From c9910cf0dc7294821c643ab5b74e34de612896c5 Mon Sep 17 00:00:00 2001 From: Masanori Tani Date: Fri, 3 Jan 2025 16:49:09 +0900 Subject: [PATCH 1/3] =?UTF-8?q?1=E7=AB=A0=E5=AE=8C=E4=BA=86?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- model-checking-book/example.go | 1 + model-checking-book/go.mod | 3 + model-checking-book/main.go | 23 ++++ model-checking-book/semantics.go | 178 +++++++++++++++++++++++++++++++ model-checking-book/syntax.go | 176 ++++++++++++++++++++++++++++++ 5 files changed, 381 insertions(+) create mode 100644 model-checking-book/example.go create mode 100644 model-checking-book/go.mod create mode 100644 model-checking-book/main.go create mode 100644 model-checking-book/semantics.go create mode 100644 model-checking-book/syntax.go diff --git a/model-checking-book/example.go b/model-checking-book/example.go new file mode 100644 index 0000000..06ab7d0 --- /dev/null +++ b/model-checking-book/example.go @@ -0,0 +1 @@ +package main diff --git a/model-checking-book/go.mod b/model-checking-book/go.mod new file mode 100644 index 0000000..13930f0 --- /dev/null +++ b/model-checking-book/go.mod @@ -0,0 +1,3 @@ +module github.com/uta8a/playground/model-checking-book + +go 1.23.4 diff --git a/model-checking-book/main.go b/model-checking-book/main.go new file mode 100644 index 0000000..c24c21a --- /dev/null +++ b/model-checking-book/main.go @@ -0,0 +1,23 @@ +package main + +// $ go run ./... +// 何も返ってこなければ成功 +func main() { + System( + Variables{"x": 0, "y": 0}, + Process("ProcessA", + Switch( + Case(When(Lt(Var("x"), Int(2))), + Assign("x", Add(Var("x"), Int(1))), + ), + ), + ), + Process("ProcessB", + For( + Case(When(Eq(Var("y"), Int(3))), + Assign("y", Add(Add(Var("x"), Var("y")), Int(1))), + ), + ), + ), + ) +} diff --git a/model-checking-book/semantics.go b/model-checking-book/semantics.go new file mode 100644 index 0000000..ba9db30 --- /dev/null +++ b/model-checking-book/semantics.go @@ -0,0 +1,178 @@ +package main + +import "fmt" + +func (expr intValueExpression) eval(_ map[varName]int) (int, error) { + return expr.value, nil +} + +func (expr variableExpression) eval(vars map[varName]int) (int, error) { + if val, ok := vars[expr.name]; ok { + return val, nil + } + return 0, fmt.Errorf("undefined variable: %s", expr.name) +} + +func (expr addExpression) eval(vars map[varName]int) (int, error) { + l, err := expr.left.eval(vars) + if err != nil { + return 0, err + } + r, err := expr.right.eval(vars) + if err != nil { + return 0, err + } + return l + r, nil +} + +func (expr subExpression) eval(vars map[varName]int) (int, error) { + l, err := expr.left.eval(vars) + if err != nil { + return 0, err + } + r, err := expr.right.eval(vars) + if err != nil { + return 0, err + } + return l - r, nil +} + +func (expr boolValueExpression) eval(_ map[varName]int) (bool, error) { + return expr.value, nil +} + +func (expr eqExpression) eval(vars map[varName]int) (bool, error) { + l, err := expr.left.eval(vars) + if err != nil { + return false, err + } + r, err := expr.right.eval(vars) + if err != nil { + return false, err + } + return l == r, nil +} + +func (expr ltExpression) eval(vars map[varName]int) (bool, error) { + l, err := expr.left.eval(vars) + if err != nil { + return false, err + } + r, err := expr.right.eval(vars) + if err != nil { + return false, err + } + return l < r, nil +} + +func (expr notExpression) eval(vars map[varName]int) (bool, error) { + val, err := expr.expression.eval(vars) + if err != nil { + return false, err + } + return !val, nil +} + +func (expr orExpression) eval(vars map[varName]int) (bool, error) { + l, err := expr.left.eval(vars) + if