author | wenzelm |
Sat, 17 Sep 2005 18:11:25 +0200 | |
changeset 17465 | 93fc1211603f |
parent 16836 | 45a3dc4688bc |
child 18155 | e5ab63ca6b0f |
permissions | -rw-r--r-- |
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(* Title: HOL/Integ/presburger.ML |
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ID: $Id$ |
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Author: Amine Chaieb and Stefan Berghofer, TU Muenchen |
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Tactic for solving arithmetical Goals in Presburger Arithmetic. |
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This version of presburger deals with occurences of functional symbols |
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in the subgoal and abstract over them to try to prove the more general |
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formula. It then resolves with the subgoal. To enable this feature |
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call the procedure with the parameter abs. |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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*) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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signature PRESBURGER = |
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sig |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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val presburger_tac : bool -> bool -> int -> tactic |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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val presburger_method : bool -> bool -> int -> Proof.method |
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val setup : (theory -> theory) list |
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val trace : bool ref |
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end; |
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structure Presburger: PRESBURGER = |
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struct |
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val trace = ref false; |
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fun trace_msg s = if !trace then tracing s else (); |
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(*-----------------------------------------------------------------*) |
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(*cooper_pp: provefunction for the one-exstance quantifier elimination*) |
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(* Here still only one problem : The proof for the arithmetical transformations done on the dvd atomic formulae*) |
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(*-----------------------------------------------------------------*) |
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val presburger_ss = simpset_of (theory "Presburger"); |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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fun cooper_pp sg (fm as e$Abs(xn,xT,p)) = |
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let val (xn1,p1) = variant_abs (xn,xT,p) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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in (CooperProof.cooper_prv sg (Free (xn1, xT)) p1) end; |
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fun mnnf_pp sg fm = CooperProof.proof_of_cnnf sg fm |
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(CooperProof.proof_of_evalc sg); |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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fun tmproof_of_int_qelim sg fm = |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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Qelim.tproof_of_mlift_qelim sg CooperDec.is_arith_rel |
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(CooperProof.proof_of_linform sg) (mnnf_pp sg) (cooper_pp sg) fm; |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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(* Theorems to be used in this tactic*) |
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val zdvd_int = thm "zdvd_int"; |
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val zdiff_int_split = thm "zdiff_int_split"; |
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val all_nat = thm "all_nat"; |
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val ex_nat = thm "ex_nat"; |
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val number_of1 = thm "number_of1"; |
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val number_of2 = thm "number_of2"; |
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val split_zdiv = thm "split_zdiv"; |
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val split_zmod = thm "split_zmod"; |
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val mod_div_equality' = thm "mod_div_equality'"; |
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val split_div' = thm "split_div'"; |
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val Suc_plus1 = thm "Suc_plus1"; |
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val imp_le_cong = thm "imp_le_cong"; |
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val conj_le_cong = thm "conj_le_cong"; |
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(* extract all the constants in a term*) |
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fun add_term_typed_consts (Const (c, T), cs) = (c,T) ins cs |
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| add_term_typed_consts (t $ u, cs) = |
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add_term_typed_consts (t, add_term_typed_consts (u, cs)) |
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| add_term_typed_consts (Abs (_, _, t), cs) = add_term_typed_consts (t, cs) |
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| add_term_typed_consts (_, cs) = cs; |
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fun term_typed_consts t = add_term_typed_consts(t,[]); |
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(* Some Types*) |
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val bT = HOLogic.boolT; |
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val bitT = HOLogic.bitT; |
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val iT = HOLogic.intT; |
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val binT = HOLogic.binT; |
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val nT = HOLogic.natT; |
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(* Allowed Consts in formulae for presburger tactic*) |
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val allowed_consts = |
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[("All", (iT --> bT) --> bT), |
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("Ex", (iT --> bT) --> bT), |
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("All", (nT --> bT) --> bT), |
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("Ex", (nT --> bT) --> bT), |
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("op &", bT --> bT --> bT), |
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("op |", bT --> bT --> bT), |
