z3-z3-4.13.0.examples.ml.ml_example.ml Maven / Gradle / Ivy
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(*
Copyright (C) 2012 Microsoft Corporation
Author: CM Wintersteiger (cwinter) 2012-12-17
*)
open Z3
open Z3.Symbol
open Z3.Sort
open Z3.Expr
open Z3.Boolean
open Z3.FuncDecl
open Z3.Goal
open Z3.Tactic
open Z3.Tactic.ApplyResult
open Z3.Probe
open Z3.Solver
open Z3.Arithmetic
open Z3.Arithmetic.Integer
open Z3.Arithmetic.Real
open Z3.BitVector
exception TestFailedException of string
(**
Model Converter test
*)
let model_converter_test ( ctx : context ) =
Printf.printf "ModelConverterTest\n";
let xr = (Expr.mk_const ctx (Symbol.mk_string ctx "x") (Real.mk_sort ctx)) in
let yr = (Expr.mk_const ctx (Symbol.mk_string ctx "y") (Real.mk_sort ctx)) in
let g4 = (mk_goal ctx true false false ) in
(Goal.add g4 [ (mk_gt ctx xr (Real.mk_numeral_nd ctx 10 1)) ]) ;
(Goal.add g4 [ (mk_eq ctx
yr
(Arithmetic.mk_add ctx [ xr; (Real.mk_numeral_nd ctx 1 1) ])) ]) ;
(Goal.add g4 [ (mk_gt ctx yr (Real.mk_numeral_nd ctx 1 1)) ]) ;
(
let ar = (Tactic.apply (mk_tactic ctx "simplify") g4 None) in
if ((get_num_subgoals ar) == 1 &&
((is_decided_sat (get_subgoal ar 0)) ||
(is_decided_unsat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(
let ar = (Tactic.apply (and_then ctx (mk_tactic ctx ("simplify")) (mk_tactic ctx "solve-eqs") []) g4 None) in
if ((get_num_subgoals ar) == 1 &&
((is_decided_sat (get_subgoal ar 0)) ||
(is_decided_unsat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
;
let solver = (mk_solver ctx None) in
let f e = (Solver.add solver [ e ]) in
ignore (List.map f (get_formulas (get_subgoal ar 0))) ;
let q = (check solver []) in
if q != SATISFIABLE then
raise (TestFailedException "")
else
let m = (get_model solver) in
match m with
| None -> raise (TestFailedException "")
| Some (m) ->
Printf.printf "Solver says: %s\n" (string_of_status q) ;
Printf.printf "Model: \n%s\n" (Model.to_string m)
)
(**
Some basic tests.
*)
let basic_tests ( ctx : context ) =
Printf.printf "BasicTests\n" ;
let fname = (mk_string ctx "f") in
let x = (mk_string ctx "x") in
let y = (mk_string ctx "y") in
let bs = (Boolean.mk_sort ctx) in
let domain = [ bs; bs ] in
let f = (FuncDecl.mk_func_decl ctx fname domain bs) in
let fapp = (mk_app ctx f
[ (Expr.mk_const ctx x bs); (Expr.mk_const ctx y bs) ]) in
let fargs2 = [ (mk_fresh_const ctx "cp" bs) ] in
let domain2 = [ bs ] in
let fapp2 = (mk_app ctx (mk_fresh_func_decl ctx "fp" domain2 bs) fargs2) in
let trivial_eq = (mk_eq ctx fapp fapp) in
let nontrivial_eq = (mk_eq ctx fapp fapp2) in
let g = (mk_goal ctx true false false) in
(Goal.add g [ trivial_eq ]) ;
(Goal.add g [ nontrivial_eq ]) ;
Printf.printf "%s\n" ("Goal: " ^ (Goal.to_string g)) ;
(
let solver = (mk_solver ctx None) in
(List.iter (fun a -> (Solver.add solver [ a ])) (get_formulas g)) ;
if (check solver []) != SATISFIABLE then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(
let ar = (Tactic.apply (mk_tactic ctx "simplify") g None) in
