 |
| None => absent ixn); |
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diff
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|
176 |
val ixnsTs = map mkty vs; |
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|
177 |
val ixns = map fst ixnsTs |
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|
178 |
and sTs = map snd ixnsTs |
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|
179 |
val (cts,tye2) = read_def_cterms(sign,types,sorts) used false sTs; |
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|
180 |
fun mkcVar(ixn,T) = |
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|
181 |
let val U = typ_subst_TVars tye2 T |
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|
182 |
in cterm_of sign (Var(ixn,U)) end |
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|
183 |
val ixnTs = ListPair.zip(ixns, map snd sTs) |
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|
184 |
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) (tye2 @ tye), |
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|
185 |
ListPair.zip(map mkcVar ixnTs,cts)) |
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|
186 |
end; |
229
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214
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|
187 |
|
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214
diff
changeset
|
188 |
|
252
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wenzelm
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|
189 |
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term |
0 | 190 |
Used for establishing default types (of variables) and sorts (of |
191 |
type variables) when reading another term. |
|
192 |
Index -1 indicates that a (T)Free rather than a (T)Var is wanted. |
|
193 |
***) |
|
194 |
||
195 |
fun types_sorts thm = |
|
196 |
let val {prop,hyps,...} = rep_thm thm; |
|
252
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|
197 |
val big = list_comb(prop,hyps); (* bogus term! *) |
7532f95d7f44
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wenzelm
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229
diff
changeset
|
198 |
val vars = map dest_Var (term_vars big); |
7532f95d7f44
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wenzelm
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diff
changeset
|
199 |
val frees = map dest_Free (term_frees big); |
7532f95d7f44
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wenzelm
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229
diff
changeset
|
200 |
val tvars = term_tvars big; |
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wenzelm
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229
diff
changeset
|
201 |
val tfrees = term_tfrees big; |
7532f95d7f44
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wenzelm
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diff
changeset
|
202 |
fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i)); |
7532f95d7f44
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diff
changeset
|
203 |
fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); |
0 | 204 |
in (typ,sort) end; |
205 |
||
206 |
(** Standardization of rules **) |
|
207 |
||
208 |
(*Generalization over a list of variables, IGNORING bad ones*) |
|
209 |
fun forall_intr_list [] th = th |
|
210 |
| forall_intr_list (y::ys) th = |
|
252
7532f95d7f44
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wenzelm
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229
diff
changeset
|
211 |
let val gth = forall_intr_list ys th |
7532f95d7f44
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wenzelm
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229
diff
changeset
|
212 |
in forall_intr y gth handle THM _ => gth end; |
0 | 213 |
|
214 |
(*Generalization over all suitable Free variables*) |
|
215 |
fun forall_intr_frees th = |
|
216 |
let val {prop,sign,...} = rep_thm th |
|
217 |
in forall_intr_list |
|
4440 | 218 |
(map (cterm_of sign) (sort (make_ord atless) (term_frees prop))) |
0 | 219 |
th |
220 |
end; |
|
221 |
||
222 |
(*Replace outermost quantified variable by Var of given index. |
|
223 |
Could clash with Vars already present.*) |
|
252
7532f95d7f44
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wenzelm
