master > master: protokoll woche 16

.gitignore

@@ -4,6 +4,8 @@
 
 !/docs
 !/notes
+!/notes/*.pdf
+!/notes/*.md
 !/protocol
 !/protocol/*.md
 

README.md

@@ -4,11 +4,13 @@ Diese Repository ist für die Übungsgruppe am Mittwoch.
 
 - Protokolle findet man [hier](./protocol).
 - Notizen findet man [hier](./notes).
+- Symbolverzeichnis findet man in [notes/glossar.md](./notes/glossar.md).
 
 ## LaTeX ##
 
 Folgendes Einführungsvideo hat Emanuel erstellt <https://www.youtube.com/watch?v=HPUGlcZNG2k>.
-Alternativ kann es auch sinnvoll(er) mit Markdown/Pandocs zu arbeiten.
+<br>
+Alternativ zu LaTeX kann es evtl. sinnvoller sein, mit Markdown/Pandocs zu arbeiten.
 
 ## Wahrheitstabelle-Generator ##
 
@@ -23,3 +25,30 @@ Beispiele aus der Übung:
 
 Das Tool ist klug genug, um das Weglassen der äußersten Klammern
 und `A0 && A1 && A2` statt `((A0 && A1) && A2)` u. Ä. zu zulassen.
+
+## Zur Klausur ##
+
+- Datum: (siehe VL + Moodle)
+- Zulassung: TBA
+
+### Vorbereitung ###
+
+Empfehlung:
+
+1. die Definitionen + Resultate im den VL-Folien komplett durchgehen:
+    - prüfen, dass man die Hauptaspekte begreift;
+    - strikt zw. den paar Dingen, die wirklich zur Definition / zum Resultat gehören,
+        <br/>
+        und den Anmerkungen unterscheiden.
+2. in die assoziierten Übungsaufgaben schauen und sowohl die Lehre als auch die Anwendungen vertiefen;
+3. Stichpunkte von »häufigen Fehlern« (bspw. die man persönlich macht)
+    sowie »gewöhnlichen Missverständnissen« erstellen.
+
+Vor der Klausur gut ausschlafen und auf die Ernährung aufpassen.
+
+Während der Klausur:
+
+1. Keine Ablenkungen oder Kommunikationsquellen.
+2. Aufgaben sorgfältig durchlesen und auf Antwortformat achten (insbes. bei „leeren“ Feldern).
+3. Zeit gut managen. Mal muss man entscheiden _»Soll ich jetzt bei dieser Frage auf Kosten der anderen weitere Zeit verbringen, oder weitermachen und später darauf zurück kommen?«_
+4. Übersicht über Fortschritt vor Augen halten.

codego/.gitignore

@@ -18,9 +18,9 @@
 
 ## Go Source
 !/aussagenlogik
-!/aussagenlogik/rekursion
+!/aussagenlogik/recursion
 !/aussagenlogik/schema
-!/aussagenlogik/syntaxbaum
+!/aussagenlogik/formulae
 !/core
 !/core/environment
 !/core/utils

codego/README.md

@@ -64,7 +64,7 @@ run_programme;
 
 ## Offene Challenges ##
 
-In der Datei `aussagenlogik/rekursion.go` (relativ zu diesem Ordner) findet man mehrere leere Methoden (mit dem Kommentar `// Herausforderung...`). Wer es mag, kann versuchen, an seinem Rechner diese Methoden zu definieren und auszuprobieren.
+In dem Ordner `aussagenlogik/recursion` (relativ zum aktuellen Ordner) findet man mehrere leere Methoden (mit dem Kommentar `// Herausforderung...`). Wer es mag, kann versuchen, an seinem Rechner diese Methoden zu definieren und auszuprobieren.
 
 ### Händisch testen ###
 
@@ -79,7 +79,7 @@ Diese Tests existieren parallel zu jedem Modul und folgen dem Namensschema `..._
     ```bash
     chmod +x scripts/test.sh
     ```
-- In `aussagenlogik/rekursion/rekursion_test.go` beim relevanten Testteil eine oder mehrere der Zeilen
+- In `aussagenlogik/recursion/recursion_test.go` beim relevanten Testteil eine oder mehrere der Zeilen
     ```go
     test.Skip("Methode noch nicht implementiert")
     ```

codego/aussagenlogik/formulae/formulae_advanced.go

@@ -0,0 +1,178 @@
+package formulae
+
+import "logik/core/utils"
+
+/* ---------------------------------------------------------------- *
+ * METHOD Get Atoms
+ * ---------------------------------------------------------------- */
+
+func schemeGetAtoms(fml Formula, prevValues [](*[]Formula)) *[]Formula {
+	if fml.IsAtom() {
+		return &[]Formula{fml.Copy()}
+	} else {
+		var results = []Formula{}
+		for _, prevValue := range prevValues {
+			results = append(results, *prevValue...)
+		}
+		return &results
+	}
+}
+
+var fnGetAtoms = CreateFromSchemeFmlsValued(schemeGetAtoms)
+
+func (fml Formula) GetAtoms() []Formula {
+	return *fnGetAtoms(fml)
+}
+
+/* ---------------------------------------------------------------- *
+ * TYPE FormulaPair, FormulaPairs
+ * ---------------------------------------------------------------- */
+
+type FormulaPair struct {
+	Pos Formula
+	Neg Formula
+}
+
+type FormulaPairs []FormulaPair
+
+/* ---------------------------------------------------------------- *
+ * Methods for FormulaPairs
+ * ---------------------------------------------------------------- */
+
+func NewFormulaPairs(pairs []FormulaPair) FormulaPairs { return pairs }
+
+func (pairs FormulaPairs) Pos() []Formula {
+	var fmls = make([]Formula, len(pairs))
+	for i, pair := range pairs {
+		fmls[i] = pair.Pos
+	}
+	return fmls
+}
+
+func (pairs FormulaPairs) Neg() []Formula {
+	var fmls = make([]Formula, len(pairs))
+	for i, pair := range pairs {
+		fmls[i] = pair.Neg
+	}
+	return fmls
+}
+
+/* ---------------------------------------------------------------- *
+ * TYPE KNF, DNF, Horn
+ * ---------------------------------------------------------------- */
+
+type FormulaConjunct []Formula
+type FormulaDisjunct []Formula
+type FormulaKNF []FormulaDisjunct
+type FormulaDNF []FormulaConjunct
+type FormulaHornClause struct {
+	Pos FormulaDisjunct
+	Neg FormulaConjunct
+}
+type FormulaHorn []FormulaHornClause
+
+/* ---------------------------------------------------------------- *
+ * Methods for KNF, DNF, Horn
+ * ---------------------------------------------------------------- */
+
+func (fml FormulaDisjunct) ToFormula() Formula {
+	return Disjunction(fml)
+}
+
+func (fml FormulaConjunct) ToFormula() Formula {
+	return Conjunction(fml)
+}
+
+func (fml FormulaKNF) ToFormula() Formula {
+	var termsAsFormulae = make([]Formula, len(fml))
+	for i, term := range fml {
+		termsAsFormulae[i] = term.ToFormula()
+	}
+	return Conjunction(termsAsFormulae)
+}
+
+func (fml FormulaDNF) ToFormula() Formula {
+	var termsAsFormulae = make([]Formula, len(fml))
+	for i, term := range fml {
+		termsAsFormulae[i] = term.ToFormula()
+	}
+	return Disjunction(termsAsFormulae)
+}
+
+func (fml FormulaHornClause) ToFormula() Formula {
+	return Implies(fml.Neg.ToFormula(), fml.Pos.ToFormula())
+}
+
+func (fml FormulaHorn) ToFormula() Formula {
+	var hornclausesAsFormulae = make([]Formula, len(fml))
+	for i, hornclause := range fml {
+		hornclausesAsFormulae[i] = hornclause.ToFormula()
+	}
+	return Conjunction(hornclausesAsFormulae)
+}
+
+func getAtomsFromArrayOfLiterals(fmls []Formula) []string {
+	var atoms = []string{}
+	var m = map[string]bool{}
+	for _, fml := range fmls {
+		if fml.IsLiteral() {
+			m[fml.GetName()] = true
+		}
+	}
+	for name, _ := range m {
+		atoms = append(atoms, name)
+	}
+	utils.SortStrings(&atoms)
+	return atoms
+}
+
+func getAtomsFromArrayOfArraysOfLiterals(fmlArrays [][]Formula) []string {
+	var atoms = []string{}
+	var m = map[string]bool{}
+	for _, fmls := range fmlArrays {
+		for _, atom := range getAtomsFromArrayOfLiterals(fmls) {
+			m[atom] = true
+		}
+	}
+	for name, _ := range m {
+		atoms = append(atoms, name)
+	}
+	utils.SortStrings(&atoms)
+	return atoms
+}
+
+func (fml FormulaConjunct) GetAtoms() []string {
+	return getAtomsFromArrayOfLiterals(fml)
+}
+
+func (fml FormulaDisjunct) GetAtoms() []string {
+	return getAtomsFromArrayOfLiterals(fml)
+}
+
+func (fml FormulaHornClause) GetAtoms() []string {
+	return getAtomsFromArrayOfArraysOfLiterals([][]Formula{fml.Pos, fml.Neg})
+}
+
+func (fml FormulaKNF) GetAtoms() []string {
+	var fmlArrays = make([][]Formula, len(fml))
+	for i, term := range fml {
+		fmlArrays[i] = term
+	}
+	return getAtomsFromArrayOfArraysOfLiterals(fmlArrays)
+}
+
+func (fml FormulaDNF) GetAtoms() []string {
+	var fmlArrays = make([][]Formula, len(fml))
+	for i, term := range fml {
+		fmlArrays[i] = term
+	}
+	return getAtomsFromArrayOfArraysOfLiterals(fmlArrays)
+}
+
+func (fml FormulaHorn) GetAtoms() []string {
+	var fmlArrays = make([][]Formula, 2*len(fml))
+	for i, hornclause := range fml {
+		fmlArrays[i] = append(hornclause.Neg, hornclause.Pos...)
+	}
+	return getAtomsFromArrayOfArraysOfLiterals(fmlArrays)
+}