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("op -->", bT --> bT --> bT), |
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("op =", bT --> bT --> bT), |
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("Not", bT --> bT), |
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("op <=", iT --> iT --> bT), |
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("op =", iT --> iT --> bT), |
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("op <", iT --> iT --> bT), |
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("Divides.op dvd", iT --> iT --> bT), |
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("Divides.op div", iT --> iT --> iT), |
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("Divides.op mod", iT --> iT --> iT), |
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("op +", iT --> iT --> iT), |
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("op -", iT --> iT --> iT), |
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("op *", iT --> iT --> iT), |
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("HOL.abs", iT --> iT), |
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("uminus", iT --> iT), |
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("HOL.max", iT --> iT --> iT), |
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("HOL.min", iT --> iT --> iT), |
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("op <=", nT --> nT --> bT), |
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("op =", nT --> nT --> bT), |
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("op <", nT --> nT --> bT), |
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("Divides.op dvd", nT --> nT --> bT), |
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("Divides.op div", nT --> nT --> nT), |
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("Divides.op mod", nT --> nT --> nT), |
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("op +", nT --> nT --> nT), |
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("op -", nT --> nT --> nT), |
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("op *", nT --> nT --> nT), |
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("Suc", nT --> nT), |
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("HOL.max", nT --> nT --> nT), |
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("HOL.min", nT --> nT --> nT), |
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("Numeral.bit.B0", bitT), |
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("Numeral.bit.B1", bitT), |
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("Numeral.Bit", binT --> bitT --> binT), |
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("Numeral.Pls", binT), |
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("Numeral.Min", binT), |
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("Numeral.number_of", binT --> iT), |
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("Numeral.number_of", binT --> nT), |
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("0", nT), |
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("0", iT), |
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("1", nT), |
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("1", iT), |
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("False", bT), |
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("True", bT)]; |
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(* Preparation of the formula to be sent to the Integer quantifier *) |
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(* elimination procedure *) |
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(* Transforms meta implications and meta quantifiers to object *) |
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(* implications and object quantifiers *) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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(*==================================*) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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(* Abstracting on subterms ========*) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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(*==================================*) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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(* Returns occurences of terms that are function application of type int or nat*) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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fun getfuncs fm = case strip_comb fm of |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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(Free (_, T), ts as _ :: _) => |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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if body_type T mem [iT, nT] |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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andalso not (ts = []) andalso forall (null o loose_bnos) ts |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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then [fm] |
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else Library.foldl op union ([], map getfuncs ts) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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| (Var (_, T), ts as _ :: _) => |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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if body_type T mem [iT, nT] |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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andalso not (ts = []) andalso forall (null o loose_bnos) ts then [fm] |
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else Library.foldl op union ([], map getfuncs ts) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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| (Const (s, T), ts) => |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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if (s, T) mem allowed_consts orelse not (body_type T mem [iT, nT]) |
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then Library.foldl op union ([], map getfuncs ts) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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else [fm] |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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| (Abs (s, T, t), _) => getfuncs t |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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| _ => []; |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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fun abstract_pres sg fm = |
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foldr (fn (t, u) => |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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let val T = fastype_of t |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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in all T $ Abs ("x", T, abstract_over (t, u)) end) |