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229
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|
224 |
fun forall_elim_var i th = |
0 | 225 |
let val {prop,sign,...} = rep_thm th |
226 |
in case prop of |
|
252
7532f95d7f44
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wenzelm
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229
diff
changeset
|
227 |
Const("all",_) $ Abs(a,T,_) => |
7532f95d7f44
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wenzelm
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229
diff
changeset
|
228 |
forall_elim (cterm_of sign (Var((a,i), T))) th |
7532f95d7f44
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wenzelm
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229
diff
changeset
|
229 |
| _ => raise THM("forall_elim_var", i, [th]) |
0 | 230 |
end; |
231 |
||
232 |
(*Repeat forall_elim_var until all outer quantifiers are removed*) |
|
252
7532f95d7f44
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wenzelm
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changeset
|
233 |
fun forall_elim_vars i th = |
0 | 234 |
forall_elim_vars i (forall_elim_var i th) |
252
7532f95d7f44
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wenzelm
parents:
229
diff
changeset
|
235 |
handle THM _ => th; |
0 | 236 |
|
237 |
(*Specialization over a list of cterms*) |
|
238 |
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th); |
|
239 |
||
240 |
(* maps [A1,...,An], B to [| A1;...;An |] ==> B *) |
|
241 |
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th); |
|
242 |
||
243 |
(* maps [| A1;...;An |] ==> B and [A1,...,An] to B *) |
|
244 |
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths); |
|
245 |
||
246 |
(*Reset Var indexes to zero, renaming to preserve distinctness*) |
|
252
7532f95d7f44
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wenzelm
parents:
229
diff
changeset
|
247 |
fun zero_var_indexes th = |
0 | 248 |
let val {prop,sign,...} = rep_thm th; |
249 |
val vars = term_vars prop |
|
250 |
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
|
251 |
val inrs = add_term_tvars(prop,[]); |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
252 |
val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); |
2266 | 253 |
val tye = ListPair.map (fn ((v,rs),a) => (v, TVar((a,0),rs))) |
254 |
(inrs, nms') |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
255 |
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
|
256 |
fun varpairs([],[]) = [] |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
257 |
| 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
|
258 |
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
|
259 |
in (cterm_of sign (Var(v,T')), |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
260 |
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
|
261 |
end |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
262 |
| varpairs _ = raise TERM("varpairs", []); |
0 | 263 |
in instantiate (ctye, varpairs(vars,rev bs)) th end; |
264 |
||
265 |
||
266 |
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers; |
|
267 |
all generality expressed by Vars having index 0.*) |
|
268 |
fun standard th = |
|
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
269 |
let val {maxidx,...} = rep_thm th |
1237 | 270 |
in |
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
271 |
th |> implies_intr_hyps |
1412 | 272 |
|> forall_intr_frees |> forall_elim_vars (maxidx + 1) |
1439 | 273 |
|> Thm.strip_shyps |> Thm.implies_intr_shyps |
1412 | 274 |
|> zero_var_indexes |> Thm.varifyT |> Thm.compress |
1218
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
275 |
end; |
59ed8ef1a3a1
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm
parents:
1194
diff
changeset
|
276 |
|
0 | 277 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
278 |
(*Assume a new formula, read following the same conventions as axioms. |
0 | 279 |
Generalizes over Free variables, |
280 |
creates the assumption, and then strips quantifiers. |
|
281 |
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
|
282 |
[ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ] *) |
0 | 283 |
fun assume_ax thy sP = |
284 |
let val sign = sign_of thy |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