if ((get_num_subgoals ar) == 1 &&
((is_decided_sat (get_subgoal ar 0)) ||
(is_decided_unsat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(
let ar = (Tactic.apply (mk_tactic ctx "smt") g None) in
if ((get_num_subgoals ar) == 1 &&
(not (is_decided_sat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(Goal.add g [ (mk_eq ctx
(mk_numeral_int ctx 1 (BitVector.mk_sort ctx 32))
(mk_numeral_int ctx 2 (BitVector.mk_sort ctx 32))) ] )
;
(
let ar = (Tactic.apply (mk_tactic ctx "smt") g None) in
if ((get_num_subgoals ar) == 1 &&
(not (is_decided_unsat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(
let g2 = (mk_goal ctx true true false) in
let ar = (Tactic.apply (mk_tactic ctx "smt") g2 None) in
if ((get_num_subgoals ar) == 1 &&
(not (is_decided_sat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(
let g2 = (mk_goal ctx true true false) in
(Goal.add g2 [ (Boolean.mk_false ctx) ]) ;
let ar = (Tactic.apply (mk_tactic ctx "smt") g2 None) in
if ((get_num_subgoals ar) == 1 &&
(not (is_decided_unsat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(
let g3 = (mk_goal ctx true true false) in
let xc = (Expr.mk_const ctx (Symbol.mk_string ctx "x") (Integer.mk_sort ctx)) in
let yc = (Expr.mk_const ctx (Symbol.mk_string ctx "y") (Integer.mk_sort ctx)) in
(Goal.add g3 [ (mk_eq ctx xc (mk_numeral_int ctx 1 (Integer.mk_sort ctx))) ]) ;
(Goal.add g3 [ (mk_eq ctx yc (mk_numeral_int ctx 2 (Integer.mk_sort ctx))) ]) ;
let constr = (mk_eq ctx xc yc) in
(Goal.add g3 [ constr ] ) ;
let ar = (Tactic.apply (mk_tactic ctx "smt") g3 None) in
if ((get_num_subgoals ar) == 1 &&
(not (is_decided_unsat (get_subgoal ar 0)))) then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
) ;
model_converter_test ctx ;
(* Real num/den test. *)
let rn = Real.mk_numeral_nd ctx 42 43 in
let inum = (get_numerator rn) in
let iden = get_denominator rn in
Printf.printf "Numerator: %s Denominator: %s\n" (Real.numeral_to_string inum) (Real.numeral_to_string iden) ;
if ((Real.numeral_to_string inum) <> "42" || (Real.numeral_to_string iden) <> "43") then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
;
if ((to_decimal_string rn 3) <> "0.976?") then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
;
if (to_decimal_string (Real.mk_numeral_s ctx "-1231231232/234234333") 5 <> "-5.25640?") then
raise (TestFailedException "")
else if (to_decimal_string (Real.mk_numeral_s ctx "-123123234234234234231232/234234333") 5 <> "-525641278361333.28170?") then
raise (TestFailedException "")
else if (to_decimal_string (Real.mk_numeral_s ctx "-234234333") 5 <> "-234234333") then
raise (TestFailedException "")
else if (to_decimal_string (Real.mk_numeral_s ctx "234234333/2") 5 <> "117117166.5") then
raise (TestFailedException "")
;
(* Error handling test. *)
try (
let i = Integer.mk_numeral_s ctx "1/2" in
Printf.printf "%s\n" (Expr.to_string i) ;
raise (TestFailedException "check")
)
with Z3.Error(_) -> (
Printf.printf "Exception caught, OK.\n"
)
(**
A basic example of how to use quantifiers.
