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(*
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* Copyright (c) 2019-present, Facebook, Inc.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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let%test_module _ =
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( module struct
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(* let () = Trace.init ~margin:160 ~config:all () *)
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let () =
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Trace.init ~margin:68
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~config:(Result.ok_exn (Trace.parse "+Solver.infer_frame"))
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()
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let infer_frame p xs q =
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Solver.infer_frame p (Var.Set.of_list xs) q
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|> (ignore : Sh.t option -> _)
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let check_frame p xs q =
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Solver.infer_frame p (Var.Set.of_list xs) q
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|> fun r -> assert (Option.is_some r)
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let ( ! ) i = Exp.integer (Z.of_int i) Typ.siz
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let ( + ) = Exp.add Typ.ptr
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let ( - ) = Exp.sub Typ.siz
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let ( * ) = Exp.mul Typ.siz
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let wrt = Var.Set.empty
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let a_, wrt = Var.fresh "a" ~wrt
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let a2_, wrt = Var.fresh "a" ~wrt
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let a3_, wrt = Var.fresh "a" ~wrt
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let b_, wrt = Var.fresh "b" ~wrt
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let k_, wrt = Var.fresh "k" ~wrt
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let l_, wrt = Var.fresh "l" ~wrt
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let l2_, wrt = Var.fresh "l" ~wrt
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let m_, wrt = Var.fresh "m" ~wrt
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let n_, _ = Var.fresh "n" ~wrt
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let a = Exp.var a_
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let a2 = Exp.var a2_
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let a3 = Exp.var a3_
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let b = Exp.var b_
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let k = Exp.var k_
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let l = Exp.var l_
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let l2 = Exp.var l2_
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let m = Exp.var m_
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let n = Exp.var n_
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let%expect_test _ =
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check_frame Sh.emp [] Sh.emp ;
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[%expect
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{|
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( infer_frame: emp \- emp
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) infer_frame: emp |}]
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let%expect_test _ =
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check_frame (Sh.false_ Var.Set.empty) [] Sh.emp ;
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[%expect
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{|
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( infer_frame: emp * false \- emp
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) infer_frame: emp * false |}]
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let%expect_test _ =
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check_frame
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(Sh.seg {loc= l; bas= b; len= m; siz= n; arr= a})
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[] Sh.emp ;
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[%expect
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{|
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( infer_frame: %l_6 -[ %b_4, %m_8 )-> ⟨%n_9,%a_1⟩ \- emp
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) infer_frame: %l_6 -[ %b_4, %m_8 )-> ⟨%n_9,%a_1⟩ |}]
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let%expect_test _ =
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check_frame
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(Sh.seg {loc= l; bas= b; len= m; siz= n; arr= a})
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[]
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(Sh.seg {loc= l; bas= b; len= m; siz= n; arr= a}) ;
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[%expect
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{|
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( infer_frame:
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%l_6 -[ %b_4, %m_8 )-> ⟨%n_9,%a_1⟩
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\- %l_6 -[ %b_4, %m_8 )-> ⟨%n_9,%a_1⟩
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) infer_frame: emp |}]
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let%expect_test _ =
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check_frame
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(Sh.star
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(Sh.seg {loc= l; bas= b; len= m; siz= n; arr= a})
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(Sh.seg {loc= l2; bas= b; len= m; siz= n; arr= a2}))
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[]
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(Sh.seg {loc= l; bas= b; len= m; siz= n; arr= a}) ;
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[%expect
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{|
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( infer_frame:
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%l_6 -[ %b_4, %m_8 )-> ⟨%n_9,%a_1⟩
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* %l_7 -[ %b_4, %m_8 )-> ⟨%n_9,%a_2⟩
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\- %l_6 -[ %b_4, %m_8 )-> ⟨%n_9,%a_1⟩
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) infer_frame: %l_7 -[ %b_4, %m_8 )-> ⟨%n_9,%a_2⟩ |}]
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let%expect_test _ =
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check_frame
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(Sh.star
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(Sh.seg {loc= l; bas= l; len= !16; siz= !8; arr= a})
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(Sh.seg {loc= l + !8; bas= l; len= !16; siz= !8; arr= a2}))
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[a3_]
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(Sh.seg {loc= l; bas= l; len= !16; siz= !16; arr= a3}) ;
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[%expect
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{|
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( infer_frame:
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(%l_6 + 8) -[ %l_6, 16 )-> ⟨8,%a_2⟩
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* %l_6 -[ %l_6, 16 )-> ⟨8,%a_1⟩
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\- ∃ %a_3 .