285 |
val prop = Logic.close_form (term_of (read_cterm sign |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
286 |
(sP, propT))) |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
287 |
in forall_elim_vars 0 (assume (cterm_of sign prop)) end; |
0 | 288 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
289 |
(*Resolution: exactly one resolvent must be produced.*) |
0 | 290 |
fun tha RSN (i,thb) = |
4270 | 291 |
case Seq.chop (2, biresolution false [(false,tha)] i thb) of |
0 | 292 |
([th],_) => th |
293 |
| ([],_) => raise THM("RSN: no unifiers", i, [tha,thb]) |
|
294 |
| _ => raise THM("RSN: multiple unifiers", i, [tha,thb]); |
|
295 |
||
296 |
(*resolution: P==>Q, Q==>R gives P==>R. *) |
|
297 |
fun tha RS thb = tha RSN (1,thb); |
|
298 |
||
299 |
(*For joining lists of rules*) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
300 |
fun thas RLN (i,thbs) = |
0 | 301 |
let val resolve = biresolution false (map (pair false) thas) i |
4270 | 302 |
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
|
303 |
in List.concat (map resb thbs) end; |
0 | 304 |
|
305 |
fun thas RL thbs = thas RLN (1,thbs); |
|
306 |
||
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
307 |
(*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
|
308 |
makes proof trees*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
309 |
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
|
310 |
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
|
311 |
| 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
|
312 |
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
|
313 |
|
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset
|
314 |
(*As above, but for rule lists*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
315 |
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
|
316 |
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
|
317 |
| 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
|
318 |
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
|
319 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
320 |
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R |
0 | 321 |
with no lifting or renaming! Q may contain ==> or meta-quants |
322 |
ALWAYS deletes premise i *) |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
323 |
fun compose(tha,i,thb) = |
4270 | 324 |
Seq.list_of (bicompose false (false,tha,0) i thb); |
0 | 325 |
|
326 |
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*) |
|
327 |
fun tha COMP thb = |
|
328 |
case compose(tha,1,thb) of |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
329 |
[th] => th |
0 | 330 |
| _ => raise THM("COMP", 1, [tha,thb]); |
331 |
||
332 |
(*Instantiate theorem th, reading instantiations under signature sg*) |
|
333 |
fun read_instantiate_sg sg sinsts th = |
|
334 |
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
|
335 |
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
|
336 |
in instantiate (read_insts sg ts ts used sinsts) th end; |
0 | 337 |
|
338 |
(*Instantiate theorem th, reading instantiations under theory of th*) |
|
339 |
fun read_instantiate sinsts th = |
|
340 |
read_instantiate_sg (#sign (rep_thm th)) sinsts th; |
|
341 |
||
342 |
||
343 |
(*Left-to-right replacements: tpairs = [...,(vi,ti),...]. |
|
344 |
Instantiates distinct Vars by terms, inferring type instantiations. *) |
|
345 |
local |
|
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
346 |
fun add_types ((ct,cu), (sign,tye,maxidx)) = |
2152 | 347 |
let val {sign=signt, t=t, T= T, maxidx=maxt,...} = rep_cterm ct |
348 |
and {sign=signu, t=u, T= U, maxidx=maxu,...} = rep_cterm cu; |
|
349 |
val maxi = Int.max(maxidx, Int.max(maxt, maxu)); |
|
0 | 350 |
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
|
351 |
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
|
352 |
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
|
353 |
in (sign', tye', maxi') end; |
0 | 354 |
in |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
355 |
fun cterm_instantiate ctpairs0 th = |
1435
aefcd255ed4a
Removed bug in type unification. Negative indexes are not used any longer.
nipkow
parents:
1412
diff
changeset
|
356 |
let val (sign,tye,_) = foldr add_types (ctpairs0, (#sign(rep_thm th),[],0)) |
0 | 357 |