err != nil { + return false, err + } + r, err := expr.right.eval(vars) + if err != nil { + return false, err + } + return l || r, nil +} + +type environment struct { + variables map[varName]int +} + +type localState struct { + environment environment + statements []statement +} + +func (stmt assignStatement) execute(env environment, pname procName, cont []statement) ([]localState, error) { + if _, ok := env.variables[stmt.varName]; !ok { + return []localState{}, fmt.Errorf("undefined variable: %s", stmt.varName) + } + vars := map[varName]int{} + + // 新しい環境に詰め替える + for name, val := range env.variables { + if name == stmt.varName { + // 右辺として代入すべき値の評価 + newVal, err := stmt.expression.eval(env.variables) + if err != nil { + return []localState{}, err + } + vars[name] = newVal + } else { + vars[name] = val // 評価されない部分はそのままコピー + } + } + + state := localState{ + environment: environment{variables: vars}, + statements: cont, + } + return []localState{state}, nil +} + +func (grd whenGuard) execute(env environment, pname procName) (environment, bool, error) { + condition, err := grd.expression.eval(env.variables) // NOTE: envがガード中に更新される可能性がある + if err != nil { + return environment{}, false, err + } + // ガードの実行可能性の確認 + if !condition { + return env, false, nil + } + return env, true, nil +} + +func (stmt switchStatement) execute(env environment, pname procName, cont []statement) ([]localState, error) { + states := []localState{} + + for _, c := range stmt.cases { // stmt.casesはstructの配列 + newEnv, condition, err := c.guard.execute(env, pname) + if err != nil { + return []localState{}, err + } + // ガードの実行可能性の確認 + if condition { + stmts := append(c.statements, cont...) + state := localState{ + environment: newEnv, + statements: stmts, + } + states = append(states, state) // この時点ではランダムではなく、前から順にtrueなconditionのものがstatesに積まれる。しかしstatesは全て拾われるので、後続処理で並列に実行され、結果が非決定的になる? + } + } + return states, nil +} + +// PramoのForは抜けられない(caseが空の場合はプロセスがブロックされる) +func (stmt forStatement) execute(env environment, pname procName, cont []statement) ([]localState, error) { + states := []localState{} + + for _, c := range stmt.cases { + newEnv, condition, err := c.guard.execute(env, pname) + if err != nil { + return []localState{}, err + } + // ガードの実行可能性の確認 + if condition { + stmts := append(c.statements, stmt) // NOTE: ここがswitch, forの違い。stmtは自身(forStatement)なので、もう一度この処理が後続として入るようになる。それによってループする。 + stmts = append(stmts, cont...) // NOTE: ここがswitch, forの違い + state := localState{ + environment: newEnv, + statements: stmts, + } + states = append(states, state) + } + } + return states, nil +} diff --git a/model-checking-book/syntax.go b/model-checking-book/syntax.go new file mode 100644 index 0000000..ebe3730 --- /dev/null +++ b/model-checking-book/syntax.go @@ -0,0 +1,176 @@ +package main + +type system struct { + variables Variables + processes []process +} + +func System(vars Variables, procs ...process) system { + return system{variables: vars, processes: procs} +} + +type varName string +type Variables map[varName]int + +type procName string + +type process struct { + name procName + statements []statement +} + +func Process(name procName, stmts ...statement) process { + return process{name: name, statements: stmts} +} + +type intExpression interface { + eval(map[varName]int) (int, error) +} + +var _ intExpression = intValueExpression{} +var _ intExpression = variableExpression{} +var _ intExpression = addExpression{} +var _ intExpression = subExpression{} + +type intValueExpression struct { + value int +} + +func Int(val int) intValueExpression { + return intValueExpression{value: