author | nipkow |
Fri, 27 Nov 1998 16:54:59 +0100 | |
changeset 5982 | aeb97860d352 |
child 6056 | b21813d1b701 |
permissions | -rw-r--r-- |
5982
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
1 |
(* Title: Provers/Arith/fast_lin_arith.ML |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
2 |
ID: $Id$ |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
3 |
Author: Tobias Nipkow |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
4 |
Copyright 1998 TU Munich |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
5 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
6 |
A generic linear arithmetic package. At the moment only used for nat. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
7 |
The two tactics provided: |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
8 |
lin_arith_tac: int -> tactic |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
9 |
cut_lin_arith_tac: thms -> int -> tactic |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
10 |
Only take premises and conclusions into account |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
11 |
that are already (negated) (in)equations. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
12 |
*) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
13 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
14 |
(*** Data needed for setting up the linear arithmetic package ***) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
15 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
16 |
signature LIN_ARITH_DATA = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
17 |
sig |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
18 |
val add_mono_thms: thm list |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
19 |
(* [| i rel1 j; m rel2 n |] ==> i + m rel3 j + n *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
20 |
val conjI: thm |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
21 |
val ccontr: thm (* (~ P ==> False) ==> P *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
22 |
val lessD: thm (* m < n ==> Suc m <= n *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
23 |
val nat_neqE: thm (* [| m ~= n; m < n ==> P; n < m ==> P |] ==> P *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
24 |
val notI: thm (* (P ==> False) ==> ~ P *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
25 |
val not_leD: thm (* ~(m <= n) ==> Suc n <= m *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
26 |
val not_lessD: thm (* ~(m < n) ==> n < m *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
27 |
val sym: thm (* x = y ==> y = x *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
28 |
val decomp: term -> |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
29 |
((term * int)list * int * string * (term * int)list * int)option |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
30 |
val simp: thm -> thm |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
31 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
32 |
(* |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
33 |
decomp(`x Rel y') should yield (p,i,Rel,q,j) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
34 |
where Rel is one of "<", "~<", "<=", "~<=" and "=" and |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
35 |
p/q is the decomposition of the sum terms x/y into a list |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
36 |
of summand * multiplicity pairs and a constant summand. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
37 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
38 |
simp must reduce contradictory <= to False. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
39 |
It should also cancel common summands to keep <= reduced; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
40 |
otherwise <= can grow to massive proportions. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
41 |
*) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
42 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
43 |
functor Fast_Lin_Arith(LA_Data:LIN_ARITH_DATA) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
44 |
struct |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
45 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
46 |
(*** A fast decision procedure ***) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
47 |
(*** Code ported from HOL Light ***) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
48 |
(* possible optimizations: eliminate eqns first; use (var,coeff) rep *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
49 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
50 |
datatype lineq_type = Eq | Le | Lt; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
51 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
52 |
datatype injust = Given of int |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
53 |
| Fwd of injust * thm |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
54 |
| Multiplied of int * injust |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
55 |
| Added of injust * injust; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
56 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
57 |
datatype lineq = Lineq of int * lineq_type * int list * injust; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
58 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
59 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
60 |
(* Calculate new (in)equality type after addition. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
61 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
62 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
63 |
fun find_add_type(Eq,x) = x |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
64 |
| find_add_type(x,Eq) = x |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
65 |
| find_add_type(_,Lt) = Lt |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
66 |
| find_add_type(Lt,_) = Lt |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
67 |
| find_add_type(Le,Le) = Le; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
68 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
69 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
70 |
(* Multiply out an (in)equation. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
71 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
72 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
73 |
fun multiply_ineq n (i as Lineq(k,ty,l,just)) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
74 |
if n = 1 then i |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
75 |
else if n = 0 andalso ty = Lt then sys_error "multiply_ineq" |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
76 |
else if n < 0 andalso (ty=Le orelse ty=Lt) then sys_error "multiply_ineq" |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
77 |
else Lineq(n * k,ty,map (apl(n,op * )) l,Multiplied(n,just)); |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
78 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
79 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
80 |
(* Add together (in)equations. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
81 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
82 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
83 |
fun add_ineq (i1 as Lineq(k1,ty1,l1,just1)) (i2 as Lineq(k2,ty2,l2,just2)) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
84 |
let val l = map2 (op +) (l1,l2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
85 |
in Lineq(k1+k2,find_add_type(ty1,ty2),l,Added(just1,just2)) end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
86 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
87 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
88 |
(* Elimination of variable between a single pair of (in)equations. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
89 |
(* If they're both inequalities, 1st coefficient must be +ve, 2nd -ve. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
90 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
91 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
92 |
fun gcd x y = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
93 |
let fun gxd x y = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
94 |
if y = 0 then x else gxd y (x mod y) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
95 |
in if x < y then gxd y x else gxd x y end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