val tsig = #tsig(Sign.rep_sg sign); |
358 |
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
|
359 |
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
|
360 |
fun ctyp2 (ix,T) = (ix, ctyp_of sign T) |
0 | 361 |
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
|
362 |
handle TERM _ => |
0 | 363 |
raise THM("cterm_instantiate: incompatible signatures",0,[th]) |
4057 | 364 |
| TYPE (msg, _, _) => raise THM("cterm_instantiate: " ^ msg, 0, [th]) |
0 | 365 |
end; |
366 |
||
367 |
||
4016 | 368 |
(** theorem equality **) |
0 | 369 |
|
370 |
(*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
|
371 |
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); |
0 | 372 |
|
373 |
(*Useful "distance" function for BEST_FIRST*) |
|
374 |
val size_of_thm = size_of_term o #prop o rep_thm; |
|
375 |
||
376 |
||
1194
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
377 |
(** 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
|
378 |
(some) type variable renaming **) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
379 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
380 |
(* 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
|
381 |
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
|
382 |
in the term. *) |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
383 |
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
|
384 |
| 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
|
385 |
| 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
|
386 |
| term_vars' _ = []; |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
387 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
388 |
fun forall_intr_vars th = |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
389 |
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
|
390 |
val vars = distinct (term_vars' prop); |
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
391 |
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
|
392 |
|
1237 | 393 |
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
|
394 |
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
|
395 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
396 |
|
563ecd14c1d8
Added weak_eq_thm and forall_intr_vars (thanks to Mark Staples)
lcp
parents:
952
diff
changeset
|
397 |
|
0 | 398 |
(*** Meta-Rewriting Rules ***) |
399 |
||
4016 | 400 |
fun store_thm name thm = PureThy.smart_store_thm (name, standard thm); |
401 |
||
0 | 402 |
val reflexive_thm = |
3991 | 403 |
let val cx = cterm_of (sign_of ProtoPure.thy) (Var(("x",0),TVar(("'a",0),logicS))) |
4016 | 404 |
in store_thm "reflexive" (Thm.reflexive cx) end; |
0 | 405 |
|
406 |
val symmetric_thm = |
|
3991 | 407 |
let val xy = read_cterm (sign_of ProtoPure.thy) ("x::'a::logic == y",propT) |
4016 | 408 |
in store_thm "symmetric" (Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end; |
0 | 409 |
|
410 |
val transitive_thm = |
|
3991 | 411 |
let val xy = read_cterm (sign_of ProtoPure.thy) ("x::'a::logic == y",propT) |
412 |
val yz = read_cterm (sign_of ProtoPure.thy) ("y::'a::logic == z",propT) |
|
0 | 413 |
val xythm = Thm.assume xy and yzthm = Thm.assume yz |
4016 | 414 |
in store_thm "transitive" (Thm.implies_intr yz (Thm.transitive xythm yzthm)) end; |
0 | 415 |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
416 |
(** 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
|
417 |
|
3991 | 418 |
val refl_implies = reflexive (cterm_of (sign_of ProtoPure.thy) implies); |
0 | 419 |
|
420 |
(*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
|
421 |
(*Do not rewrite flex-flex pairs*) |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
422 |
fun goals_conv pred cv = |
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
423 |
let fun gconv i ct = |
2004
3411fe560611
New operations on cterms. Now same names as in Logic
paulson
parents:
1906
diff
changeset
|
424 |
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
|
425 |
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
|
426 |
Const("=?=",_)$_$_ => (reflexive A, i) |
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
427 |
| _ => (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
|
428 |
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
|
429 |
handle TERM _ => reflexive ct |
0 | 430 |
in gconv 1 end; |