val} +} + +type variableExpression struct { + name varName +} + +func Var(name varName) variableExpression { + return variableExpression{name: name} +} + +type addExpression struct { + left intExpression + right intExpression +} + +func Add(l intExpression, r intExpression) addExpression { + return addExpression{left: l, right: r} +} + +type subExpression struct { + left intExpression + right intExpression +} + +func Sub(l intExpression, r intExpression) subExpression { + return subExpression{left: l, right: r} +} + +type boolExpression interface { + eval(map[varName]int) (bool, error) +} + +var _ boolExpression = boolValueExpression{} +var _ boolExpression = eqExpression{} +var _ boolExpression = ltExpression{} +var _ boolExpression = notExpression{} +var _ boolExpression = orExpression{} + +type boolValueExpression struct { + value bool +} + +func True() boolValueExpression { + return boolValueExpression{value: true} +} + +type eqExpression struct { + left intExpression + right intExpression +} + +func Eq(l intExpression, r intExpression) eqExpression { + return eqExpression{left: l, right: r} +} + +type ltExpression struct { + left intExpression + right intExpression +} + +func Lt(l intExpression, r intExpression) ltExpression { + return ltExpression{left: l, right: r} +} + +type notExpression struct { + expression boolExpression +} + +func Not(bexpr boolExpression) notExpression { + return notExpression{expression: bexpr} +} + +type orExpression struct { + left boolExpression + right boolExpression +} + +func Or(l boolExpression, r boolExpression) orExpression { + return orExpression{left: l, right: r} +} + +type statement interface { + execute(env environment, pname procName, cont []statement) ([]localState, error) +} + +var _ statement = assignStatement{} +var _ statement = switchStatement{} +var _ statement = forStatement{} + +type assignStatement struct { + varName varName + expression intExpression +} + +func Assign(x varName, iexpr intExpression) assignStatement { + return assignStatement{varName: x, expression: iexpr} +} + +type guard interface { + execute(env environment, pname procName) (environment, bool, error) +} + +var _ guard = whenGuard{} + +type whenGuard struct { + expression boolExpression +} + +func When(bexpr boolExpression) whenGuard { + return whenGuard{expression: bexpr} +} + +type guardCase struct { + guard guard + statements []statement +} + +func Case(grd guard, stmts ...statement) guardCase { + return guardCase{guard: grd, statements: stmts} +} + +type switchStatement struct { + cases []guardCase +} + +func Switch(cases ...guardCase) switchStatement { + return switchStatement{cases: cases} +} + +type forStatement struct { + cases []guardCase +} + +func For(cases ...guardCase) forStatement { + return forStatement{cases: cases} +} From 39bdb7b0e912c813e9d51272d18fda763baedcf9 Mon Sep 17 00:00:00 2001 From: Masanori Tani Date: Sun, 19 Jan 2025 15:57:57 +0900 Subject: [PATCH 2/3] =?UTF-8?q?=E6=AC=A1=E3=81=AFp33=E3=81=8B=E3=82=89?= =?UTF-8?q?=E3=82=84=E3=82=8B?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- model-checking-book/kripke.go | 119 ++++++++++++++++++++++++++++++++++ 1 file changed, 119 insertions(+) create mode 100644 model-checking-book/kripke.go diff --git a/model-checking-book/kripke.go b/model-checking-book/kripke.go new file mode 100644 index 0000000..eb83a91 --- /dev/null +++ b/model-checking-book/kripke.go @@ -0,0 +1,119 @@ +package main + +import ( + "fmt" + "hash/fnv" + "sort" + "strings" +) + +type kripkeModel struct { + worlds worlds + initial worldID + accessible map[worldID][]worldID +} + +type worldID