codego/aussagenlogik/formulae/formulae_basic.go

@@ -0,0 +1,151 @@
+package formulae
+
+import (
+	"fmt"
+	"strings"
+)
+
+/* ---------------------------------------------------------------- *
+ * TYPE Formula
+ * ---------------------------------------------------------------- */
+
+type Formula struct {
+	kind        string
+	name        string
+	expr        string
+	valence     int
+	subformulae [](*Formula)
+}
+
+/* ---------------------------------------------------------------- *
+ * METHODS
+ * ---------------------------------------------------------------- */
+
+func (fml *Formula) SetKind(kind string) { fml.kind = kind }
+
+func (fml Formula) GetKind() string { return fml.kind }
+
+func (fml *Formula) SetExpr(expr string) { fml.expr = expr }
+
+func (fml Formula) GetExpr() string { return fml.expr }
+
+func (fml Formula) GetName() string { return fml.name }
+
+func (fml *Formula) SetSubformulae(subFmls [](*Formula)) {
+	fml.subformulae = subFmls
+	fml.valence = len(subFmls)
+}
+
+func (fml Formula) GetSubFormulae() []Formula {
+	var n int = fml.valence
+	var subFmls = make([]Formula, n)
+	for i, subFml := range fml.subformulae {
+		subFmls[i] = *subFml
+	}
+	return subFmls
+}
+
+func (fml Formula) GetAllSubFormulae() []Formula {
+	var subFml = fml.GetSubFormulae()
+	var result = []Formula{fml.Copy()}
+	for _, child := range subFml {
+		result = append(result, child.GetAllSubFormulae()...)
+	}
+	return result
+}
+
+func (fml Formula) GetAllSubFormulaeStrict() []Formula {
+	var subFml = fml.GetSubFormulae()
+	var result = []Formula{}
+	for _, child := range subFml {
+		result = append(result, child.GetAllSubFormulae()...)
+	}
+	return result
+}
+
+func (fml Formula) GetChild(indexOpt ...int) Formula {
+	var index int = 0
+	if len(indexOpt) > 0 {
+		index = indexOpt[0]
+	}
+	var subFml Formula
+	if 0 <= index && index < fml.valence {
+		subFml = *(fml.subformulae[index])
+	} else {
+		panic(fmt.Sprintf("Instance has no child of index %d !", index))
+	}
+	return subFml
+}
+
+func (fml Formula) Pretty(preindentOpt ...string) string {
+	var preindent string = ""
+	if len(preindentOpt) > 0 {
+		preindent = preindentOpt[0]
+	}
+	return fml.pretty(preindent, "  ", "", 0)
+}
+
+func (fml Formula) pretty(preindent string, tab string, prepend string, depth int) string {
+	var indent string = preindent + strings.Repeat(tab, depth)
+	switch fml.valence {
+	case 0:
+		switch kind := fml.kind; kind {
+		case "atom", "generic":
+			return indent + prepend + kind + " " + fml.expr
+		default:
+			return indent + prepend + kind
+		}
+	default:
+		var lines string = indent + prepend + fml.kind
+		prepend = "|__ "
+		for _, subFml := range fml.subformulae {
+			lines += "\n" + subFml.pretty(preindent, tab, prepend, depth+1)
+		}
+		return lines
+	}
+}
+
+// shallow copy
+func (fml Formula) Copy() Formula {
+	return Formula{
+		expr:        fml.expr,
+		kind:        fml.kind,
+		valence:     fml.valence,
+		subformulae: fml.subformulae,
+	}
+}
+
+func (fml Formula) Deepcopy() Formula {
+	var subFmls = make([](*Formula), len(fml.subformulae))
+	for i, subFml := range fml.subformulae {
+		subFmlCopy := subFml.Deepcopy()
+		subFmls[i] = &subFmlCopy
+	}
+	return Formula{
+		expr:        fml.expr,
+		kind:        fml.kind,
+		valence:     fml.valence,
+		subformulae: subFmls,
+	}
+}
+
+/* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ *
+ * METHODS: Recognition of Formula-Types
+ * ---------------------------------------------------------------- */
+
+func (fml Formula) IsIrreducible() bool         { return fml.valence == 0 }
+func (fml Formula) IsAtom() bool                { return fml.kind == "atom" }
+func (fml Formula) IsPositiveLiteral() bool     { return fml.IsAtom() }
+func (fml Formula) IsNegativeLiteral() bool     { return fml.IsNegation() && fml.GetChild().IsAtom() }
+func (fml Formula) IsLiteral() bool             { return fml.IsPositiveLiteral() || fml.IsNegativeLiteral() }
+func (fml Formula) IsGeneric() bool             { return fml.kind == "generic" }
+func (fml Formula) IsTautologySymbol() bool     { return fml.kind == "taut" }
+func (fml Formula) IsContradictionSymbol() bool { return fml.kind == "contradiction" }
+func (fml Formula) IsConnective() bool          { return fml.valence > 0 }
+func (fml Formula) IsNegation() bool            { return fml.kind == "not" }
+func (fml Formula) IsConjunction2() bool        { return fml.kind == "and2" }
+func (fml Formula) IsConjunction() bool         { return fml.kind == "and" || fml.kind == "and2" }
+func (fml Formula) IsDisjunction2() bool        { return fml.kind == "or2" }
+func (fml Formula) IsDisjunction() bool         { return fml.kind == "or" || fml.kind == "or2" }
+func (fml Formula) IsImplication() bool         { return fml.kind == "implies" }
+func (fml Formula) IsDoubleImplication() bool   { return fml.kind == "iff" }

codego/aussagenlogik/formulae/formulae_construction.go

@@ -0,0 +1,147 @@
+package formulae
+
+/* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ *
+ * CONSTANTS
+ * ---------------------------------------------------------------- */
+
+var Tautology = Formula{
+	kind:        "taut",
+	expr:        "1",
+	valence:     0,
+	subformulae: [](*Formula){},
+}
+
+var Contradiction = Formula{
+	kind:        "contradiction",
+	expr:        "0",
+	valence:     0,
+	subformulae: [](*Formula){},
+}
+
+/* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ *
+ * METHODS: Constructions
+ * ---------------------------------------------------------------- */
+
+func Atom(name string) Formula {
+	return Formula{
+		kind:        "atom",
+		name:        name,
+		expr:        name,
+		valence:     0,
+		subformulae: [](*Formula){},
+	}
+}
+
+func NegatedAtom(name string) Formula {
+	return Negation(Atom(name))
+}
+
+func Generic(name string) Formula {
+	return Formula{
+		kind:        "generic",
+		name:        name,
+		expr:        "{" + name + "}",
+		valence:     0,
+		subformulae: [](*Formula){},
+	}
+}
+
+func Negation(fml Formula) Formula {
+	var name string
+	if fml.IsAtom() {
+		name = fml.GetName()
+	}
+	var expr = fml.expr
+	expr = "!" + expr
+	return Formula{
+		kind:        "not",
+		name:        name, // preserves name of negated atoms
+		expr:        expr,
+		valence:     1,
+		subformulae: [](*Formula){&fml},
+	}
+}
+
+func Conjunction2(fml1 Formula, fml2 Formula) Formula {
+	return Formula{
+		kind:        "and2",
+		expr:        "(" + fml1.expr + " && " + fml2.expr + ")",
+		valence:     2,
+		subformulae: [](*Formula){&fml1, &fml2},
+	}
+}
+
+func Conjunction(fmls []Formula) Formula {
+	switch len(fmls) {
+	case 0:
+		return Tautology
+	case 1:
+		return fmls[0]
+	}
+	var expr string = ""
+	var subFmls = make([](*Formula), len(fmls))
+	for i, fml := range fmls {
+		(func(i int, subFml Formula) { subFmls[i] = &subFml })(i, fml)
+		if i > 0 {
+			expr += " && "
+		}
+		expr += fml.expr
+	}
+	return Formula{
+		kind:        "and",
+		expr:        "(" + expr + ")",
+		valence:     len(subFmls),
+		subformulae: subFmls,
+	}
+}
+
+func Disjunction2(fml1 Formula, fml2 Formula) Formula {
+	return Formula{
+		kind:        "or2",
+		expr:        "(" + fml1.expr + " || " + fml2.expr + ")",
+		valence:     2,
+		subformulae: [](*Formula){&fml1, &fml2},
+	}
+}
+
+func Disjunction(fmls []Formula) Formula {
+	switch len(fmls) {
+	case 0:
+		return Contradiction
+	case 1:
+		return fmls[0]
+	}
+	var expr string = ""
+	var subFmls = make([](*Formula), len(fmls))
+	for i, fml := range fmls {
+		(func(i int, subFml Formula) { subFmls[i] = &subFml })(i, fml)
+		if i > 0 {
+			expr += " || "
+		}
+		expr += fml.expr
+	}
+	return Formula{
+		kind:        "or",
+		expr:        "(" + expr + ")",
+		valence:     len(subFmls),
+		subformulae: subFmls,
+	}
+}
+
+func Implies(fml1 Formula, fml2 Formula) Formula {
+	return Formula{
+		kind:        "implies",
+		expr:        "(" + fml1.expr + " -> " + fml2.expr + ")",
+		valence:     2,
+		subformulae: [](*Formula){&fml1, &fml2},
+	}
+}
+
+func DoubleImplication(fml1 Formula, fml2 Formula) Formula {
+	return Formula{
+		kind:        "iff",
+		expr:        "(" + fml1.expr + " <-> " + fml2.expr + ")",
+		valence:     2,
+		subformulae: [](*Formula){&fml1, &fml2},
+	}
+}