**)
let quantifier_example1 ( ctx : context ) =
Printf.printf "QuantifierExample\n" ;
let is = (Integer.mk_sort ctx) in
let types = [ is; is; is ] in
let names = [ (Symbol.mk_string ctx "x_0");
(Symbol.mk_string ctx "x_1");
(Symbol.mk_string ctx "x_2") ] in
let vars = [ (Quantifier.mk_bound ctx 2 (List.nth types 0));
(Quantifier.mk_bound ctx 2 (List.nth types 1));
(Quantifier.mk_bound ctx 2 (List.nth types 2)) ] in
let xs = [ (Integer.mk_const ctx (List.nth names 0));
(Integer.mk_const ctx (List.nth names 1));
(Integer.mk_const ctx (List.nth names 2)) ] in
let body_vars = (Boolean.mk_and ctx
[ (mk_eq ctx
(Arithmetic.mk_add ctx [ (List.nth vars 0) ; (Integer.mk_numeral_i ctx 1)])
(Integer.mk_numeral_i ctx 2)) ;
(mk_eq ctx
(Arithmetic.mk_add ctx [ (List.nth vars 1); (Integer.mk_numeral_i ctx 2)])
(Arithmetic.mk_add ctx [ (List.nth vars 2); (Integer.mk_numeral_i ctx 3)])) ]) in
let body_const = (Boolean.mk_and ctx
[ (mk_eq ctx
(Arithmetic.mk_add ctx [ (List.nth xs 0); (Integer.mk_numeral_i ctx 1)])
(Integer.mk_numeral_i ctx 2)) ;
(mk_eq ctx
(Arithmetic.mk_add ctx [ (List.nth xs 1); (Integer.mk_numeral_i ctx 2)])
(Arithmetic.mk_add ctx [ (List.nth xs 2); (Integer.mk_numeral_i ctx 3)])) ]) in
let x = (Quantifier.mk_forall ctx types names body_vars (Some 1) [] [] (Some (Symbol.mk_string ctx "Q1")) (Some (Symbol.mk_string ctx "skid1"))) in
Printf.printf "Quantifier X: %s\n" (Quantifier.to_string x) ;
let y = (Quantifier.mk_forall_const ctx xs body_const (Some 1) [] [] (Some (Symbol.mk_string ctx "Q2")) (Some (Symbol.mk_string ctx "skid2"))) in
Printf.printf "Quantifier Y: %s\n" (Quantifier.to_string y) ;
if (is_true (Quantifier.expr_of_quantifier x)) then
raise (TestFailedException "") (* unreachable *)
else if (is_false (Quantifier.expr_of_quantifier x)) then
raise (TestFailedException "") (* unreachable *)
else if (is_const (Quantifier.expr_of_quantifier x)) then
raise (TestFailedException "") (* unreachable *)
open Z3.FloatingPoint
(**
A basic example of floating point arithmetic
**)
let fpa_example ( ctx : context ) =
Printf.printf "FPAExample\n" ;
(* let str = ref "" in *)
(* (read_line ()) ; *)
let double_sort = (FloatingPoint.mk_sort_double ctx) in
let rm_sort = (FloatingPoint.RoundingMode.mk_sort ctx) in
(** Show that there are x, y s.t. (x + y) = 42.0 (with rounding mode). *)
let s_rm = (mk_string ctx "rm") in
let rm = (mk_const ctx s_rm rm_sort) in
let s_x = (mk_string ctx "x") in
let s_y = (mk_string ctx "y") in
let x = (mk_const ctx s_x double_sort) in
let y = (mk_const ctx s_y double_sort)in
let n = (FloatingPoint.mk_numeral_f ctx 42.0 double_sort) in
let s_x_plus_y = (mk_string ctx "x_plus_y") in
let x_plus_y = (mk_const ctx s_x_plus_y double_sort) in
let c1 = (mk_eq ctx x_plus_y (mk_add ctx rm x y)) in
let args = [ c1 ; (mk_eq ctx x_plus_y n) ] in