uint64 +type worlds map[worldID]world + +func (wlds worlds) member(wld world) bool { + _, ok := wlds[wld.id] + return ok +} + +func (wlds worlds) insert(wld world) { + wlds[wld.id] = wld +} + +type world struct { + id worldID + environment environment + programCounters map[procName][]statement +} + +func NewWorld(env environment, counters map[procName][]statement) world { + id := id(env, counters) + return world{id: id, environment: env, programCounters: counters} +} + +func id(env environment, counters map[procName][]statement) worldID { + strs := []string{} + vnames := []string{} + + for name := range env.variables { + vnames = append(vnames, string(name)) + } + sort.Strings(vnames) + + for _, name := range vnames { + val := env.variables[varName(name)] + strs = append(strs, fmt.Sprintf("%s=%d", name, val)) + } + + pnames := []string{} + for name := range counters { + pnames = append(pnames, string(name)) + } + sort.Strings(pnames) + for _, name := range pnames { + stmts := counters[procName(name)] + strs = append(strs, fmt.Sprintf("%s=%+v", name, stmts)) + } + + hasher := fnv.New64a() + hasher.Write(([]byte(strings.Join(strs, ",")))) + return worldID(hasher.Sum64()) +} + +func initialWorld(sys system) world { + vars := map[varName]int{} + for name, val := range sys.variables { + vars[name] = val + } + + counters := map[procName][]statement{} + for _, proc := range sys.processes { + counters[proc.name] = proc.statements + } + + newEnv := environment{ + variables: vars, + } + + return NewWorld(newEnv, counters) +} + +func stepLocal(env environment, pname procName, stmts []statement) ([]localState, error) { + if len(stmts) == 0 { + return []localState{}, nil + } + + return stmts[0].execute(env, pname, stmts[1:]) +} + +func stepGlobal(wld world) ([]world, error) { + wlds := []world{} + + // プロセスを選ぶループ + for pname, stmts := range wld.programCounters { + states, err := stepLocal(wld.environment, pname, stmts) + if err != nil { + return []world{}, err + } + // そのプロセスの動作の可能性に対するループ + for _, state := range states { + counters := map[procName][]statement{} + for n, ss := range wld.programCounters { + if n == pname { + counters[n] = state.statements + } else { + counters[n] = ss + } + } + wld := NewWorld(state.environment, counters) + wlds = append(wlds, wld) + } + } + + return wlds, nil +} From a24fd103643775fe33ab9c820f1993a100aeda58 Mon Sep 17 00:00:00 2001 From: Masanori Tani Date: Sun, 2 Feb 2025 19:02:21 +0900 Subject: [PATCH 3/3] =?UTF-8?q?=E6=AC=A1=E3=81=AFp38=E3=81=8B=E3=82=89?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- model-checking-book/kripke.go | 35 ++++++++++ model-checking-book/main.go | 29 ++++---- model-checking-book/mutex.dot | 111 ++++++++++++++++++++++++++++++ model-checking-book/mutex.go | 22 ++++++ model-checking-book/mutex.png | Bin 0 -> 594662 bytes model-checking-book/sample.dot | 8 +++ model-checking-book/sample.png | Bin 0 -> 5291 bytes model-checking-book/visualizer.go | 41 +++++++++++ 8 files changed, 229 insertions(+), 17 deletions(-) create mode 100644 model-checking-book/mutex.dot create mode 100644 model-checking-book/mutex.go create mode 100644 model-checking-book/mutex.png create mode 100644 model-checking-book/sample.dot create mode 100644 model-checking-book/sample.png create mode 100644 model-checking-book/visualizer.go diff --git a/model-checking-book/kripke.go b/model-checking-book/kripke.go index eb83a91..8062599 100644 --- a/model-checking-book/kripke.go +++ b/model-checking-book/kripke.go @@ -117,3 +117,38 @@ func stepGlobal(wld world) ([]world, error) { return wlds, nil } + +func KripkeModel(sys