codego/aussagenlogik/formulae/formulae_generate.go

@@ -0,0 +1,165 @@
+package formulae
+
+// NOTE: GoLang hat noch keine generics. Erst 2022.
+
+/* ---------------------------------------------------------------- *
+ * Generate int-value FN from scheme
+ * ---------------------------------------------------------------- */
+
+func CreateFromSchemeIntValued(scheme func(fml Formula, prevValues []int) int) func(fml Formula) int {
+	var fn func(fml Formula) int
+	var subFn = func(ch chan int, subFml Formula) { ch <- fn(subFml) }
+	fn = func(fml Formula) int {
+		var subFmls = fml.GetSubFormulae()
+		var n = len(subFmls)
+		var subChan = make([](chan int), n)
+		var prevValues = make([]int, len(subFmls))
+		// start parallel computations on subformulas
+		for i, subFml := range subFmls {
+			subChan[i] = make(chan int) // create Channel, since currently nil
+			go subFn(subChan[i], subFml)
+		}
+		// successively read values
+		for i := 0; i < n; i++ {
+			prevValues[i] = <-subChan[i]
+		}
+		// apply schema to get value for formula
+		return scheme(fml, prevValues)
+	}
+	return fn
+}
+
+/* ---------------------------------------------------------------- *
+ * Generate string-value FN from scheme
+ * ---------------------------------------------------------------- */
+
+func CreateFromSchemeStringValued(scheme func(fml Formula, prevValues []string) string) func(fml Formula) string {
+	var fn func(fml Formula) string
+	var subFn = func(ch chan string, subFml Formula) { ch <- fn(subFml) }
+	fn = func(fml Formula) string {
+		var subFmls = fml.GetSubFormulae()
+		var n = len(subFmls)
+		var subChan = make([](chan string), n)
+		var prevValues = make([]string, len(subFmls))
+		// start parallel computations on subformulas
+		for i, subFml := range subFmls {
+			subChan[i] = make(chan string) // create Channel, since currently nil
+			go subFn(subChan[i], subFml)
+		}
+		// successively read values
+		for i := 0; i < n; i++ {
+			prevValues[i] = <-subChan[i]
+		}
+		// apply schema to get value for formula
+		return scheme(fml, prevValues)
+	}
+	return fn
+}
+
+/* ---------------------------------------------------------------- *
+ * Generate *[]string-value Fn from scheme
+ * ---------------------------------------------------------------- */
+
+func CreateFromSchemeStringsValued(scheme func(fml Formula, prevValues [][]string) []string) func(fml Formula) []string {
+	var fn func(fml Formula) []string
+	var subFn = func(ch chan []string, subFml Formula) { ch <- fn(subFml) }
+	fn = func(fml Formula) []string {
+		var subFmls = fml.GetSubFormulae()
+		var n = len(subFmls)
+		var subChan = make([](chan []string), n)
+		var prevValues = make([][]string, len(subFmls))
+		// start parallel computations on subformulas
+		for i, subFml := range subFmls {
+			subChan[i] = make(chan []string) // create Channel, since currently nil
+			go subFn(subChan[i], subFml)
+		}
+		// successively read values
+		for i := 0; i < n; i++ {
+			prevValues[i] = <-subChan[i]
+		}
+		// apply schema to get value for formula
+		return scheme(fml, prevValues)
+	}
+	return fn
+}
+
+/* ---------------------------------------------------------------- *
+ * Generate Formula-value Fn from scheme
+ * ---------------------------------------------------------------- */
+
+func CreateFromSchemeFmlValued(scheme func(fml Formula, prevValues []Formula) Formula) func(fml Formula) Formula {
+	var fn func(fml Formula) Formula
+	var subFn = func(ch chan Formula, subFml Formula) { ch <- fn(subFml) }
+	fn = func(fml Formula) Formula {
+		var subFmls = fml.GetSubFormulae()
+		var n = len(subFmls)
+		var subChan = make([](chan Formula), n)
+		var prevValues = make([]Formula, len(subFmls))
+		// start parallel computations on subformulas
+		for i, subFml := range subFmls {
+			subChan[i] = make(chan Formula) // create Channel, since currently nil
+			go subFn(subChan[i], subFml)
+		}
+		// successively read values
+		for i := 0; i < n; i++ {
+			prevValues[i] = <-subChan[i]
+		}
+		// apply schema to get value for formula
+		return scheme(fml, prevValues)
+	}
+	return fn
+}
+
+/* ---------------------------------------------------------------- *
+ * Generate *[]Formula-value Fn from scheme
+ * ---------------------------------------------------------------- */
+
+func CreateFromSchemeFmlsValued(scheme func(fml Formula, prevValues [](*[]Formula)) *[]Formula) func(fml Formula) *[]Formula {
+	var fn func(fml Formula) *[]Formula
+	var subFn = func(ch chan *[]Formula, subFml Formula) { ch <- fn(subFml) }
+	fn = func(fml Formula) *[]Formula {
+		var subFmls = fml.GetSubFormulae()
+		var n = len(subFmls)
+		var subChan = make([](chan *[]Formula), n)
+		var prevValues = make([](*[]Formula), len(subFmls))
+		// start parallel computations on subformulas
+		for i, subFml := range subFmls {
+			subChan[i] = make(chan *[]Formula) // create Channel, since currently nil
+			go subFn(subChan[i], subFml)
+		}
+		// successively read values
+		for i := 0; i < n; i++ {
+			prevValues[i] = <-subChan[i]
+		}
+		// apply schema to get value for formula
+		return scheme(fml, prevValues)
+	}
+	return fn
+}
+
+/* ---------------------------------------------------------------- *
+ * Generate {pos: Formula, ne: Formula}-value Fn from scheme
+ * ---------------------------------------------------------------- */
+
+func CreateFromSchemeFmlPairValued(scheme func(fml Formula, prevValues []FormulaPair) FormulaPair) func(fml Formula) FormulaPair {
+	var fn func(fml Formula) FormulaPair
+	var subFn = func(ch chan FormulaPair, subFml Formula) { ch <- fn(subFml) }
+	fn = func(fml Formula) FormulaPair {
+		var subFmls = fml.GetSubFormulae()
+		var n = len(subFmls)
+		var subChan = make([](chan FormulaPair), n)
+		var prevValues = make([]FormulaPair, len(subFmls))
+		// start parallel computations on subformulas
+		for i, subFml := range subFmls {
+			subChan[i] = make(chan FormulaPair) // create Channel, since currently nil
+			go subFn(subChan[i], subFml)
+		}
+		// successively read values
+		for i := 0; i < n; i++ {
+			prevValues[i] = <-subChan[i]
+		}
+		// apply schema to get value for formula
+		return scheme(fml, prevValues)
+	}
+	return fn
+}

codego/aussagenlogik/formulae/formulae_normalforms.go

@@ -0,0 +1,151 @@
+package formulae
+
+/* ---------------------------------------------------------------- *
+ * METHODS: get KNF/DNF
+ * ---------------------------------------------------------------- */
+
+func (fml Formula) GetKNFparts() FormulaKNF {
+	var subFmls []Formula
+	if fml.IsDisjunctOfLiterals() {
+		subFmls = []Formula{fml}
+	} else if fml.IsKNF() {
+		subFmls = fml.GetSubFormulae()
+	} else {
+		panic("Formula not in KNF!")
+	}
+	var terms = make([]FormulaDisjunct, len(subFmls))
+	for i, subFml := range subFmls {
+		if subFml.IsLiteral() {
+			terms[i] = []Formula{subFml}
+		} else {
+			terms[i] = subFml.GetSubFormulae()
+		}
+	}
+	return terms
+}
+
+func (fml Formula) GetDNFparts() FormulaDNF {
+	var subFmls []Formula
+	if fml.IsDisjunctOfLiterals() {
+		subFmls = []Formula{fml}
+	} else if fml.IsKNF() {
+		subFmls = fml.GetSubFormulae()
+	} else {
+		panic("Formula not in DNF!")
+	}
+	var terms = make([]FormulaConjunct, len(subFmls))
+	for i, subFml := range subFmls {
+		if subFml.IsLiteral() {
+			terms[i] = []Formula{subFml}
+		} else {
+			terms[i] = subFml.GetSubFormulae()
+		}
+	}
+	return terms
+}
+
+func (fml Formula) GetHornParts() FormulaHorn {
+	var subFmls []Formula
+	if fml.IsHornClause() {
+		subFmls = []Formula{fml}
+	} else if fml.IsHornFml() {
+		subFmls = fml.GetSubFormulae()
+	} else {
+		panic("Formula not a Horn-Formula!")
+	}
+	var parts = make([]FormulaHornClause, len(subFmls))
+	for i, subFml := range subFmls {
+		Pos := []Formula{}
+		Neg := []Formula{}
+		var subSubFml []Formula
+		if subFml.IsLiteral() {
+			subSubFml = []Formula{subFml}
+		} else {
+			subSubFml = subFml.GetSubFormulae()
+		}
+		for _, L := range subSubFml {
+			if L.IsPositiveLiteral() {
+				Pos = append(Pos, L)
+			} else {
+				Neg = append(Neg, L.GetChild())
+			}
+		}
+		parts[i] = FormulaHornClause{Pos, Neg}
+	}
+	return parts
+}
+
+/* ---------------------------------------------------------------- *
+ * METHODS: check if KNF/DNF
+ * ---------------------------------------------------------------- */
+
+func onlyLiterals(fmls []Formula) bool {
+	for _, fml := range fmls {
+		if !fml.IsLiteral() {
+			return false
+		}
+	}
+	return true
+}
+
+func numPositiveLiterals(fmls []Formula) int {
+	var n = 0
+	for _, fml := range fmls {
+		if fml.IsPositiveLiteral() {
+			n++
+		}
+	}
+	return n
+}
+
+func (fml Formula) IsConjunctOfLiterals() bool {
+	return fml.IsLiteral() || (fml.IsConjunction() && onlyLiterals(fml.GetSubFormulae()))
+}
+
+func (fml Formula) IsDisjunctOfLiterals() bool {
+	return fml.IsLiteral() || (fml.IsDisjunction() && onlyLiterals(fml.GetSubFormulae()))
+}
+
+func (fml Formula) IsHornClause() bool {
+	var literals = fml.GetSubFormulae()
+	return fml.IsLiteral() || (fml.IsDisjunction() && onlyLiterals(literals) && (numPositiveLiterals(literals) <= 1))
+}
+
+func (fml Formula) IsKNF() bool {
+	if fml.IsConjunction() {
+		for _, subFml := range fml.GetSubFormulae() {
+			if !subFml.IsDisjunctOfLiterals() {
+				return false
+			}
+		}
+		return true
+	} else {
+		return fml.IsDisjunctOfLiterals()
+	}
+}
+
+func (fml Formula) IsDNF() bool {
+	if fml.IsDisjunction() {
+		for _, subFml := range fml.GetSubFormulae() {
+			if !subFml.IsConjunctOfLiterals() {
+				return false
+			}
+		}
+		return true
+	} else {
+		return fml.IsConjunctOfLiterals()
+	}
+}
+
+func (fml Formula) IsHornFml() bool {
+	if fml.IsConjunction() {
+		for _, subFml := range fml.GetSubFormulae() {
+			if !subFml.IsHornClause() {
+				return false
+			}
+		}
+		return true
+	} else {
+		return fml.IsHornClause()
+	}
+}

