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products/Sources/formale Sprachen/VDM/VDMPP/memoryproofPP/ (Wiener Entwicklungsmethode ^©) Datei vom 13.4.2020 mit Größe 2 kB

SSL memory.vdmpp Sprache: VDM

class Example3

types

ADDR = <a0> | <a1> | <a2>;
CON  = <c0> | <c1> | <c2>;

types

State :: mem    : map ADDR to CON
         access : set of ADDR
         used    : set of ADDR

inv mk_State(mem,access,used) == used = dom mem;

functions

Safe : State -> bool
Safe (mk_State(-,access,used)) ==
  used subset access;

Alloc : ADDR * State -> State
Alloc (addr,mk_State(mem,access,used)) ==
  let used' = used union {addr},
      mem' = mem ++ {addr |-> let c:CON in c}
  in
      mk_State(mem',access,used')
pre addr not in set used;

Alloc2 : ADDR * State -> State
Alloc2 (addr,mk_State(mem,access,used)) ==
  let used' = used union {addr},
--      mem'  = mem ++ {addr |-> <c0>}
      mem' = mem munion {addr |-> let c:CON in c}
  in
      mk_State(mem',access,used')
pre addr not in set used and
    addr in set access;

Alloc20 : ADDR * State -> State
Alloc20 (addr,mk_State(mem,access,used)) ==
  let used' = used union {addr},
      mem' = mem ++ {addr |-> }
  in
      mk_State(mem',access,used')
pre addr not in set used and
    addr in set access;

Alloc21 : ADDR * State -> State
Alloc21 (addr,mk_State(-,access,used)) ==
  let used' = used union {addr},
--      mem'  = mem ++ {addr |-> <c0>}
      mem' = {addr |-> let c:CON in c}
  in
      mk_State(mem',access,used')
pre addr not in set used and
    addr in set access;

Alloc3 : ADDR * State * map ADDR to CON -> State
Alloc3 (addr,mk_State(mem,access,used),mem2) ==
  let used' = used union {addr},
--      mem'  = mem ++ {addr |-> <c0>}
      mem' = mem munion {addr |-> let c:CON in c}
  in
      mk_State(mem',access,used')
pre addr not in set used and
    addr in set access
post mem2 =  mem munion {addr |-> let c:CON in c};

functions -- conjecture

AllocSafe : ADDR * State -> bool
AllocSafe (addr,sta) ==
     Safe(sta) => Safe(Alloc(addr,sta))
post RESULT = true;

AllocSafe0 : ADDR * State -> bool
AllocSafe0 (addr,sta) ==
     Safe(sta) => Safe(Alloc(addr,sta))
pre addr not in set sta.used
post RESULT = true;

AllocSafe2 : ADDR * State -> bool
AllocSafe2 (addr,sta) ==
     Safe(sta) => Safe(Alloc(addr,sta))
pre addr not in set sta.used and
    addr in set sta.access
post RESULT = true;

operations

public RunTest : () ==> bool
RunTest () ==
  (let s : State = mk_State({<a0> |-> <c0>}, {<a0>,<a1>}, {<a0>})
   in
     AllocSafe2(<a1>,s);
  );

end Example3

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Beweissystem der NASA

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NIST Cobol Testsuite

Cephes Mathematical Library

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