system) (kripkeModel, error) { + init := initialWorld(sys) + + visited := worlds{} + visited.insert(init) + accs := map[worldID][]worldID{} + + stack := []world{init} + for len(stack) > 0 { + current := stack[len(stack)-1] + stack = stack[:len(stack)-1] + + acc := []worldID{} + nexts, err := stepGlobal(current) + if err != nil { + return kripkeModel{}, err + } + for _, next := range nexts { + acc = append(acc, next.id) + + if !visited.member(next) { + visited.insert(next) + stack = append(stack, next) + } + } + accs[current.id] = acc + } + + return kripkeModel{ + worlds: visited, + initial: init.id, + accessible: accs, + }, nil +} diff --git a/model-checking-book/main.go b/model-checking-book/main.go index c24c21a..bbe0fb9 100644 --- a/model-checking-book/main.go +++ b/model-checking-book/main.go @@ -1,23 +1,18 @@ package main +import ( + "log" + "os" +) + // $ go run ./... // 何も返ってこなければ成功 func main() { - System( - Variables{"x": 0, "y": 0}, - Process("ProcessA", - Switch( - Case(When(Lt(Var("x"), Int(2))), - Assign("x", Add(Var("x"), Int(1))), - ), - ), - ), - Process("ProcessB", - For( - Case(When(Eq(Var("y"), Int(3))), - Assign("y", Add(Add(Var("x"), Var("y")), Int(1))), - ), - ), - ), - ) + sys := Mutex() + model, err := KripkeModel(sys) + if err != nil { + log.Fatal(err) + + } + model.WriteAsDot(os.Stdout) } diff --git a/model-checking-book/mutex.dot b/model-checking-book/mutex.dot new file mode 100644 index 0000000..65fea8b --- /dev/null +++ b/model-checking-book/mutex.dot @@ -0,0 +1,111 @@ +digraph { + 11221991691700317303 [label="critical=0"]; + 11221991691700317303 [ penwidth = 5 ]; + 921510197053021043 [label="critical=0"]; + 3487952452228750286 [label="critical=1"]; + 1719250695456733177 [label="critical=2"]; + 7436987335548333450 [label="critical=1"]; + 1280363200138696619 [label="critical=0"]; + 15882637993728910432 [label="critical=1"]; + 15782641524140305967 [label="critical=2"]; + 7036388809428607951 [label="critical=0"]; + 3238549733672927470 [label="critical=1"]; + 17929327978746845670 [label="critical=1"]; + 5752008125370460663 [label="critical=2"]; + 12639326343918287883 [label="critical=2"]; + 3372605456242150480 [label="critical=1"]; + 1161750338396871911 [label="critical=0"]; + 10778493553980671058 [label="critical=3"]; + 9472190305011600930 [label="critical=1"]; + 12398303882891926298 [label="critical=1"]; + 3649300105249688795 [label="critical=0"]; + 3019680412146324886 [label="critical=1"]; + 5126610833276348920 [label="critical=1"]; + 2808960358517481579 [label="critical=2"]; + 1394296989391464834 [label="critical=1"]; + 17106298229703682801 [label="critical=2"]; + 4058687436091955395 [label="critical=0"]; + 3975512886879023247 [label="critical=0"]; + 11490742439060118968 [label="critical=1"]; + 11490742439060118968 -> 15882637993728910432; + 11490742439060118968 -> 3372605456242150480; + 11490742439060118968 -> 11221991691700317303; + 921510197053021043 -> 7036388809428607951; + 921510197053021043 -> 12398303882891926298; + 921510197053021043 -> 3649300105249688795; + 11221991691700317303 -> 4058687436091955395; + 11221991691700317303 -> 921510197053021043; + 11221991691700317303 -> 3975512886879023247; + 12398303882891926298 -> 11221991691700317303; + 12398303882891926298 -> 17929327978746845670; + 12398303882891926298 -> 1394296989391464834; + 17106298229703682801 -> 3019680412146324886; + 17106298229703682801 -> 10778493553980671058; + 17106298229703682801 -> 17929327978746845670; + 3487952452228750286 -> 1280363200138696619; + 3487952452228750286 -> 5752008125370460663; + 3487952452228750286 -> 17106298229703682801; + 17929327978746845670 -> 