codego/aussagenlogik/formulae/formulae_test.go

@@ -0,0 +1,158 @@
+package formulae_test
+
+/* ---------------------------------------------------------------- *
+ * UNIT TESTING
+ * ---------------------------------------------------------------- */
+
+import (
+	"logik/aussagenlogik/formulae"
+	"logik/aussagenlogik/schema"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE KNF
+ * ---------------------------------------------------------------- */
+
+func TestRecogniseKNF(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+
+	fml = schema.ParseExpr("A7")
+	assert.True(fml.IsKNF())
+	fml = schema.ParseExpr("! A7")
+	assert.True(fml.IsKNF())
+	fml = schema.ParseExpr("!! A7")
+	assert.False(fml.IsKNF())
+
+	fml = schema.ParseExpr("(A0 || ! A1 || A7)")
+	assert.True(fml.IsKNF())
+	fml = schema.ParseExpr("(A0 && ! A1 && A7)")
+	assert.True(fml.IsKNF())
+	fml = schema.ParseExpr("(A0 && !! A1 && A7)")
+	assert.False(fml.IsKNF())
+
+	fml = schema.ParseExpr("(A0 || ! A1 || A7) && (A4 || ! A5) && A1")
+	assert.True(fml.IsKNF())
+	fml = schema.ParseExpr("(A0 && ! A1 && A7) || (A4 && ! A5) || A1")
+	assert.False(fml.IsKNF())
+	fml = schema.ParseExpr("((A0 || ! A1 || A7) && (A4 || ! A5)) || A8")
+	assert.False(fml.IsKNF())
+}
+
+func TestRecogniseDNF(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+
+	fml = schema.ParseExpr("A7")
+	assert.True(fml.IsDNF())
+	fml = schema.ParseExpr("! A7")
+	assert.True(fml.IsDNF())
+	fml = schema.ParseExpr("!! A7")
+	assert.False(fml.IsDNF())
+
+	fml = schema.ParseExpr("(A0 && ! A1 && A7)")
+	assert.True(fml.IsDNF())
+	fml = schema.ParseExpr("(A0 || ! A1 || A7)")
+	assert.True(fml.IsDNF())
+	fml = schema.ParseExpr("(A0 || !! A1 || A7)")
+	assert.False(fml.IsDNF())
+
+	fml = schema.ParseExpr("(A0 && ! A1 && A7) || (A4 && ! A5) || A1")
+	assert.True(fml.IsDNF())
+	fml = schema.ParseExpr("(A0 || ! A1 || A7) && (A4 || ! A5) && A1")
+	assert.False(fml.IsDNF())
+	fml = schema.ParseExpr("((A0 && ! A1 && A7) || (A4 && ! A5)) && A8")
+	assert.False(fml.IsDNF())
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE Horn
+ * ---------------------------------------------------------------- */
+
+func TestRecogniseHorn(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+
+	fml = schema.ParseExpr("A7")
+	assert.True(fml.IsHornFml())
+	fml = schema.ParseExpr("! A7")
+	assert.True(fml.IsHornFml())
+	fml = schema.ParseExpr("!! A7")
+	assert.False(fml.IsHornFml())
+
+	fml = schema.ParseExpr("(! A0 || ! A1 || A7)")
+	assert.True(fml.IsHornFml())
+	fml = schema.ParseExpr("(A0 && ! A1 && A7)")
+	assert.True(fml.IsHornFml())
+	fml = schema.ParseExpr("(A0 && !! A1 && A7)")
+	assert.False(fml.IsHornFml())
+
+	fml = schema.ParseExpr("(A0 && ! A1 && ! A7) || (A4 && ! A5) || (! A1 && ! A8)")
+	assert.False(fml.IsHornFml())
+	fml = schema.ParseExpr("(A0 && ! A1 && ! A7) || (A4 && ! A5) || (! A1 && ! A8)")
+	assert.False(fml.IsHornFml())
+	fml = schema.ParseExpr("(A0 || ! A1 || ! A7) && (A4 || ! A5) && (! A1 || ! A8)")
+	assert.True(fml.IsHornFml())
+	fml = schema.ParseExpr("((A0 || ! A1 || A7) && (A4 || ! A5)) || A8")
+	assert.False(fml.IsHornFml())
+}
+
+func TestTransformHornToFormula(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var horn formulae.FormulaHorn
+	var hornClauses []formulae.FormulaHornClause
+
+	fml = schema.ParseExpr("A8")
+	assert.True(fml.IsHornFml())
+	horn = fml.GetHornParts()
+	hornClauses = horn
+	assert.Equal(1, len(hornClauses))
+	assert.ElementsMatch([]string{"A8"}, hornClauses[0].Pos.GetAtoms())
+	assert.ElementsMatch([]string{}, hornClauses[0].Neg.GetAtoms())
+	assert.Equal("(1 -> A8)", horn.ToFormula().GetExpr())
+
+	fml = schema.ParseExpr("!A8")
+	assert.True(fml.IsHornFml())
+	horn = fml.GetHornParts()
+	hornClauses = horn
+	assert.Equal(1, len(hornClauses))
+	assert.ElementsMatch([]string{}, hornClauses[0].Pos.GetAtoms())
+	assert.ElementsMatch([]string{"A8"}, hornClauses[0].Neg.GetAtoms())
+	assert.Equal("(A8 -> 0)", horn.ToFormula().GetExpr())
+
+	fml = schema.ParseExpr("!A3 || A2 || !A7 || !A9")
+	assert.True(fml.IsHornFml())
+	horn = fml.GetHornParts()
+	hornClauses = horn
+	assert.Equal(1, len(hornClauses))
+	assert.ElementsMatch([]string{"A2"}, hornClauses[0].Pos.GetAtoms())
+	assert.ElementsMatch([]string{"A3", "A7", "A9"}, hornClauses[0].Neg.GetAtoms())
+	assert.Equal("((A3 && A7 && A9) -> A2)", horn.ToFormula().GetExpr())
+
+	fml = schema.ParseExpr("!A3 || !A2 || !A7 || !A9")
+	assert.True(fml.IsHornFml())
+	horn = fml.GetHornParts()
+	hornClauses = horn
+	assert.Equal(1, len(hornClauses))
+	assert.ElementsMatch([]string{}, hornClauses[0].Pos.GetAtoms())
+	assert.ElementsMatch([]string{"A2", "A3", "A7", "A9"}, hornClauses[0].Neg.GetAtoms())
+	assert.Equal("((A3 && A2 && A7 && A9) -> 0)", horn.ToFormula().GetExpr())
+
+	fml = schema.ParseExpr("!A3 && A2 && !A7 && A9 && A7")
+	assert.True(fml.IsHornFml())
+	horn = fml.GetHornParts()
+	hornClauses = horn
+	assert.Equal(5, len(hornClauses))
+	assert.Equal("((A3 -> 0) && (1 -> A2) && (A7 -> 0) && (1 -> A9) && (1 -> A7))", horn.ToFormula().GetExpr())
+
+	fml = schema.ParseExpr("(A0 || ! A1 || ! A7) && (A4 || ! A5) && (! A1 || ! A8)")
+	assert.True(fml.IsHornFml())
+	horn = fml.GetHornParts()
+	hornClauses = horn
+	assert.Equal(3, len(hornClauses))
+	assert.Equal("(((A1 && A7) -> A0) && (A5 -> A4) && ((A1 && A8) -> 0))", horn.ToFormula().GetExpr())
+}

codego/aussagenlogik/recursion/recursion_atoms.go

@@ -0,0 +1,35 @@
+package recursion
+
+import (
+	"logik/aussagenlogik/formulae"
+)
+
+/* ---------------------------------------------------------------- *
+ * METHOD: Atoms
+ * ---------------------------------------------------------------- */
+
+func Atoms(fml formulae.Formula) []string {
+	// Definiere Schema:
+	var schema = func(fml formulae.Formula, prevValues [][]string) []string {
+		// Herausforderung: schreibe diese Funktion!
+		return []string{}
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeStringsValued(schema)
+	return fn(fml)
+}
+
+/* ---------------------------------------------------------------- *
+ * METHOD: Subformulae
+ * ---------------------------------------------------------------- */
+
+func Subformulae(fml formulae.Formula) []string {
+	// Definiere Schema:
+	var schema = func(fml formulae.Formula, prevValues [][]string) []string {
+		// Herausforderung: schreibe diese Funktion!
+		return []string{}
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeStringsValued(schema)
+	return fn(fml)
+}