96 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
97 |
fun lcm x y = (x * y) div gcd x y; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
98 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
99 |
fun el 0 (h::_) = h |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
100 |
| el n (_::t) = el (n - 1) t |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
101 |
| el _ _ = sys_error "el"; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
102 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
103 |
fun elim_var v (i1 as Lineq(k1,ty1,l1,just1)) (i2 as Lineq(k2,ty2,l2,just2)) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
104 |
let val c1 = el v l1 and c2 = el v l2 |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
105 |
val m = lcm (abs c1) (abs c2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
106 |
val m1 = m div (abs c1) and m2 = m div (abs c2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
107 |
val (n1,n2) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
108 |
if (c1 >= 0) = (c2 >= 0) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
109 |
then if ty1 = Eq then (~m1,m2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
110 |
else if ty2 = Eq then (m1,~m2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
111 |
else sys_error "elim_var" |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
112 |
else (m1,m2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
113 |
val (p1,p2) = if ty1=Eq andalso ty2=Eq andalso (n1 = ~1 orelse n2 = ~1) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
114 |
then (~n1,~n2) else (n1,n2) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
115 |
in add_ineq (multiply_ineq n1 i1) (multiply_ineq n2 i2) end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
116 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
117 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
118 |
(* The main refutation-finding code. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
119 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
120 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
121 |
fun is_trivial (Lineq(_,_,l,_)) = forall (fn i => i=0) l; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
122 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
123 |
fun is_answer (ans as Lineq(k,ty,l,_)) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
124 |
case ty of Eq => k <> 0 | Le => k > 0 | Lt => k >= 0; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
125 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
126 |
fun calc_blowup l = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
127 |
let val (p,n) = partition (apl(0,op<)) (filter (apl(0,op<>)) l) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
128 |
in (length p) * (length n) end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
129 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
130 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
131 |
(* Main elimination code: *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
132 |
(* *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
133 |
(* (1) Looks for immediate solutions (false assertions with no variables). *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
134 |
(* *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
135 |
(* (2) If there are any equations, picks a variable with the lowest absolute *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
136 |
(* coefficient in any of them, and uses it to eliminate. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
137 |
(* *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
138 |
(* (3) Otherwise, chooses a variable in the inequality to minimize the *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
139 |
(* blowup (number of consequences generated) and eliminates it. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
140 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
141 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
142 |
fun allpairs f xs ys = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
143 |
flat(map (fn x => map (fn y => f x y) ys) xs); |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
144 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
145 |
fun extract_first p = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
146 |
let fun extract xs (y::ys) = if p y then (Some y,xs@ys) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
147 |
else extract (y::xs) ys |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
148 |
| extract xs [] = (None,xs) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
149 |
in extract [] end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
150 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
151 |
fun elim ineqs = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
152 |
let val (triv,nontriv) = partition is_trivial ineqs in |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
153 |
if not(null triv) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
154 |
then case find_first is_answer triv of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
155 |
None => elim nontriv | some => some |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
156 |
else |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
157 |
if null nontriv then None else |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
158 |
let val (eqs,noneqs) = partition (fn (Lineq(_,ty,_,_)) => ty=Eq) nontriv in |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
159 |
if not(null eqs) then |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
160 |
let val clist = foldl (fn (cs,Lineq(_,_,l,_)) => l union cs) ([],eqs) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
161 |
val sclist = sort (fn (x,y) => int_ord(abs(x),abs(y))) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
162 |
(filter (fn i => i<>0) clist) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
163 |
val c = hd sclist |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
164 |
val (Some(eq as Lineq(_,_,ceq,_)),othereqs) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
165 |
extract_first (fn Lineq(_,_,l,_) => c mem l) eqs |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
166 |
val v = find_index (fn k => k=c) ceq |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
167 |
val (ioth,roth) = partition (fn (Lineq(_,_,l,_)) => el v l = 0) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
168 |
(othereqs @ noneqs) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
169 |
val others = map (elim_var v eq) roth @ ioth |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
170 |
in elim others end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
171 |
else |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
172 |
let val lists = map (fn (Lineq(_,_,l,_)) => l) noneqs |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
173 |
val numlist = 0 upto (length(hd lists) - 1) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
174 |
val coeffs = map (fn i => map (el i) lists) numlist |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
175 |
val blows = map calc_blowup coeffs |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
176 |
val iblows = blows ~~ numlist |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
177 |
val nziblows = filter (fn (i,_) => i<>0) iblows |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
178 |
in if null nziblows then None else |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
179 |
let val (c,v) = hd(sort (fn (x,y) => int_ord(fst(x),fst(y))) nziblows) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
180 |
val (no,yes) = partition (fn (Lineq(_,_,l,_)) => el v l = 0) ineqs |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
181 |
val (pos,neg) = partition(fn (Lineq(_,_,l,_)) => el v l > 0) yes |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
182 |
in elim (no @ allpairs (elim_var v) pos neg) end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
183 |
end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
184 |
end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
185 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
186 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
187 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
188 |
(* Translate back a proof. *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
189 |
(* ------------------------------------------------------------------------- *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
