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Extending ACL2 with SMT Solvers

“…We plan to do this in the near future. Even greater confidence could be achieved by adopting the "skeptical" approach advocated by Harrison [11], for example by using proof reconstruction [6,9,17,2,18] or proof certificates [5]. We see such efforts as complementary to the approach that we have taken with Smtlink.…”

“…Our solution is to allow the user to give hints to the clause processor. These hints allow the user to direct the clause pro-Program 2.3 A claim with non-polynomial arithmetic 1 (defthm poly-of-expt-example 2 (implies (and (rationalp x) (rationalp y) (rationalp z) (integerp m) 3 (integerp n) (< 0 z) (< z 1) (< 0 m) (< m n)) 4 (<= (* 2 (expt z n) x y) (* (expt z m) (+ (* x x) (* y y))))) 5 :hints(("Goal" 6 :clause-processor 7 (Smtlink clause '((:let ((expt_z_m (expt z m) rationalp) 8 (expt_z_n (expt z n) rationalp))) 9 (:hypothesize ((< expt_z_n expt_z_m) 10 (< 0 expt_z_m) 11 (< 0 expt_z_n))) 12 ) )))) cessor to replace all occurrences of a given expression with a new, free variable, and to express constraints that are satisfied by these variables. A complete description of these hints is presented in Section 3.…”

“…Works on integrating SMT solvers or techniques into other theorem provers include [17,9,5,2,18,6,7]. Many of these papers have followed Harrison and Théry's "skeptical" approach [11] and focused on methods for verifying SMT results within the theorem prover using proof reconstruction, certificates, and similar methods. Several of the papers showed how their methods could be used for the verification of concurrent algorithms such as clock synchronization [9], and the Bakery and Memoir algorithms [18].…”

An Extensible Ad Hoc Interface between Lean and Mathematica

“…Harrison and Théry [12] describe a "skeptical" link between HOL and Maple that follows a similar approach to our bridge. Computation is done in a standard, standalone version of the CAS, and sent to the proof assistant for certification.…”

“…We contribute another such bridge, between the proof assistant Lean [17] and the computer algebra system Mathematica [22]. Our connection is inspired by the architecture described by Harrison and Théry [12]. By integrating with the Lean metaprogramming framework, our design allows users to verify results from the CAS without leaving the Lean environment.…”