codego/aussagenlogik/recursion/recursion_count.go

@@ -0,0 +1,49 @@
+package recursion
+
+import (
+	"logik/aussagenlogik/formulae"
+)
+
+/* ---------------------------------------------------------------- *
+ * METHOD: Formula Depth
+ * ---------------------------------------------------------------- */
+
+func FmlDepth(fml formulae.Formula) int {
+	// Definiere Schema:
+	var schema = func(fml formulae.Formula, prevValues []int) int {
+		// Herausforderung: schreibe diese Funktion!
+		return 0
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeIntValued(schema)
+	return fn(fml)
+}
+
+/* ---------------------------------------------------------------- *
+ * METHOD: Formula Length
+ * ---------------------------------------------------------------- */
+
+func FmlLength(fml formulae.Formula) int {
+	// Definiere Schema:
+	var schema = func(fml formulae.Formula, prevValues []int) int {
+		// Herausforderung: schreibe diese Funktion!
+		return 0
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeIntValued(schema)
+	return fn(fml)
+}
+
+/* ---------------------------------------------------------------- *
+ * METHOD: Number of Parentheses
+ * ---------------------------------------------------------------- */
+func NrParentheses(fml formulae.Formula) int {
+	// Definiere Schema:
+	var schema = func(fml formulae.Formula, prevValues []int) int {
+		// Herausforderung: schreibe diese Funktion!
+		return 0
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeIntValued(schema)
+	return fn(fml)
+}

codego/aussagenlogik/recursion/recursion_eval.go

@@ -0,0 +1,44 @@
+package recursion
+
+import (
+	"logik/aussagenlogik/formulae"
+	"logik/core/utils"
+)
+
+/* ---------------------------------------------------------------- *
+ * METHOD: Evaluation of fomulae in models
+ * ---------------------------------------------------------------- */
+
+func Eval(fml formulae.Formula, I []string) int {
+	// Definiere (parameterisiertes) Schema:
+	var schema = func(_I []string) func(formulae.Formula, []int) int {
+		return func(fml formulae.Formula, prevValues []int) int {
+			if fml.IsAtom() || fml.IsGeneric() {
+				return utils.BoolToInt(utils.StrListContains(_I, fml.GetName()))
+			} else if fml.IsTautologySymbol() {
+				return 1
+			} else if fml.IsContradictionSymbol() {
+				return 0
+			} else if fml.IsNegation() {
+				return 1 - prevValues[0]
+			} else if fml.IsConjunction2() {
+				return utils.Min2(prevValues[0], prevValues[1])
+			} else if fml.IsConjunction() {
+				return utils.MinList(prevValues)
+			} else if fml.IsDisjunction2() {
+				return utils.Max2(prevValues[0], prevValues[1])
+			} else if fml.IsDisjunction() {
+				return utils.MaxList(prevValues)
+			} else if fml.IsImplication() {
+				return utils.BoolToInt(prevValues[0] <= prevValues[1])
+			} else if fml.IsDoubleImplication() {
+				return utils.BoolToInt(prevValues[0] == prevValues[1])
+			} else {
+				panic("Could not evaluate expression!")
+			}
+		}
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeIntValued(schema(I))
+	return fn(fml)
+}

codego/aussagenlogik/recursion/recursion_nnf.go

@@ -0,0 +1,88 @@
+package recursion
+
+import (
+	"logik/aussagenlogik/formulae"
+)
+
+/* ---------------------------------------------------------------- *
+ * METHOD: compute NNF
+ * ---------------------------------------------------------------- */
+
+// NOTE: diese bedarf einer Art Doppeltrekursion
+func NNF(fml formulae.Formula) formulae.Formula {
+	// Definiere Schema:
+	var schema = func(fml formulae.Formula, prevValues []formulae.FormulaPair) formulae.FormulaPair {
+		// separate out positive and negative parts:
+		var pairs = formulae.NewFormulaPairs(prevValues)
+		var prevPos = pairs.Pos()
+		var prevNeg = pairs.Neg()
+		// compute value from previous positive/negative parts:
+		if fml.IsPositiveLiteral() {
+			return formulae.FormulaPair{
+				Pos: fml.Deepcopy(),
+				Neg: formulae.Negation(fml),
+			}
+		} else if fml.IsNegativeLiteral() {
+			return formulae.FormulaPair{
+				Pos: fml.Deepcopy(),
+				Neg: prevPos[0],
+			}
+		} else if fml.IsTautologySymbol() {
+			return formulae.FormulaPair{
+				Pos: formulae.Tautology,
+				Neg: formulae.Contradiction,
+			}
+		} else if fml.IsContradictionSymbol() {
+			return formulae.FormulaPair{
+				Pos: formulae.Contradiction,
+				Neg: formulae.Tautology,
+			}
+		} else if fml.IsNegation() {
+			return formulae.FormulaPair{
+				Pos: prevNeg[0],
+				Neg: prevPos[0],
+			}
+		} else if fml.IsConjunction2() {
+			return formulae.FormulaPair{
+				Pos: formulae.Conjunction2(prevPos[0], prevPos[1]),
+				Neg: formulae.Disjunction2(prevNeg[0], prevNeg[1]),
+			}
+		} else if fml.IsConjunction() {
+			return formulae.FormulaPair{
+				Pos: formulae.Conjunction(prevPos),
+				Neg: formulae.Disjunction(prevNeg),
+			}
+		} else if fml.IsDisjunction2() {
+			return formulae.FormulaPair{
+				Pos: formulae.Disjunction2(prevPos[0], prevPos[1]),
+				Neg: formulae.Conjunction2(prevNeg[0], prevNeg[1]),
+			}
+		} else if fml.IsDisjunction() {
+			return formulae.FormulaPair{
+				Pos: formulae.Disjunction(prevPos),
+				Neg: formulae.Conjunction(prevNeg),
+			}
+		} else if fml.IsImplication() {
+			return formulae.FormulaPair{
+				Pos: formulae.Disjunction2(prevNeg[0], prevPos[1]),
+				Neg: formulae.Conjunction2(prevPos[0], prevNeg[1]),
+			}
+		} else if fml.IsDoubleImplication() {
+			return formulae.FormulaPair{
+				Pos: formulae.Conjunction2(
+					formulae.Disjunction2(prevNeg[0], prevPos[1]),
+					formulae.Disjunction2(prevNeg[1], prevPos[0]),
+				),
+				Neg: formulae.Disjunction2(
+					formulae.Conjunction2(prevPos[0], prevNeg[1]),
+					formulae.Conjunction2(prevPos[1], prevNeg[0]),
+				),
+			}
+		} else {
+			panic("Could not evaluate expression!")
+		}
+	}
+	// Erzeuge Funktion aus Schema und berechne Wert:
+	fn := formulae.CreateFromSchemeFmlPairValued(schema)
+	return fn(fml).Pos
+}