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%l_6 -[)-> ⟨16,%a_3⟩
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) infer_frame:
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∃ %a1_7 . ⟨16,%a_3⟩ = ⟨8,%a_1⟩^⟨8,%a1_7⟩ ∧ %a_2 = %a1_7 ∧ emp |}]
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let%expect_test _ =
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check_frame
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(Sh.star
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(Sh.seg {loc= l; bas= l; len= !16; siz= !8; arr= a})
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(Sh.seg {loc= l + !8; bas= l; len= !16; siz= !8; arr= a2}))
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[a3_; m_]
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(Sh.seg {loc= l; bas= l; len= m; siz= !16; arr= a3}) ;
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[%expect
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{|
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( infer_frame:
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(%l_6 + 8) -[ %l_6, 16 )-> ⟨8,%a_2⟩
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* %l_6 -[ %l_6, 16 )-> ⟨8,%a_1⟩
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\- ∃ %a_3, %m_8 .
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%l_6 -[ %l_6, %m_8 )-> ⟨16,%a_3⟩
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) infer_frame:
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∃ %a1_9 .
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⟨16,%a_3⟩ = ⟨8,%a_1⟩^⟨8,%a1_9⟩
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∧ %a_2 = %a1_9
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∧ 16 = %m_8
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∧ emp |}]
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let%expect_test _ =
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check_frame
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(Sh.star
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(Sh.seg {loc= l; bas= l; len= !16; siz= !8; arr= a})
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(Sh.seg {loc= l + !8; bas= l; len= !16; siz= !8; arr= a2}))
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[a3_; m_]
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(Sh.seg {loc= l; bas= l; len= m; siz= m; arr= a3}) ;
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[%expect
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{|
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( infer_frame:
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(%l_6 + 8) -[ %l_6, 16 )-> ⟨8,%a_2⟩
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* %l_6 -[ %l_6, 16 )-> ⟨8,%a_1⟩
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\- ∃ %a_3, %m_8 .
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%l_6 -[)-> ⟨%m_8,%a_3⟩
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) infer_frame:
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∃ %a1_9 .
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⟨%m_8,%a_3⟩ = ⟨8,%a_1⟩^⟨8,%a1_9⟩
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∧ %a_2 = %a1_9
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∧ 16 = %m_8
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∧ emp |}]
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let%expect_test _ =
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check_frame
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(Sh.star
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(Sh.seg {loc= k; bas= k; len= !16; siz= !32; arr= a})
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(Sh.seg {loc= l; bas= l; len= !8; siz= !8; arr= !16}))
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[a2_; m_; n_]
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(Sh.star
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(Sh.seg {loc= l; bas= l; len= !8; siz= !8; arr= n})
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(Sh.seg {loc= k; bas= k; len= m; siz= n; arr= a2})) ;
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[%expect
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{|
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( infer_frame:
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%k_5 -[ %k_5, 16 )-> ⟨32,%a_1⟩ * %l_6 -[)-> ⟨8,16⟩
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\- ∃ %a_2, %m_8, %n_9 .
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%k_5 -[ %k_5, %m_8 )-> ⟨%n_9,%a_2⟩ * %l_6 -[)-> ⟨8,%n_9⟩
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) infer_frame:
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∃ %a0_10, %a1_11 .