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fm (getfuncs fm); |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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(* hasfuncs_on_bounds dont care of the type of the functions applied! |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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It returns true if there is a subterm coresponding to the application of |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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a function on a bounded variable. |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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Function applications are allowed only for well predefined functions a |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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consts*) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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fun has_free_funcs fm = case strip_comb fm of |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
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(Free (_, T), ts as _ :: _) => |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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if (body_type T mem [iT,nT]) andalso (not (T mem [iT,nT])) |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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then true |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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else exists (fn x => x) (map has_free_funcs ts) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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| (Var (_, T), ts as _ :: _) => |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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diff
changeset
|
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if (body_type T mem [iT,nT]) andalso not (T mem [iT,nT]) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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then true |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
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else exists (fn x => x) (map has_free_funcs ts) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
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| (Const (s, T), ts) => exists (fn x => x) (map has_free_funcs ts) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
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188 |
| (Abs (s, T, t), _) => has_free_funcs t |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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189 |
|_ => false; |
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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190 |
|
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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191 |
|
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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192 |
(*returns true if the formula is relevant for presburger arithmetic tactic |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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193 |
The constants occuring in term t should be a subset of the allowed_consts |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
194 |
There also should be no occurences of application of functions on bounded |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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|
195 |
variables. Whenever this function will be used, it will be ensured that t |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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196 |
will not contain subterms with function symbols that could have been |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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197 |
abstracted over.*) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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198 |
|
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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199 |
fun relevant ps t = (term_typed_consts t) subset allowed_consts andalso |
15570 | 200 |
map (fn i => snd (List.nth (ps, i))) (loose_bnos t) @ |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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201 |
map (snd o dest_Free) (term_frees t) @ map (snd o dest_Var) (term_vars t) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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202 |
subset [iT, nT] |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
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203 |
andalso not (has_free_funcs t); |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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|
204 |
|
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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|
205 |
|
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A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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206 |
fun prepare_for_presburger sg q fm = |
13876 | 207 |
let |
208 |
val ps = Logic.strip_params fm |
|
209 |
val hs = map HOLogic.dest_Trueprop (Logic.strip_assums_hyp fm) |
|
210 |
val c = HOLogic.dest_Trueprop (Logic.strip_assums_concl fm) |
|
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
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|
211 |
val _ = if relevant (rev ps) c then () |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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|
212 |
else (trace_msg ("Conclusion is not a presburger term:\n" ^ |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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|
213 |
Sign.string_of_term sg c); raise CooperDec.COOPER) |
13876 | 214 |
fun mk_all ((s, T), (P,n)) = |
215 |
if 0 mem loose_bnos P then |
|
216 |
(HOLogic.all_const T $ Abs (s, T, P), n) |
|
217 |
else (incr_boundvars ~1 P, n-1) |
|
218 |
fun mk_all2 (v, t) = HOLogic.all_const (fastype_of v) $ lambda v t; |
|
15570 | 219 |
val (rhs,irhs) = List.partition (relevant (rev ps)) hs |
13876 | 220 |
val np = length ps |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
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221 |
val (fm',np) = foldr (fn ((x, T), (fm,n)) => mk_all ((x, T), (fm,n))) |
b1d1b5bfc464
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222 |
(foldr HOLogic.mk_imp c rhs, np) ps |
15570 | 223 |
val (vs, _) = List.partition (fn t => q orelse (type_of t) = nT) |
13876 | 224 |
(term_frees fm' @ term_vars fm'); |
15574
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Removed practically all references to Library.foldr.
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225 |
val fm2 = foldr mk_all2 fm' vs |
13876 | 226 |
in (fm2, np + length vs, length rhs) end; |
227 |
||
228 |
(*Object quantifier to meta --*) |
|
229 |
fun spec_step n th = if (n=0) then th else (spec_step (n-1) th) RS spec ; |
|
230 |
||
231 |
(* object implication to meta---*) |
|
232 |
fun mp_step n th = if (n=0) then th else (mp_step (n-1) th) RS mp; |
|
233 |
||
234 |