codego/aussagenlogik/recursion/recursion_test.go

@@ -0,0 +1,455 @@
+package recursion_test
+
+/* ---------------------------------------------------------------- *
+ * UNIT TESTING
+ * ---------------------------------------------------------------- */
+
+import (
+	"logik/aussagenlogik/formulae"
+	"logik/aussagenlogik/recursion"
+	"logik/aussagenlogik/schema"
+	"logik/core/utils"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE eval(·, ·)
+ * ---------------------------------------------------------------- */
+
+func TestEvalLiteral(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+
+	fml = schema.ParseExpr("A0")
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	fml = schema.ParseExpr("A0")
+	I = []string{}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	fml = schema.ParseExpr("! A0")
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	fml = schema.ParseExpr("! A0")
+	I = []string{}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+}
+
+func TestEvalNegation(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+
+	fml = schema.ParseExpr("A4 || ! A4")
+	I = []string{}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	fml = schema.ParseExpr("A4 && ! A4")
+	I = []string{}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+}
+
+func TestEvalConjunction(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+
+	fml = schema.ParseExpr("A0 && A1")
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	fml = schema.ParseExpr("A0 && A1")
+	I = []string{"A0", "A1"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+}
+
+func TestEvalDisjunction(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+
+	fml = schema.ParseExpr("A0 || A1")
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	fml = schema.ParseExpr("A0 || A1")
+	I = []string{"A7"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+}
+
+func TestEvalImplication(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+
+	fml = schema.ParseExpr("A0 -> A1")
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	fml = schema.ParseExpr("A0 -> A1")
+	I = []string{"A0", "A1"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	fml = schema.ParseExpr("A0 -> A1")
+	I = []string{"A7"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+}
+
+func TestEvalIff(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+
+	fml = schema.ParseExpr("A0 <-> A1")
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	fml = schema.ParseExpr("A0 <-> A1")
+	I = []string{"A0", "A1"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	fml = schema.ParseExpr("A0 <-> A1")
+	I = []string{"A7"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+}
+
+func TestEvalComplex(test *testing.T) {
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	var I []string
+	fml = schema.ParseExpr("( ! A0 || (( A0 && A3 ) || A2 ))")
+	I = []string{"A0", "A2"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	I = []string{"A0", "A3"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	I = []string{"A0"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	I = []string{"A4", "A8"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+
+	fml = schema.ParseExpr("( ! A0 || (( A0 && A3 ) || ! A2 ))")
+	I = []string{"A0", "A2"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(0, val)
+
+	I = []string{"A0", "A3"}
+	val = recursion.Eval(fml, I)
+	assert.Equal(1, val)
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE Atoms(·)
+ * ---------------------------------------------------------------- */
+
+func TestAtomsNoduplicates(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var val []string
+	fml = schema.ParseExpr("( A4 && ( A4 || A4 ))")
+	val = recursion.Atoms(fml)
+	var n int = len(utils.FilterStrings(&val, func(x string) bool { return x == "A4" }))
+	assert.Equal(1, n, "Atome dürfen nicht mehrfach vorkommen!")
+}
+
+func TestAtomsNoNonAtoms(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var val []string
+	fml = schema.ParseExpr("( {F} || A3 )")
+	val = recursion.Atoms(fml)
+	utils.SortStrings(&val)
+	assert.NotContains(val, "F", "Nichtatomare Formeln dürfen nicht vorkommen!")
+}
+
+func TestAtomsCalc1(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var val []string
+	fml = schema.ParseExpr("A0")
+	val = recursion.Atoms(fml)
+	assert.ElementsMatch([]string{"A0"}, val)
+}
+
+func TestAtomsCalc2(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var val []string
+	fml = schema.ParseExpr("((( ! A8 && A3 ) || A4 ) && A0 )")
+	val = recursion.Atoms(fml)
+	assert.ElementsMatch([]string{"A0", "A3", "A4", "A8"}, val)
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE depth(·, ·)
+ * ---------------------------------------------------------------- */
+
+func TestDepthCalc1(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("A0")
+	val = recursion.FmlDepth(fml)
+	assert.Equal(0, val)
+}
+
+func TestDepthCalc2(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("!! A8")
+	val = recursion.FmlDepth(fml)
+	assert.Equal(2, val)
+}
+
+func TestDepthCalc3(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("( ! A0 && A3 )")
+	val = recursion.FmlDepth(fml)
+	assert.Equal(2, val)
+}
+
+func TestDepthCalc4(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("((( ! A0 && A3 ) || A4 ) && A8 )")
+	val = recursion.FmlDepth(fml)
+	assert.Equal(4, val)
+}
+
+func TestDepthCalc5(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("! ((( ! A0 && A3 ) || A4 ) && A8 )")
+	val = recursion.FmlDepth(fml)
+	assert.Equal(5, val)
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE length(·)
+ * ---------------------------------------------------------------- */
+
+func TestLengthCalc1(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("A0")
+	val = recursion.FmlLength(fml)
+	assert.Equal(1, val)
+}
+
+func TestLengthCalc2(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("!! A8")
+	val = recursion.FmlLength(fml)
+	assert.Equal(3, val)
+}
+
+func TestLengthCalc3(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("( ! A0 && A3 )")
+	val = recursion.FmlLength(fml)
+	assert.Equal(4, val)
+}
+
+func TestLengthCalc4(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("((( ! A0 && A3 ) || A4 ) && A8 )")
+	val = recursion.FmlLength(fml)
+	assert.Equal(8, val)
+}
+
+func TestLengthCalc5(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("! ((( ! A0 && A3 ) || A4 ) && A8 )")
+	val = recursion.FmlLength(fml)
+	assert.Equal(9, val)
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE #Parentheses(·)
+ * ---------------------------------------------------------------- */
+
+func TestParenthesesCalc1(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("A0")
+	val = recursion.NrParentheses(fml)
+	assert.Equal(0, val)
+}
+
+func TestParenthesesCalc2(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("!! A8")
+	val = recursion.NrParentheses(fml)
+	assert.Equal(0, val)
+}
+
+func TestParenthesesCalc3(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("( ! A0 && A3 )")
+	val = recursion.NrParentheses(fml)
+	assert.Equal(2, val)
+}
+
+func TestParenthesesCalc4(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("((( ! A0 && A3 ) || A4 ) && A8 )")
+	val = recursion.NrParentheses(fml)
+	assert.Equal(6, val)
+}
+
+func TestParenthesesCalc5(test *testing.T) {
+	test.Skip("Methode noch nicht implementiert")
+	var assert = assert.New(test)
+	var val int
+	var fml formulae.Formula
+	fml = schema.ParseExpr("! ((( ! A0 && A3 ) || A4 ) && A8 )")
+	val = recursion.NrParentheses(fml)
+	assert.Equal(6, val)
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE NNF
+ * ---------------------------------------------------------------- */
+
+func TestNNFatoms(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var nnf_expected formulae.Formula
+
+	nnf_expected = formulae.Atom("A7")
+	fml = schema.ParseExpr("A7")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	fml = schema.ParseExpr("!! A7")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	nnf_expected = formulae.NegatedAtom("A7")
+	fml = schema.ParseExpr("! A7")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	fml = schema.ParseExpr("!!! A7")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+}
+
+func TestNNFconj(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var nnf_expected formulae.Formula
+
+	nnf_expected = formulae.Disjunction2(formulae.NegatedAtom("A0"), formulae.NegatedAtom("A1"))
+	fml = schema.ParseExpr("! (A0 && A1)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	nnf_expected = formulae.Disjunction2(formulae.Atom("A0"), formulae.Atom("A1"))
+	fml = schema.ParseExpr("! (! A0 && ! A1)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	nnf_expected = formulae.Conjunction2(formulae.Atom("A0"), formulae.NegatedAtom("A1"))
+	fml = schema.ParseExpr("(A0 && ! A1)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+}
+
+func TestNNFdisj(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var nnf_expected formulae.Formula
+
+	nnf_expected = formulae.Conjunction2(formulae.NegatedAtom("A0"), formulae.NegatedAtom("A1"))
+	fml = schema.ParseExpr("! (A0 || A1)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	nnf_expected = formulae.Conjunction2(formulae.Atom("A0"), formulae.Atom("A1"))
+	fml = schema.ParseExpr("! (! A0 || ! A1)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	nnf_expected = formulae.Disjunction2(formulae.Atom("A0"), formulae.NegatedAtom("A1"))
+	fml = schema.ParseExpr("(A0 || ! A1)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+}
+
+func TestNNFcalcComplex(test *testing.T) {
+	var assert = assert.New(test)
+	var fml formulae.Formula
+	var nnf_expected formulae.Formula
+
+	fml = schema.ParseExpr("! (! (!A0 || A1) || ! ! A8)")
+	nnf_expected = schema.ParseExpr("((!A0 || A1) && ! A8)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+
+	fml = schema.ParseExpr("! (! (!A0 || !(A1 && ! A7)) && ! A8)")
+	nnf_expected = schema.ParseExpr("((!A0 || (! A1 || A7)) || A8)")
+	assert.Equal(nnf_expected.GetExpr(), recursion.NNF(fml).GetExpr())
+}

codego/aussagenlogik/rekursion/rekursion.go

@@ -1,81 +0,0 @@
-package rekursion
-
-import (
-	"log"
-	"logik/aussagenlogik/syntaxbaum"
-	"logik/core/utils"
-)
-
-/* ---------------------------------------------------------------- *
- * EXPORTS
- * ---------------------------------------------------------------- */
-
-func RekursivEval(tree syntaxbaum.SyntaxBaum, I []string) int {
-	var children = tree.GetChildren()
-	if tree.IsAtom() || tree.IsGeneric() {
-		if utils.StrListContains(I, tree.Expr) {
-			return 1
-		}
-		return 0
-	} else if tree.IsTautologySymbol() {
-		return 1
-	} else if tree.IsContradictionSymbol() {
-		return 0
-	} else if tree.IsNegation() {
-		subtree0, _ := tree.GetChild()
-		val0 := RekursivEval(subtree0, I)
-		return 1 - val0
-	} else if tree.IsConjunction2() {
-		val0 := RekursivEval(children[0], I)
-		val1 := RekursivEval(children[1], I)
-		return utils.Min2(val0, val1)
-	} else if tree.IsConjunction() {
-		var val = 1
-		for _, subtree := range children {
-			var val_ = RekursivEval(subtree, I)
-			val = utils.Min2(val, val_)
-		}
-		return val
-	} else if tree.IsDisjunction2() {
-		val0 := RekursivEval(children[0], I)
-		val1 := RekursivEval(children[1], I)
-		return utils.Max2(val0, val1)
-	} else if tree.IsDisjunction() {
-		var val = 0
-		for _, subtree := range children {
-			var val_ = RekursivEval(subtree, I)
-			val = utils.Max2(val, val_)
-		}
-		return val
-	} else if tree.IsImplication() {
-		val0 := RekursivEval(children[0], I)
-		val1 := RekursivEval(children[1], I)
-		if val0 <= val1 {
-			return 1
-		}
-		return 0
-	} else {
-		log.Fatal("Could not evaluate expression!")
-		return 0
-	}
-}
-
-func RekursivAtoms(tree syntaxbaum.SyntaxBaum) []string {
-	// Herausforderung: schreibe diese Funktion!
-	return []string{}
-}
-
-func RekursivDepth(tree syntaxbaum.SyntaxBaum) int {
-	// Herausforderung: schreibe diese Funktion!
-	return 0
-}
-
-func RekursivLength(tree syntaxbaum.SyntaxBaum) int {
-	// Herausforderung: schreibe diese Funktion!
-	return 0
-}
-
-func RekursivParentheses(tree syntaxbaum.SyntaxBaum) int {
-	// Herausforderung: schreibe diese Funktion!
-	return 0
-}

