Results 1 
4 of
4
Verifying mixed realinteger quantifier elimination
 IJCAR 2006, LNCS 4130
, 2006
"... We present a formally verified quantifier elimination procedure for the first order theory over linear mixed realinteger arithmetics in higherorder logic based on a work by Weispfenning. To this end we provide two verified quantifier elimination procedures: for Presburger arithmitics and for lin ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
We present a formally verified quantifier elimination procedure for the first order theory over linear mixed realinteger arithmetics in higherorder logic based on a work by Weispfenning. To this end we provide two verified quantifier elimination procedures: for Presburger arithmitics and for linear real arithmetics.
Proof synthesis and reflection for linear arithmetic. Submitted
, 2006
"... This article presents detailed implementations of quantifier elimination for both integer and real linear arithmetic for theorem provers. The underlying algorithms are those by Cooper (for Z) and by Ferrante and Rackoff (for R). Both algorithms are realized in two entirely different ways: once in ta ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
This article presents detailed implementations of quantifier elimination for both integer and real linear arithmetic for theorem provers. The underlying algorithms are those by Cooper (for Z) and by Ferrante and Rackoff (for R). Both algorithms are realized in two entirely different ways: once in tactic style, i.e. by a proofproducing functional program, and once by reflection, i.e. by computations inside the logic rather than in the metalanguage. Both formalizations are highly generic because they make only minimal assumptions w.r.t. the underlying logical system and theorem prover. An implementation in Isabelle/HOL shows that the reflective approach is between one and two orders of magnitude faster. 1
Proofproducing program analysis
, 2006
"... Proofproducing program analysis augments the invariants inferred by an abstract interpreter with their correctness proofs. If these invariants are precise enough to guarantee safety, this method is an automatic verification tool. We present proofsynthesis algorithms for a simple flow chart languag ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Proofproducing program analysis augments the invariants inferred by an abstract interpreter with their correctness proofs. If these invariants are precise enough to guarantee safety, this method is an automatic verification tool. We present proofsynthesis algorithms for a simple flow chart language and domains V → V mapping variables to abstract values and discuss some benefits for proof carrying code systems. Our work has been carried out in Isabelle/HOL and incorporated within a verified proof carrying code system.
Mechanized quantifier elimination for linear realarithmetic in Isabelle/HOL
"... Abstract. We integrate Ferrante and Rackoff’s quantifier elimination procedure for linear real arithmetic in Isabelle/HOL in two manners: (a) tacticstyle, i.e. for every problem instance a proof is generated by invoking a series of inference rules, and (b) reflection, where the whole algorithm is i ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We integrate Ferrante and Rackoff’s quantifier elimination procedure for linear real arithmetic in Isabelle/HOL in two manners: (a) tacticstyle, i.e. for every problem instance a proof is generated by invoking a series of inference rules, and (b) reflection, where the whole algorithm is implemented and verified within Isabelle/HOL. We discuss the performance obtained for both integrations. 1