(* the presburger tactic*) |
|
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
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changeset
|
235 |
|
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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|
236 |
(* Parameters : q = flag for quantify ofer free variables ; |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
237 |
a = flag for abstracting over function occurences |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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|
238 |
i = subgoal *) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
239 |
|
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
240 |
fun presburger_tac q a i = ObjectLogic.atomize_tac i THEN (fn st => |
13876 | 241 |
let |
17465 | 242 |
val g = List.nth (prems_of st, i - 1) |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
243 |
val sg = sign_of_thm st |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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|
244 |
(* The Abstraction step *) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
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parents:
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245 |
val g' = if a then abstract_pres sg g else g |
13876 | 246 |
(* Transform the term*) |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
247 |
val (t,np,nh) = prepare_for_presburger sg q g' |
15661
9ef583b08647
reverted renaming of Some/None in comments and strings;
wenzelm
parents:
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diff
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|
248 |
(* Some simpsets for dealing with mod div abs and nat*) |
13876 | 249 |
val simpset0 = HOL_basic_ss |
250 |
addsimps [mod_div_equality', Suc_plus1] |
|
13997 | 251 |
addsplits [split_zdiv, split_zmod, split_div', split_min, split_max] |
13876 | 252 |
(* Simp rules for changing (n::int) to int n *) |
253 |
val simpset1 = HOL_basic_ss |
|
254 |
addsimps [nat_number_of_def, zdvd_int] @ map (fn r => r RS sym) |
|
255 |
[int_int_eq, zle_int, zless_int, zadd_int, zmult_int] |
|
256 |
addsplits [zdiff_int_split] |
|
257 |
(*simp rules for elimination of int n*) |
|
258 |
||
259 |
val simpset2 = HOL_basic_ss |
|
260 |
addsimps [nat_0_le, all_nat, ex_nat, number_of1, number_of2, int_0, int_1] |
|
261 |
addcongs [conj_le_cong, imp_le_cong] |
|
262 |
(* simp rules for elimination of abs *) |
|
14353
79f9fbef9106
Added lemmas to Ring_and_Field with slightly modified simplification rules
paulson
parents:
14130
diff
changeset
|
263 |
val simpset3 = HOL_basic_ss addsplits [abs_split] |
13876 | 264 |
val ct = cterm_of sg (HOLogic.mk_Trueprop t) |
265 |
(* Theorem for the nat --> int transformation *) |
|
266 |
val pre_thm = Seq.hd (EVERY |
|
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
267 |
[simp_tac simpset0 1, |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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changeset
|
268 |
TRY (simp_tac simpset1 1), TRY (simp_tac simpset2 1), |
14801
2d27b5ebc447
- deleted unneeded function eta_long (now in Pure/pattern.ML
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parents:
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diff
changeset
|
269 |
TRY (simp_tac simpset3 1), TRY (simp_tac presburger_ss 1)] |
13876 | 270 |
(trivial ct)) |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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diff
changeset
|
271 |
fun assm_tac i = REPEAT_DETERM_N nh (assume_tac i) |
13876 | 272 |
(* The result of the quantifier elimination *) |
273 |
val (th, tac) = case (prop_of pre_thm) of |
|
274 |
Const ("==>", _) $ (Const ("Trueprop", _) $ t1) $ _ => |
|
14920
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
275 |
let val pth = |
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
276 |
(* If quick_and_dirty then run without proof generation as oracle*) |
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
277 |
if !quick_and_dirty |
16836 | 278 |
then presburger_oracle sg (Pattern.eta_long [] t1) |
14941 | 279 |
(* |
280 |
assume (cterm_of sg |
|
14920
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
281 |
(HOLogic.mk_Trueprop(HOLogic.mk_eq(t1,CooperDec.integer_qelim (Pattern.eta_long [] t1))))) |
14941 | 282 |
*) |
14920
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
283 |
else tmproof_of_int_qelim sg (Pattern.eta_long [] t1) |
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
284 |
in |
13876 | 285 |
(trace_msg ("calling procedure with term:\n" ^ |
286 |
Sign.string_of_term sg t1); |
|
14920
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
287 |
((pth RS iffD2) RS pre_thm, |
13876 | 288 |
assm_tac (i + 1) THEN (if q then I else TRY) (rtac TrueI i))) |
14920
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
289 |
end |
13876 | 290 |
| _ => (pre_thm, assm_tac i) |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
291 |
in (rtac (((mp_step nh) o (spec_step np)) th) i |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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diff
changeset
|
292 |
THEN tac) st |
14130 | 293 |
end handle Subscript => no_tac st | CooperDec.COOPER => no_tac st); |
13876 | 294 |
|
295 |
fun presburger_args meth = |
|
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
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diff
changeset
|
296 |
let val parse_flag = |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
297 |
Args.$$$ "no_quantify" >> K (apfst (K false)) |
14811
9144ec118703
abstraction over functions is no default any more.
chaieb
parents:
14801
diff
changeset
|
298 |
|| Args.$$$ "abs" >> K (apsnd (K true)); |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
299 |
in |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
300 |
Method.simple_args |
14882 | 301 |
(Scan.optional (Args.$$$ "(" |-- Scan.repeat1 parse_flag --| Args.$$$ ")") [] >> |
15570 | 302 |
curry (Library.foldl op |>) (true, false)) |
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
303 |
(fn (q,a) => fn _ => meth q a 1) |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
304 |
end; |
13876 | 305 |
|
14758
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
306 |
fun presburger_method q a i = Method.METHOD (fn facts => |
af3b71a46a1c
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller.
chaieb
parents:
14353
diff
changeset
|
307 |
Method.insert_tac facts 1 THEN presburger_tac q a i) |
13876 | 308 |
|
309 |
val setup = |
|
310 |
[Method.add_method ("presburger", |
|
311 |
presburger_args presburger_method, |
|
312 |
"decision procedure for Presburger arithmetic"), |
|
313 |
ArithTheoryData.map (fn {splits, inj_consts, discrete, presburger} => |
|
314 |
{splits = splits, inj_consts = inj_consts, discrete = discrete, |
|
15531 | 315 |
presburger = SOME (presburger_tac true false)})]; |
13876 | 316 |
|
317 |
end; |
|
318 |
||
14920
a7525235e20f
An oracle is built in. The tactic will not generate any proofs any more, if the quick_and_dirty flag is set on.
chaieb
parents:
14882
diff
changeset
|
319 |
val presburger_tac = Presburger.presburger_tac true false; |