author | nipkow |
Tue, 21 Dec 2010 08:38:03 +0100 | |
changeset 41341 | e65a122057ad |
parent 38864 | 4abe644fcea5 |
child 41453 | c03593812297 |
permissions | -rw-r--r-- |
23489 | 1 |
(* Title: HOL/Tools/Qelim/qelim.ML |
23904 | 2 |
Author: Amine Chaieb, TU Muenchen |
23466 | 3 |
|
23904 | 4 |
Generic quantifier elimination conversions for HOL formulae. |
23466 | 5 |
*) |
6 |
||
7 |
signature QELIM = |
|
8 |
sig |
|
23904 | 9 |
val gen_qelim_conv: conv -> conv -> conv -> (cterm -> 'a -> 'a) -> 'a |
10 |
-> ('a -> conv) -> ('a -> conv) -> ('a -> conv) -> conv |
|
11 |
val standard_qelim_conv: (cterm list -> conv) -> (cterm list -> conv) |
|
12 |
-> (cterm list -> conv) -> conv |
|
23466 | 13 |
end; |
14 |
||
23489 | 15 |
structure Qelim: QELIM = |
23466 | 16 |
struct |
17 |
||
18 |
open Conv; |
|
19 |
||
23489 | 20 |
val all_not_ex = mk_meta_eq @{thm "all_not_ex"}; |
21 |
||
23524 | 22 |
fun gen_qelim_conv precv postcv simpex_conv ins env atcv ncv qcv = |
23489 | 23 |
let |
23466 | 24 |
fun conv env p = |
23489 | 25 |
case (term_of p) of |
23904 | 26 |
Const(s,T)$_$_ => |
27 |
if domain_type T = HOLogic.boolT |
|
38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38786
diff
changeset
|
28 |
andalso member (op =) [@{const_name HOL.conj}, @{const_name HOL.disj}, |
38864
4abe644fcea5
formerly unnamed infix equality now named HOL.eq
haftmann
parents:
38795
diff
changeset
|
29 |
@{const_name HOL.implies}, @{const_name HOL.eq}] s |
23904 | 30 |
then binop_conv (conv env) p |
31 |
else atcv env p |
|
32603 | 32 |
| Const(@{const_name Not},_)$_ => arg_conv (conv env) p |
33 |
| Const(@{const_name Ex},_)$Abs(s,_,_) => |
|
23489 | 34 |
let |
23466 | 35 |
val (e,p0) = Thm.dest_comb p |
36 |
val (x,p') = Thm.dest_abs (SOME s) p0 |
|
37 |
val env' = ins x env |
|
38 |
val th = Thm.abstract_rule s x ((conv env' then_conv ncv env') p') |
|
39 |
|> Drule.arg_cong_rule e |
|
40 |
val th' = simpex_conv (Thm.rhs_of th) |
|
41 |
val (l,r) = Thm.dest_equals (cprop_of th') |
|
23593 | 42 |
in if Thm.is_reflexive th' then Thm.transitive th (qcv env (Thm.rhs_of th)) |
23466 | 43 |
else Thm.transitive (Thm.transitive th th') (conv env r) end |
32603 | 44 |
| Const(@{const_name Ex},_)$ _ => (Thm.eta_long_conversion then_conv conv env) p |
45 |
| Const(@{const_name All},_)$_ => |
|
23489 | 46 |
let |
23466 | 47 |
val p = Thm.dest_arg p |
48 |
val ([(_,T)],[]) = Thm.match (@{cpat "All"}, Thm.dest_fun p) |
|
23489 | 49 |
val th = instantiate' [SOME T] [SOME p] all_not_ex |
36945 | 50 |
in Thm.transitive th (conv env (Thm.rhs_of th)) |
23466 | 51 |
end |
52 |
| _ => atcv env p |
|
53 |
in precv then_conv (conv env) then_conv postcv end |
|
23489 | 54 |
|
23904 | 55 |
(* Instantiation of some parameter for most common cases *) |
23489 | 56 |
|
23904 | 57 |
local |
35410 | 58 |
val pcv = |
59 |
Simplifier.rewrite |
|
60 |
(HOL_basic_ss addsimps (@{thms simp_thms} @ @{thms ex_simps} @ @{thms all_simps} @ |
|
61 |
[@{thm all_not_ex}, not_all, @{thm ex_disj_distrib}])); |
|
23466 | 62 |
|
23904 | 63 |
in fun standard_qelim_conv atcv ncv qcv p = |
64 |
gen_qelim_conv pcv pcv pcv cons (Thm.add_cterm_frees p []) atcv ncv qcv p |
|
65 |
end; |
|
23466 | 66 |
|
67 |
end; |