let c2 = (Boolean.mk_and ctx args) in
let args2 = [ c2 ; (Boolean.mk_not ctx (Boolean.mk_eq ctx rm (RoundingMode.mk_rtz ctx))) ] in
let c3 = (Boolean.mk_and ctx args2) in
let and_args = [ (Boolean.mk_not ctx (mk_is_zero ctx y)) ;
(Boolean.mk_not ctx (mk_is_nan ctx y)) ;
(Boolean.mk_not ctx (mk_is_infinite ctx y)) ] in
let args3 = [ c3 ; (Boolean.mk_and ctx and_args) ] in
let c4 = (Boolean.mk_and ctx args3) in
(Printf.printf "c4: %s\n" (Expr.to_string c4)) ;
(
let solver = (mk_solver ctx None) in
(Solver.add solver [ c4 ]) ;
if (check solver []) != SATISFIABLE then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
);
(* Show that the following are equal: *)
(* (fp #b0 #b10000000001 #xc000000000000) *)
(* ((_ to_fp 11 53) #x401c000000000000)) *)
(* ((_ to_fp 11 53) RTZ 1.75 2))) *)
(* ((_ to_fp 11 53) RTZ 7.0))) *)
let c1 = (mk_fp ctx (mk_numeral_string ctx "0" (BitVector.mk_sort ctx 1))
(mk_numeral_string ctx "1025" (BitVector.mk_sort ctx 11))
(mk_numeral_string ctx "3377699720527872" (BitVector.mk_sort ctx 52))) in
let c2 = (mk_to_fp_bv ctx
(mk_numeral_string ctx "4619567317775286272" (BitVector.mk_sort ctx 64))
(mk_sort ctx 11 53)) in
let c3 = (mk_to_fp_int_real ctx
(RoundingMode.mk_rtz ctx)
(mk_numeral_string ctx "2" (Integer.mk_sort ctx))
(mk_numeral_string ctx "1.75" (Real.mk_sort ctx))
(FloatingPoint.mk_sort ctx 11 53)) in
let c4 = (mk_to_fp_real ctx (RoundingMode.mk_rtz ctx)
(mk_numeral_string ctx "7.0" (Real.mk_sort ctx))
(FloatingPoint.mk_sort ctx 11 53)) in
let args3 = [ (mk_eq ctx c1 c2) ;
(mk_eq ctx c1 c3) ;
(mk_eq ctx c1 c4) ] in
let c5 = (Boolean.mk_and ctx args3) in
(Printf.printf "c5: %s\n" (Expr.to_string c5)) ;
(
let solver = (mk_solver ctx None) in
(Solver.add solver [ c5 ]) ;
Printf.printf "Memory in use before `check`: %Lu bytes\n" (Statistics.get_estimated_alloc_size());
if (check solver []) != SATISFIABLE then
raise (TestFailedException "")
else
Printf.printf "Test passed.\n"
)
(**
A basic example of RCF usage
**)
let rcf_example ( ctx : context ) =
Printf.printf "RCFExample\n" ;
let pi = RCF.mk_pi ctx in
let e = RCF.mk_e ctx in
let inf0 = RCF.mk_infinitesimal ctx in
let inf1 = RCF.mk_infinitesimal ctx in
let r = RCF.mk_rational ctx "42.001" in
let pi_div_e = RCF.div ctx pi e in
let pi_div_r = RCF.div ctx pi r in
(Printf.printf "e: %s, pi: %s, e==pi: %b, e < pi: %b\n"
(RCF.num_to_string ctx e true false)
(RCF.num_to_string ctx pi true false)
(RCF.eq ctx e pi)
(RCF.lt ctx e pi)) ;
Printf.printf "pi_div_e: %s.\n" (RCF.num_to_string ctx pi_div_e true false);
Printf.printf "pi_div_r: %s.\n" (RCF.num_to_string ctx pi_div_r true false);
Printf.printf "inf0: %s.\n" (RCF.num_to_string ctx inf0 true false);
Printf.printf "(RCF.is_rational ctx pi): %b.\n" (RCF.is_rational ctx pi);
Printf.printf "(RCF.is_algebraic ctx pi): %b.\n" (RCF.is_algebraic ctx pi);