codego/aussagenlogik/rekursion/rekursion_test.go

@@ -1,287 +0,0 @@
-package rekursion_test
-
-/* ---------------------------------------------------------------- *
- * UNIT TESTING
- * ---------------------------------------------------------------- */
-
-import (
-	"logik/aussagenlogik/rekursion"
-	"logik/aussagenlogik/schema"
-	"logik/aussagenlogik/syntaxbaum"
-	"logik/core/utils"
-	"testing"
-
-	"github.com/stretchr/testify/assert"
-)
-
-/* ---------------------------------------------------------------- *
- * TESTCASE eval(·, ·)
- * ---------------------------------------------------------------- */
-
-func TestRekursivEvalLiteral(test *testing.T) {
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var I []string
-	var val int
-	tree, _ = schema.ParseExpr("A0")
-	I = []string{"A0"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 1)
-	tree, _ = schema.ParseExpr("A0")
-	I = []string{}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 0)
-	tree, _ = schema.ParseExpr("! A0")
-	I = []string{"A0"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 0)
-	tree, _ = schema.ParseExpr("! A0")
-	I = []string{}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 1)
-}
-
-func TestRekursivEvalComplex1(test *testing.T) {
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var I []string
-	var val int
-	tree, _ = schema.ParseExpr("( ! A0 || (( A0 && A3 ) || A2 ))")
-	I = []string{"A0", "A2"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 1)
-	I = []string{"A0", "A3"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 1)
-	I = []string{"A0"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 0)
-	I = []string{"A4", "A8"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 1)
-}
-
-func TestRekursivEvalComplex2(test *testing.T) {
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var I []string
-	var val int
-	tree, _ = schema.ParseExpr("( ! A0 || (( A0 && A3 ) || ! A2 ))")
-	I = []string{"A0", "A2"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 0)
-	I = []string{"A0", "A3"}
-	val = rekursion.RekursivEval(tree, I)
-	assert.Equal(val, 1)
-}
-
-/* ---------------------------------------------------------------- *
- * TESTCASE Atoms(·)
- * ---------------------------------------------------------------- */
-
-func TestRekursivAtomsNoduplicates(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val []string
-	tree, _ = schema.ParseExpr("( A4 && ( A4 || A4 ))")
-	val = rekursion.RekursivAtoms(tree)
-	var n int = len(utils.FilterStrings(&val, func(x string) bool { return x == "A4" }))
-	assert.Equal(n, 1, "Atome dürfen nicht mehrfach vorkommen!")
-}
-
-func TestRekursivAtomsNononatoms(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	test.Skip("Syntax for generic expressions in ANTLR4 g4 needs to be implemented.")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val []string
-	tree, _ = schema.ParseExpr("( {F} || A3 )")
-	val = rekursion.RekursivAtoms(tree)
-	utils.SortStrings(&val)
-	assert.NotContains(val, "F", "Nichtatomare Formeln dürfen nicht vorkommen!")
-}
-
-func TestRekursivAtomsCalc1(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val []string
-	tree, _ = schema.ParseExpr("A0")
-	val = rekursion.RekursivAtoms(tree)
-	utils.SortStrings(&val)
-	assert.Equal(val, []string{"A0"})
-}
-
-func TestRekursivAtomsCalc2(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val []string
-	tree, _ = schema.ParseExpr("((( ! A8 && A3 ) || A4 ) && A0 )")
-	val = rekursion.RekursivAtoms(tree)
-	utils.SortStrings(&val)
-	assert.Equal(val, []string{"A0", "A3", "A4", "A8"})
-}
-
-/* ---------------------------------------------------------------- *
- * TESTCASE depth(·, ·)
- * ---------------------------------------------------------------- */
-
-func TestRekursivDepthCalc1(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("A0")
-	val = rekursion.RekursivDepth(tree)
-	assert.Equal(val, 0)
-}
-
-func TestRekursivDepthCalc2(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("!! A8")
-	val = rekursion.RekursivDepth(tree)
-	assert.Equal(val, 2)
-}
-
-func TestRekursivDepthCalc3(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("( ! A0 && A3 )")
-	val = rekursion.RekursivDepth(tree)
-	assert.Equal(val, 2)
-}
-
-func TestRekursivDepthCalc4(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("((( ! A0 && A3 ) || A4 ) && A8 )")
-	val = rekursion.RekursivDepth(tree)
-	assert.Equal(val, 4)
-}
-
-func TestRekursivDepthCalc5(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("! ((( ! A0 && A3 ) || A4 ) && A8 )")
-	val = rekursion.RekursivDepth(tree)
-	assert.Equal(val, 5)
-}
-
-/* ---------------------------------------------------------------- *
- * TESTCASE length(·)
- * ---------------------------------------------------------------- */
-
-func TestRekursivLengthCalc1(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("A0")
-	val = rekursion.RekursivLength(tree)
-	assert.Equal(val, 1)
-}
-
-func TestRekursivLengthCalc2(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("!! A8")
-	val = rekursion.RekursivLength(tree)
-	assert.Equal(val, 3)
-}
-
-func TestRekursivLengthCalc3(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("( ! A0 && A3 )")
-	val = rekursion.RekursivLength(tree)
-	assert.Equal(val, 4)
-}
-
-func TestRekursivLengthCalc4(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("((( ! A0 && A3 ) || A4 ) && A8 )")
-	val = rekursion.RekursivLength(tree)
-	assert.Equal(val, 8)
-}
-
-func TestRekursivLengthCalc5(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("! ((( ! A0 && A3 ) || A4 ) && A8 )")
-	val = rekursion.RekursivLength(tree)
-	assert.Equal(val, 9)
-}
-
-/* ---------------------------------------------------------------- *
- * TESTCASE #Parentheses(·)
- * ---------------------------------------------------------------- */
-
-func TestRekursivParenthesesCalc1(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("A0")
-	val = rekursion.RekursivParentheses(tree)
-	assert.Equal(val, 0)
-}
-
-func TestRekursivParenthesesCalc2(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("!! A8")
-	val = rekursion.RekursivParentheses(tree)
-	assert.Equal(val, 0)
-}
-
-func TestRekursivParenthesesCalc3(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("( ! A0 && A3 )")
-	val = rekursion.RekursivParentheses(tree)
-	assert.Equal(val, 2)
-}
-
-func TestRekursivParenthesesCalc4(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("((( ! A0 && A3 ) || A4 ) && A8 )")
-	val = rekursion.RekursivParentheses(tree)
-	assert.Equal(val, 6)
-}
-
-func TestRekursivParenthesesCalc5(test *testing.T) {
-	test.Skip("Methode noch nicht implementiert")
-	var assert = assert.New(test)
-	var tree syntaxbaum.SyntaxBaum
-	var val int
-	tree, _ = schema.ParseExpr("! ((( ! A0 && A3 ) || A4 ) && A8 )")
-	val = rekursion.RekursivParentheses(tree)
-	assert.Equal(val, 6)
-}

codego/aussagenlogik/schema/schema.go

@@ -1,10 +1,9 @@
 package schema
 
 import (
-	"errors"
-	"logik/aussagenlogik/syntaxbaum"
+	"logik/aussagenlogik/formulae"
 	parser "logik/grammars/aussagenlogik"
-	"strings"
+	"regexp"
 
 	"github.com/antlr/antlr4/runtime/Go/antlr"
 )
@@ -13,13 +12,13 @@ import (
  * EXPORTS
  * ---------------------------------------------------------------- */
 
-func ParseExpr(u string) (syntaxbaum.SyntaxBaum, error) {
+func ParseExpr(u string) formulae.Formula {
 	var lexer = createLexer(u)
 	var tokenStream = lexerToTokenStream(lexer)
 	var prs = parser.NewaussagenlogikParser(tokenStream)
 	var t = prs.Start()
-	tree, err := createSyntaxBaum(t, prs)
-	return tree, err
+	tree := createFormula(t, prs)
+	return tree
 }
 
 /* ---------------------------------------------------------------- *
@@ -39,9 +38,9 @@ func createLexer(u string) antlr.Lexer {
 	return parser.NewaussagenlogikLexer(stream)
 }
 
-func createSyntaxBaum(tree antlr.Tree, parser antlr.Parser) (syntaxbaum.SyntaxBaum, error) {
+func createFormula(tree antlr.Tree, parser antlr.Parser) formulae.Formula {
 	var ant = antlrTree{tree: tree, parser: &parser}
-	return ant.toSyntaxBaum()
+	return ant.toFormula()
 }
 
 /* ---------------------------------------------------------------- *
@@ -67,29 +66,18 @@ func (ant antlrTree) getLabel() string {
 }
 
 func (ant antlrTree) getTextContent() string {
-	var expr string = ant.getLabel()
-	for _, subant := range ant.getChildren() {
+	var expr string = ""
+	var subants = ant.getChildren()
+	if len(subants) == 0 {
+		return ant.getLabel()
+	}
+	for _, subant := range subants {
 		expr += subant.getTextContent()
 	}
 	return expr
 }
 