190 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
191 |
(* FIXME OPTIMIZE!!!! *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
192 |
fun mkproof asms just = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
193 |
let fun addthms thm1 thm2 = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
194 |
let val conj = thm1 RS (thm2 RS LA_Data.conjI) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
195 |
in the(get_first (fn th => Some(conj RS th) handle _ => None) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
196 |
LA_Data.add_mono_thms) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
197 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
198 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
199 |
fun multn(n,thm) = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
200 |
let fun mul(i,th) = if i=1 then th else mul(i-1, addthms thm th) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
201 |
in if n < 0 then mul(~n,thm) RS LA_Data.sym else mul(n,thm) end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
202 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
203 |
fun mk(Given i) = nth_elem(i,asms) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
204 |
| mk(Fwd(j,thm)) = mk j RS thm |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
205 |
| mk(Added(j1,j2)) = LA_Data.simp(addthms (mk j1) (mk j2)) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
206 |
| mk(Multiplied(n,j)) = multn(n,mk j) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
207 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
208 |
in LA_Data.simp(mk just) end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
209 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
210 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
211 |
fun coeff poly atom = case assoc(poly,atom) of None => 0 | Some i => i; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
212 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
213 |
fun mklineq atoms = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
214 |
let val n = length atoms in |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
215 |
fn ((lhs,i,rel,rhs,j),k) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
216 |
let val lhsa = map (coeff lhs) atoms |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
217 |
and rhsa = map (coeff rhs) atoms |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
218 |
val diff = map2 (op -) (rhsa,lhsa) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
219 |
val c = i-j |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
220 |
val just = Given k |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
221 |
in case rel of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
222 |
"<=" => Some(Lineq(c,Le,diff,just)) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
223 |
| "~<=" => Some(Lineq(1-c,Le,map (op ~) diff,Fwd(just,LA_Data.not_leD))) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
224 |
| "<" => Some(Lineq(c+1,Le,diff,Fwd(just,LA_Data.lessD))) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
225 |
| "~<" => Some(Lineq(~c,Le,map (op~) diff,Fwd(just,LA_Data.not_lessD))) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
226 |
| "=" => Some(Lineq(c,Eq,diff,just)) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
227 |
| "~=" => None |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
228 |
| _ => sys_error("mklineq" ^ rel) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
229 |
end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
230 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
231 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
232 |
fun abstract items = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
233 |
let val atoms = foldl (fn (ats,((lhs,_,_,rhs,_),_)) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
234 |
(map fst lhs) union ((map fst rhs) union ats)) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
235 |
([],items) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
236 |
in mapfilter (mklineq atoms) items end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
237 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
238 |
(* Ordinary refutation *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
239 |
fun refute1_tac items = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
240 |
let val lineqs = abstract items |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
241 |
in case elim lineqs of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
242 |
None => K no_tac |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
243 |
| Some(Lineq(_,_,_,j)) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
244 |
resolve_tac [LA_Data.notI,LA_Data.ccontr] THEN' |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
245 |
METAHYPS (fn asms => rtac (mkproof asms j) 1) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
246 |
end; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
247 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
248 |
(* Double refutation caused by equality in conclusion *) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
249 |
fun refute2_tac items (rhs,i,_,lhs,j) nHs = |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
250 |
(case elim (abstract(items@[((rhs,i,"<",lhs,j),nHs)])) of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
251 |
None => K no_tac |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
252 |
| Some(Lineq(_,_,_,j1)) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
253 |
(case elim (abstract(items@[((lhs,j,"<",rhs,i),nHs)])) of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
254 |
None => K no_tac |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
255 |
| Some(Lineq(_,_,_,j2)) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
256 |
rtac LA_Data.ccontr THEN' etac LA_Data.nat_neqE THEN' |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
257 |
METAHYPS (fn asms => rtac (mkproof asms j1) 1) THEN' |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
258 |
METAHYPS (fn asms => rtac (mkproof asms j2) 1) )); |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
259 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
260 |
(* |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
261 |
Fast but very incomplete decider. Only premises and conclusions |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
262 |
that are already (negated) (in)equations are taken into account. |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
263 |
*) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
264 |
val lin_arith_tac = SUBGOAL (fn (A,n) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
265 |
let val Hs = Logic.strip_assums_hyp A |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
266 |
val nHs = length Hs |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
267 |
val His = Hs ~~ (0 upto (nHs-1)) |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
268 |
val Hitems = mapfilter (fn (h,i) => case LA_Data.decomp h of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
269 |
None => None | Some(it) => Some(it,i)) His |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
270 |
in case LA_Data.decomp(Logic.strip_assums_concl A) of |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
271 |
None => if null Hitems then no_tac else refute1_tac Hitems n |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
272 |
| Some(citem as (r,i,rel,l,j)) => |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
273 |
if rel = "=" |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
274 |
then refute2_tac Hitems citem nHs n |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
275 |
else let val neg::rel0 = explode rel |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
276 |
val nrel = if neg = "~" then implode rel0 else "~"^rel |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
277 |
in refute1_tac (Hitems@[((r,i,nrel,l,j),nHs)]) n end |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
278 |
end); |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
279 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
280 |
fun cut_lin_arith_tac thms i = cut_facts_tac thms i THEN lin_arith_tac i; |
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
281 |
|
aeb97860d352
Replaced the puny nat_transitive.ML by the general fast_lin_arith.ML.
nipkow
parents:
diff
changeset
|
282 |
end; |