Printf.printf "(RCF.is_transcendental ctx pi): %b.\n" (RCF.is_transcendental ctx pi);
Printf.printf "(RCF.is_rational ctx r): %b.\n" (RCF.is_rational ctx r);
Printf.printf "(RCF.is_algebraic ctx r): %b.\n" (RCF.is_algebraic ctx r);
Printf.printf "(RCF.is_transcendental ctx r): %b.\n" (RCF.is_transcendental ctx r);
Printf.printf "(RCF.is_infinitesimal ctx inf0): %b.\n" (RCF.is_infinitesimal ctx inf0);
Printf.printf "(RCF.extension_index ctx inf0): %d.\n" (RCF.extension_index ctx inf0);
Printf.printf "(RCF.extension_index ctx inf1): %d.\n" (RCF.extension_index ctx inf1);
let poly:RCF.rcf_num list = [ e; pi; inf0 ] in
let rs:RCF.root list = RCF.roots ctx poly in
let print_root (x:RCF.root) =
begin
Printf.printf "root: %s\n%!" (RCF.num_to_string ctx x.obj true false);
if RCF.is_algebraic ctx x.obj then (
(match x.interval with
| Some ivl -> Printf.printf " interval: (%b, %b, %s, %b, %b, %s)\n"
ivl.lower_is_inf
ivl.lower_is_open
(RCF.num_to_string ctx ivl.lower true false)
ivl.upper_is_inf
ivl.upper_is_open
(RCF.num_to_string ctx ivl.upper true false);
| None -> ());
Printf.printf " polynomial coefficients:";
List.iter (fun c -> Printf.printf " %s" (RCF.num_to_string ctx c false false)) x.polynomial;
Printf.printf "\n";
Printf.printf " sign conditions:";
List.iter
(fun (poly, sign) ->
List.iter (fun p -> Printf.printf " %s" (RCF.num_to_string ctx p true false)) poly;
Printf.printf " %s" (if sign > 0 then "> 0" else if sign < 0 then "< 0" else "= 0"))
x.sign_conditions;
Printf.printf "\n")
end
in
List.iter print_root rs;
RCF.del_roots ctx rs;
RCF.del_list ctx [pi; e; inf0; inf1; r; pi_div_e; pi_div_r];
Printf.printf "Test passed.\n"
let _ =
try (
if not (Log.open_ "z3.log") then
raise (TestFailedException "Log couldn't be opened.")
else
(
Printf.printf "Running Z3 version %s\n" Version.to_string ;
Printf.printf "Z3 full version string: %s\n" Version.full_version ;
let cfg = [("model", "true"); ("proof", "false")] in
let ctx = (mk_context cfg) in
let is = (Symbol.mk_int ctx 42) in
let ss = (Symbol.mk_string ctx "mySymbol") in
let bs = (Boolean.mk_sort ctx) in
let ints = (Integer.mk_sort ctx) in
let rs = (Real.mk_sort ctx) in
let v = (Arithmetic.Integer.mk_numeral_i ctx 8000000000) in
Printf.printf "int symbol: %s\n" (Symbol.to_string is);
Printf.printf "string symbol: %s\n" (Symbol.to_string ss);
Printf.printf "bool sort: %s\n" (Sort.to_string bs);
Printf.printf "int sort: %s\n" (Sort.to_string ints);
Printf.printf "real sort: %s\n" (Sort.to_string rs);
Printf.printf "integer: %s\n" (Expr.to_string v);
basic_tests ctx ;
quantifier_example1 ctx ;
fpa_example ctx ;
rcf_example ctx ;
Printf.printf "Disposing...\n";
Gc.full_major ()
);
Printf.printf "Exiting.\n" ;
exit 0
) with Error(msg) -> (
Printf.printf "Z3 EXCEPTION: %s\n" msg ;
exit 1
)
;;