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⟨32,%a_1⟩ = ⟨%n_9,%a0_10⟩^⟨16,%a1_11⟩
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∧ %a_2 = %a0_10
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∧ 16 = %m_8 = %n_9
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∧ (%k_5 + 16) -[ %k_5, 16 )-> ⟨16,%a1_11⟩ |}]
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(* Incompleteness: changing the order of the subtrahend leads to
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different existential instantiation, which fails *)
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let%expect_test _ =
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infer_frame
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(Sh.star
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(Sh.seg {loc= k; bas= k; len= !16; siz= !32; arr= a})
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(Sh.seg {loc= l; bas= l; len= !8; siz= !8; arr= !16}))
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[a2_; m_; n_]
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(Sh.star
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(Sh.seg {loc= k; bas= k; len= m; siz= n; arr= a2})
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(Sh.seg {loc= l; bas= l; len= !8; siz= !8; arr= n})) ;
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[%expect
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{|
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( infer_frame:
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%k_5 -[ %k_5, 16 )-> ⟨32,%a_1⟩ * %l_6 -[)-> ⟨8,16⟩
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\- ∃ %a_2, %m_8, %n_9 .
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%k_5 -[ %k_5, %m_8 )-> ⟨%n_9,%a_2⟩ * %l_6 -[)-> ⟨8,%n_9⟩
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) infer_frame: |}]
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let seg_split_symbolically =
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Sh.star
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(Sh.seg {loc= l; bas= l; len= !16; siz= !8 * n; arr= a2})
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(Sh.seg
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{ loc= l + (!8 * n)
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; bas= l
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; len= !16
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; siz= !16 - (!8 * n)
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; arr= a3 })
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let%expect_test _ =
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check_frame
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(Sh.and_
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Exp.(or_ (or_ (eq n !0) (eq n !1)) (eq n !2))
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seg_split_symbolically)
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[m_; a_]
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(Sh.seg {loc= l; bas= l; len= m; siz= m; arr= a}) ;
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[%expect
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{|
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( infer_frame:
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(%l_6 + 8 × %n_9) -[ %l_6, 16 )-> ⟨(-8 × %n_9 + 16),%a_3⟩
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* %l_6 -[ %l_6, 16 )-> ⟨(8 × %n_9),%a_2⟩
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* ( ( 2 = %n_9 ∧ emp)
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∨ ( 0 = %n_9 ∧ emp)
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∨ ( 1 = %n_9 ∧ emp)
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)
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\- ∃ %a_1, %m_8 .
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%l_6 -[)-> ⟨%m_8,%a_1⟩
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) infer_frame:
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emp
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* ( ( %a_1 = %a_2
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∧ 2 = %n_9
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∧ 16 = %m_8
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∧ (%l_6 + 16) -[ %l_6, 16 )-> ⟨0,%a_3⟩)
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∨ (∃ %a1_10 .
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⟨%m_8,%a_1⟩ = ⟨(8 × %n_9),%a_2⟩^⟨8,%a1_10⟩
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∧ %a_3 = %a1_10
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∧ 1 = %n_9
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∧ 16 = %m_8
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∧ emp)
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∨ (∃ %a1_10 .
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⟨%m_8,%a_1⟩ = ⟨(8 × %n_9),%a_2⟩^⟨16,%a1_10⟩
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∧ %a_3 = %a1_10
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∧ 0 = %n_9
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∧ 16 = %m_8
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∧ emp)
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) |}]
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(* Incompleteness: equivalent to above but using ≤ instead of ∨ *)
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let%expect_test _ =
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infer_frame
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(Sh.and_ (Exp.le n !2) seg_split_symbolically)
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[m_; a_]
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(Sh.seg {loc= l; bas= l; len= m; siz= m; arr= a}) ;
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[%expect
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{|
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( infer_frame:
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(%n_9 ≤ 2)
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∧ (%l_6 + 8 × %n_9) -[ %l_6, 16 )-> ⟨(-8 × %n_9 + 16),%a_3⟩
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* %l_6 -[ %l_6, 16 )-> ⟨(8 × %n_9),%a_2⟩
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\- ∃ %a_1, %m_8 .
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%l_6 -[)-> ⟨%m_8,%a_1⟩
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) infer_frame: |}]
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end )
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