431 |
||
432 |
(*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
|
433 |
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th; |
0 | 434 |
|
435 |
(*rewriting conversion*) |
|
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset
|
436 |
fun rew_conv mode prover mss = rewrite_cterm mode mss prover; |
0 | 437 |
|
438 |
(*Rewrite a theorem*) |
|
3575
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
439 |
fun rewrite_rule_aux _ [] th = th |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
440 |
| rewrite_rule_aux prover thms th = |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
441 |
fconv_rule (rew_conv (true,false) prover (Thm.mss_of thms)) th; |
0 | 442 |
|
3555 | 443 |
fun rewrite_thm mode prover mss = fconv_rule (rew_conv mode prover mss); |
444 |
||
0 | 445 |
(*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
|
446 |
fun rewrite_goals_rule_aux _ [] th = th |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
447 |
| rewrite_goals_rule_aux prover thms th = |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
448 |
fconv_rule (goals_conv (K true) (rew_conv (true, true) prover |
4e9beacb5339
improved rewrite_thm / rewrite_goals to handle conditional eqns;
wenzelm
parents:
3555
diff
changeset
|
449 |
(Thm.mss_of thms))) th; |
0 | 450 |
|
451 |
(*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
|
452 |
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
|
453 |
if 0 < i andalso i <= nprems_of thm |
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset
|
454 |
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
|
455 |
else raise THM("rewrite_goal_rule",i,[thm]); |
0 | 456 |
|
457 |
||
458 |
(** Derived rules mainly for METAHYPS **) |
|
459 |
||
460 |
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*) |
|
461 |
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
|
462 |
let val {sign=signa, t=a, ...} = rep_cterm ca |
0 | 463 |
and combth = combination eqth (reflexive ca) |
464 |
val {sign,prop,...} = rep_thm eqth |
|
465 |
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
|
466 |
val cterm = cterm_of (Sign.merge (sign,signa)) |
0 | 467 |
in transitive (symmetric (beta_conversion (cterm (abst$a)))) |
468 |
(transitive combth (beta_conversion (cterm (absu$a)))) |
|
469 |
end |
|
470 |
handle THM _ => raise THM("equal_abs_elim", 0, [eqth]); |
|
471 |
||
472 |
(*Calling equal_abs_elim with multiple terms*) |
|
473 |
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th); |
|
474 |
||
475 |
local |
|
476 |
val alpha = TVar(("'a",0), []) (* type ?'a::{} *) |
|
477 |
fun err th = raise THM("flexpair_inst: ", 0, [th]) |
|
478 |
fun flexpair_inst def th = |
|
479 |
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
|
480 |
val cterm = cterm_of sign |
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
481 |
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
|
482 |
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
|
483 |
def |
0 | 484 |
in equal_elim def' th |
485 |
end |
|
486 |
handle THM _ => err th | bind => err th |
|
487 |
in |
|
3991 | 488 |
val flexpair_intr = flexpair_inst (symmetric ProtoPure.flexpair_def) |
489 |
and flexpair_elim = flexpair_inst ProtoPure.flexpair_def |
|
0 | 490 |
end; |
491 |
||
492 |
(*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
|
493 |
fun flexpair_abs_elim_list cts = |
0 | 494 |
flexpair_intr o equal_abs_elim_list cts o flexpair_elim; |
495 |
||
496 |
||
497 |
(*** Some useful meta-theorems ***) |
|
498 |
||
499 |
(*The rule V/V, obtains assumption solving for eresolve_tac*) |
|
4016 | 500 |
val asm_rl = |
501 |
store_thm "asm_rl" (trivial(read_cterm (sign_of ProtoPure.thy) ("PROP ?psi",propT))); |
|
0 | 502 |
|
503 |
(*Meta-level cut rule: [| V==>W; V |] ==> W *) |
|
4016 | 504 |
val cut_rl = |
505 |
store_thm "cut_rl" |
|
506 |
(trivial(read_cterm (sign_of ProtoPure.thy) ("PROP ?psi ==> PROP ?theta", propT))); |
|
0 | 507 |
|
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
508 |
(*Generalized elim rule for one conclusion; cut_rl with reversed premises: |
0 | 509 |
[| PROP V; PROP V ==> PROP W |] ==> PROP W *) |
510 |
val revcut_rl = |
|
3991 | 511 |
let val V = read_cterm (sign_of ProtoPure.thy) ("PROP V", propT) |
512 |