3487952452228750286; + 17929327978746845670 -> 3975512886879023247; + 17929327978746845670 -> 2808960358517481579; + 3019680412146324886 -> 15782641524140305967; + 3019680412146324886 -> 3975512886879023247; + 3019680412146324886 -> 3238549733672927470; + 3372605456242150480 -> 921510197053021043; + 3372605456242150480 -> 5126610833276348920; + 3372605456242150480 -> 2808960358517481579; + 1394296989391464834 -> 4058687436091955395; + 1394296989391464834 -> 3487952452228750286; + 1394296989391464834 -> 1719250695456733177; + 5126610833276348920 -> 5752008125370460663; + 5126610833276348920 -> 7036388809428607951; + 5126610833276348920 -> 12639326343918287883; + 1161750338396871911 -> 5126610833276348920; + 1161750338396871911 -> 3238549733672927470; + 1161750338396871911 -> 3487952452228750286; + 15882637993728910432 -> 15782641524140305967; + 15882637993728910432 -> 5126610833276348920; + 15882637993728910432 -> 4058687436091955395; + 7036388809428607951 -> 1394296989391464834; + 7036388809428607951 -> 1161750338396871911; + 7036388809428607951 -> 9472190305011600930; + 5752008125370460663 -> 10778493553980671058; + 5752008125370460663 -> 15882637993728910432; + 5752008125370460663 -> 1394296989391464834; + 15782641524140305967 -> 11490742439060118968; + 15782641524140305967 -> 12639326343918287883; + 15782641524140305967 -> 7436987335548333450; + 4058687436091955395 -> 7036388809428607951; + 4058687436091955395 -> 1280363200138696619; + 4058687436091955395 -> 7436987335548333450; + 3975512886879023247 -> 3649300105249688795; + 3975512886879023247 -> 11490742439060118968; + 3975512886879023247 -> 1280363200138696619; + 3238549733672927470 -> 12639326343918287883; + 3238549733672927470 -> 3649300105249688795; + 3238549733672927470 -> 17106298229703682801; + 10778493553980671058 -> 2808960358517481579; + 10778493553980671058 -> 15782641524140305967; + 10778493553980671058 -> 1719250695456733177; + 9472190305011600930 -> 1719250695456733177; + 9472190305011600930 -> 3238549733672927470; + 9472190305011600930 -> 921510197053021043; + 3649300105249688795 -> 3372605456242150480; + 3649300105249688795 -> 1161750338396871911; + 3649300105249688795 -> 17929327978746845670; + 1280363200138696619 -> 3019680412146324886; + 1280363200138696619 -> 1161750338396871911; + 1280363200138696619 -> 15882637993728910432; + 12639326343918287883 -> 10778493553980671058; + 12639326343918287883 -> 9472190305011600930; + 12639326343918287883 -> 3372605456242150480; + 2808960358517481579 -> 11490742439060118968; + 2808960358517481579 -> 12398303882891926298; + 2808960358517481579 -> 5752008125370460663; + 1719250695456733177 -> 7436987335548333450; + 1719250695456733177 -> 17106298229703682801; + 1719250695456733177 -> 12398303882891926298; + 7436987335548333450 -> 11221991691700317303; + 7436987335548333450 -> 9472190305011600930; + 7436987335548333450 -> 3019680412146324886; +} diff --git a/model-checking-book/mutex.go b/model-checking-book/mutex.go new file mode 100644 index 0000000..0e6a4ee --- /dev/null +++ b/model-checking-book/mutex.go @@ -0,0 +1,22 @@ +package main + +func badThread(name procName) process { + return Process(name, + For( + Case(When(True()), + Assign("critical", Add(Var("critical"), Int(1))), + // critical section + Assign("critical", Sub(Var("critical"), Int(1))), + ), + ), + ) +} + +func Mutex() system { + return System( + Variables{"critical": 0}, + badThread("A"), + badThread("B"), + badThread("C"), + ) +} diff --git a/model-checking-book/mutex.png b/model-checking-book/mutex.png new file mode 100644 index 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