and VW = read_cterm (sign_of ProtoPure.thy) ("PROP V ==> PROP W", propT); |
|
4016 | 513 |
in |
514 |
store_thm "revcut_rl" |
|
515 |
(implies_intr V (implies_intr VW (implies_elim (assume VW) (assume V)))) |
|
0 | 516 |
end; |
517 |
||
668 | 518 |
(*for deleting an unwanted assumption*) |
519 |
val thin_rl = |
|
3991 | 520 |
let val V = read_cterm (sign_of ProtoPure.thy) ("PROP V", propT) |
521 |
and W = read_cterm (sign_of ProtoPure.thy) ("PROP W", propT); |
|
4016 | 522 |
in store_thm "thin_rl" (implies_intr V (implies_intr W (assume W))) |
668 | 523 |
end; |
524 |
||
0 | 525 |
(* (!!x. PROP ?V) == PROP ?V Allows removal of redundant parameters*) |
526 |
val triv_forall_equality = |
|
3991 | 527 |
let val V = read_cterm (sign_of ProtoPure.thy) ("PROP V", propT) |
528 |
and QV = read_cterm (sign_of ProtoPure.thy) ("!!x::'a. PROP V", propT) |
|
529 |
and x = read_cterm (sign_of ProtoPure.thy) ("x", TFree("'a",logicS)); |
|
4016 | 530 |
in |
531 |
store_thm "triv_forall_equality" |
|
532 |
(equal_intr (implies_intr QV (forall_elim x (assume QV))) |
|
533 |
(implies_intr V (forall_intr x (assume V)))) |
|
0 | 534 |
end; |
535 |
||
1756 | 536 |
(* (PROP ?PhiA ==> PROP ?PhiB ==> PROP ?Psi) ==> |
537 |
(PROP ?PhiB ==> PROP ?PhiA ==> PROP ?Psi) |
|
538 |
`thm COMP swap_prems_rl' swaps the first two premises of `thm' |
|
539 |
*) |
|
540 |
val swap_prems_rl = |
|
3991 | 541 |
let val cmajor = read_cterm (sign_of ProtoPure.thy) |
1756 | 542 |
("PROP PhiA ==> PROP PhiB ==> PROP Psi", propT); |
543 |
val major = assume cmajor; |
|
3991 | 544 |
val cminor1 = read_cterm (sign_of ProtoPure.thy) ("PROP PhiA", propT); |
1756 | 545 |
val minor1 = assume cminor1; |
3991 | 546 |
val cminor2 = read_cterm (sign_of ProtoPure.thy) ("PROP PhiB", propT); |
1756 | 547 |
val minor2 = assume cminor2; |
4016 | 548 |
in store_thm "swap_prems_rl" |
1756 | 549 |
(implies_intr cmajor (implies_intr cminor2 (implies_intr cminor1 |
550 |
(implies_elim (implies_elim major minor1) minor2)))) |
|
551 |
end; |
|
552 |
||
3653 | 553 |
(* [| PROP ?phi ==> PROP ?psi; PROP ?psi ==> PROP ?phi |] |
554 |
==> PROP ?phi == PROP ?psi |
|
555 |
Introduction rule for == using ==> not meta-hyps. |
|
556 |
*) |
|
557 |
val equal_intr_rule = |
|
3991 | 558 |
let val PQ = read_cterm (sign_of ProtoPure.thy) ("PROP phi ==> PROP psi", propT) |
559 |
and QP = read_cterm (sign_of ProtoPure.thy) ("PROP psi ==> PROP phi", propT) |
|
4016 | 560 |
in |
561 |
store_thm "equal_intr_rule" |
|
562 |
(implies_intr PQ (implies_intr QP (equal_intr (assume PQ) (assume QP)))) |
|
3653 | 563 |
end; |
564 |
||
4285 | 565 |
|
566 |
||
567 |
(** instantiate' rule **) |
|
568 |
||
569 |
(* collect vars *) |
|
570 |
||
571 |
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => v ins vs | (vs, _) => vs); |
|
572 |
val add_tvars = foldl_types add_tvarsT; |
|
573 |
val add_vars = foldl_aterms (fn (vs, Var v) => v ins vs | (vs, _) => vs); |
|
574 |
||
575 |
fun tvars_of thm = rev (add_tvars ([], #prop (Thm.rep_thm thm))); |
|
576 |
fun vars_of thm = rev (add_vars ([], #prop (Thm.rep_thm thm))); |
|
577 |
||
578 |
||
579 |
(* instantiate by left-to-right occurrence of variables *) |
|
580 |
||
581 |
fun instantiate' cTs cts thm = |
|
582 |
let |
|
583 |
fun err msg = |
|
584 |
raise TYPE ("instantiate': " ^ msg, |
|
585 |
mapfilter (apsome Thm.typ_of) cTs, |
|
586 |
mapfilter (apsome Thm.term_of) cts); |
|
587 |
||
588 |
fun inst_of (v, ct) = |
|
589 |
(Thm.cterm_of (#sign (Thm.rep_cterm ct)) (Var v), ct) |
|
590 |
handle TYPE (msg, _, _) => err msg; |
|
591 |
||
592 |
fun zip_vars _ [] = [] |
|
593 |
| zip_vars (_ :: vs) (None :: opt_ts) = zip_vars vs opt_ts |
|
594 |
| zip_vars (v :: vs) (Some t :: opt_ts) = (v, t) :: zip_vars vs opt_ts |
|
595 |
| zip_vars [] _ = err "more instantiations than variables in thm"; |
|
596 |
||
597 |
(*instantiate types first!*) |
|
598 |
val thm' = |
|
599 |
if forall is_none cTs then thm |
|
600 |
else Thm.instantiate (zip_vars (map fst (tvars_of thm)) cTs, []) thm; |
|
601 |
in |
|
602 |
if forall is_none cts then thm' |
|
603 |
else Thm.instantiate ([], map inst_of (zip_vars (vars_of thm') cts)) thm' |
|
604 |
end; |
|
605 |
||
606 |
||
0 | 607 |
end; |
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset
|
608 |
|
1499 | 609 |
open Drule; |