-func (ant antlrTree) getTextContentLeaves() string {
-	var expr string = ""
-	var subants = ant.getChildren()
-	if len(subants) == 0 {
-		expr = ant.getLabel()
-	} else {
-		for _, subant := range subants {
-			expr += subant.getTextContent()
-		}
-	}
-	return expr
-}
-
-func (ant antlrTree) toSyntaxBaum() (syntaxbaum.SyntaxBaum, error) {
-	var tree syntaxbaum.SyntaxBaum
-	var err error
+func (ant antlrTree) toFormula() formulae.Formula {
 	var label string = ant.getLabel()
 	var subants = ant.getChildren()
 	var nChildren = len(subants)
@@ -97,79 +85,83 @@ func (ant antlrTree) toSyntaxBaum() (syntaxbaum.SyntaxBaum, error) {
 	switch label {
 	case "start":
 		if nChildren == 1 {
-			return subants[0].toSyntaxBaum()
+			return subants[0].toFormula()
 		}
 	case "open":
 		if nChildren == 1 {
-			return subants[0].toSyntaxBaum()
+			return subants[0].toFormula()
 		}
 	case "closed":
 		switch nChildren {
 		case 1:
-			return subants[0].toSyntaxBaum()
+			return subants[0].toFormula()
+		// expr = ( expr )
 		case 3:
-			return subants[1].toSyntaxBaum()
+			return subants[1].toFormula()
 		}
 	case "atomic":
 		if nChildren == 1 {
-			subant := subants[0]
-			tree = syntaxbaum.SyntaxBaum{}
-			tree.Expr = subant.getTextContentLeaves()
-			tree.Kind = subant.getLabel()
-			tree.Children = [](*syntaxbaum.SyntaxBaum){}
-			tree.Valence = 0
-			return tree, nil
+			return subants[0].toFormula()
 		}
+	case "taut":
+		return formulae.Tautology
+	case "contradiction":
+		return formulae.Contradiction
+	case "atom":
+		name := ant.getTextContent()
+		return formulae.Atom(name)
+	case "generic":
+		re := regexp.MustCompile(`^{|}$`)
+		name := string(re.ReplaceAll([]byte(ant.getTextContent()), []byte("")))
+		return formulae.Generic(name)
 	case "not":
-		if nChildren == 2 { // Children: [NotSymbol, Teilformel]
-			subtree, err := subants[1].toSyntaxBaum()
-			tree = syntaxbaum.SyntaxBaum{}
-			tree.Expr = subants[0].getTextContent() + " " + subtree.Expr
-			tree.Kind = label
-			tree.Children = [](*syntaxbaum.SyntaxBaum){&subtree}
-			tree.Valence = 1
-			return tree, err
+		// NOTE: expr = ! expr
+		if nChildren == 2 {
+			return formulae.Negation(subants[1].toFormula())
 		}
-	case "and2", "and", "or2", "or", "implies":
+	case "and2":
+		// NOTE: expr = expr && expr
+		if nChildren == 3 {
+			return formulae.Conjunction2(subants[0].toFormula(), subants[2].toFormula())
+		}
+	case "or2":
+		// NOTE: expr = expr || expr
+		if nChildren == 3 {
+			return formulae.Disjunction2(subants[0].toFormula(), subants[2].toFormula())
+		}
+	case "implies":
+		// NOTE: expr = expr -> expr
+		if nChildren == 3 {
+			return formulae.Implies(subants[0].toFormula(), subants[2].toFormula())
+		}
+	case "iff":
+		// NOTE: expr = expr <=> expr
+		if nChildren == 3 {
+			return formulae.DoubleImplication(subants[0].toFormula(), subants[2].toFormula())
+		}
+	case "and", "or":
+		// NOTE: expr = expr op expr op ... op expr
 		var n int = int((len(subants) + 1) / 2)
 		if nChildren == 2*n-1 && n >= 2 {
-			var isSymb bool = false
-			var subtrees = make([](*syntaxbaum.SyntaxBaum), n)
+			var subtrees = make([]formulae.Formula, n)
+			var isSymb bool = true
 			var i int = 0
-			var expr string = ""
 			for _, subant := range subants {
 				if isSymb {
-					expr += " " + subant.getTextContent() + " "
-				} else {
-					subtree, err_ := subant.toSyntaxBaum()
-					if err_ != nil {
-						err = err_
-					}
-					subtrees[i] = &subtree
-					expr += " " + subtree.Expr + " "
+					subtrees[i] = subant.toFormula()
 					i++
 				}
+				// NOTE: infix notation: alternatives between expression and symbol
 				isSymb = !isSymb
 			}
-			expr = strings.Trim(expr, " ")
-			var lbrace string = "("
-			var rbrace string = ")"
-			// var lbrace string = "( "
-			// var rbrace string = " )"
-			// if strings.HasPrefix(expr, "(") {
-			// 	lbrace = "("
-			// }
-			// if strings.HasSuffix(expr, ")") {
-			// 	rbrace = ")"
-			// }
-			tree = syntaxbaum.SyntaxBaum{}
-			tree.Expr = lbrace + expr + rbrace
-			tree.Kind = label
-			tree.Children = subtrees
-			tree.Valence = n
-			return tree, err
+			switch label {
+			case "and":
+				return formulae.Conjunction(subtrees)
+			case "or":
+				return formulae.Disjunction(subtrees)
+			}
 		}
 	}
 
-	return tree, errors.New("Could not parse expression")
+	panic("Could not parse expression")
 }

codego/aussagenlogik/schema/schema_test.go

@@ -5,6 +5,7 @@ package schema_test
  * ---------------------------------------------------------------- */
 
 import (
+	"logik/aussagenlogik/formulae"
 	"logik/aussagenlogik/schema"
 	"testing"
 
@@ -17,6 +18,30 @@ import (
 
 func TestParseExpr(test *testing.T) {
 	var assert = assert.New(test)
-	assert.Equal(0, 0)
-	schema.ParseExpr("A0")
+	var tree formulae.Formula
+
+	tree = schema.ParseExpr("A8712")
+	assert.Equal("A8712", tree.GetExpr())
+	assert.Equal("atom", tree.GetKind())
+	assert.Equal(0, len(tree.GetSubFormulae()))
+
+	tree = schema.ParseExpr("A12")
+	assert.Equal("A12", tree.GetExpr())
+	assert.Equal("atom", tree.GetKind())
+	assert.Equal(0, len(tree.GetSubFormulae()))
+
+	tree = schema.ParseExpr("  ! A5  ")
+	assert.Equal("!A5", tree.GetExpr())
+	assert.Equal("not", tree.GetKind())
+	assert.Equal(1, len(tree.GetSubFormulae()))
+
+	tree = schema.ParseExpr("A0 -> A1")
+	assert.Equal("(A0 -> A1)", tree.GetExpr())
+	assert.Equal("implies", tree.GetKind())
+	assert.Equal(2, len(tree.GetSubFormulae()))
+
+	tree = schema.ParseExpr("(  A0 && ! !  A1) || A2")
+	assert.Equal("((A0 && !!A1) || A2)", tree.GetExpr())
+	assert.Equal("or2", tree.GetKind())
+	assert.Equal(2, len(tree.GetSubFormulae()))
 }

codego/aussagenlogik/syntaxbaum/syntaxbaum.go

@@ -1,134 +0,0 @@
-package syntaxbaum
-
-import (
-	"errors"
-	"fmt"
-	"strings"
-)
-
-type SyntaxBaum struct {
-	Kind     string
-	Expr     string
-	Valence  int
-	Children [](*SyntaxBaum)
-}
-
-/* ---------------------------------------------------------------- *
- * METHODS
- * ---------------------------------------------------------------- */
-
-func (tree SyntaxBaum) GetChildren() []SyntaxBaum {
-	var n int = tree.Valence
-	var children = make([]SyntaxBaum, n)
-	for i, subtreePtr := range tree.Children {
-		children[i] = *subtreePtr
-	}
-	return children
-}
-
-func (tree SyntaxBaum) GetChild(indexOpt ...int) (SyntaxBaum, error) {
-	var index int = 0
-	if len(indexOpt) > 0 {
-		index = indexOpt[0]
-	}
-	var subtree SyntaxBaum
-	var err error
-	if 0 <= index && index < tree.Valence {
-		subtree = *(tree.Children[index])
-	} else {
-		err = errors.New(fmt.Sprintf("Instance has no child of index %d !", index))
-	}
-	return subtree, err
-}
-
-func (tree SyntaxBaum) Pretty(preindentOpt ...string) string {
-	var preindent string = ""
-	if len(preindentOpt) > 0 {
-		preindent = preindentOpt[0]
-	}
-	return tree.pretty(preindent, "  ", "", 0)
-}
-
-func (tree SyntaxBaum) pretty(preindent string, tab string, prepend string, depth int) string {
-	var indent string = preindent + strings.Repeat(tab, depth)
-	switch tree.Valence {
-	case 0:
-		switch kind := tree.Kind; kind {
-		case "atom", "generic":
-			return indent + prepend + kind + " " + tree.Expr
-		default:
-			return indent + prepend + kind
-		}
-	default:
-		var lines string = indent + prepend + tree.Kind
-		prepend = "|__ "
-		for _, subtree := range tree.Children {
-			lines += "\n" + subtree.pretty(preindent, tab, prepend, depth+1)
-		}
-		return lines
-	}
-}
-
-// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-// METHODS: Recognitong of Formula-Types
-// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-func (tree SyntaxBaum) IsIrreducible() bool {
-	return tree.Valence == 0
-}
-
-func (tree SyntaxBaum) IsAtom() bool {
-	return tree.Kind == "atom"
-}
-
-func (tree SyntaxBaum) IsLiteral() bool {
-	if tree.IsAtom() {
-		return true
-	} else if tree.IsNegation() {
-		subtree, err := tree.GetChild()
-		if err == nil {
-			return subtree.IsAtom()
-		}
-	}
-	return false
-}
-
-func (tree SyntaxBaum) IsGeneric() bool {
-	return tree.Kind == "generic"
-}
-
-func (tree SyntaxBaum) IsTautologySymbol() bool {
-	return tree.Kind == "taut"
-}
-
-func (tree SyntaxBaum) IsContradictionSymbol() bool {
-	return tree.Kind == "contradiction"
-}
-
-func (tree SyntaxBaum) IsConnective() bool {
-	return tree.Valence > 0
-}
-
-func (tree SyntaxBaum) IsNegation() bool {
-	return tree.Kind == "not"
-}
-
-func (tree SyntaxBaum) IsConjunction2() bool {
-	return tree.Kind == "and2"
-}
-
-func (tree SyntaxBaum) IsConjunction() bool {
-	return tree.Kind == "and" || tree.Kind == "and2"
-}
-
-func (tree SyntaxBaum) IsDisjunction2() bool {
-	return tree.Kind == "or2"
-}
-
-func (tree SyntaxBaum) IsDisjunction() bool {
-	return tree.Kind == "or" || tree.Kind == "or2"
-}
-
-func (tree SyntaxBaum) IsImplication() bool {
-	return tree.Kind == "implies"
-}

codego/core/utils/utils.go

@@ -1,23 +1,38 @@
 package utils
 
 import (
+	"encoding/json"
 	"sort"
 	"strings"
 )
 
 /* ---------------------------------------------------------------- *
- * EXPORTS
+ * METHODS: json
  * ---------------------------------------------------------------- */
 
-func StrListContains(list []string, x string) bool {
-	for _, obj := range list {
-		if obj == x {
-			return true
-		}
+func JsonToArrayOfStrings(s string, value *[]string) {
+	var err error
+	err = json.Unmarshal([]byte(s), &value)
+	if err != nil {
+		panic(err)
 	}
-	return false
 }
 
+/* ---------------------------------------------------------------- *
+ * METHODS: conversion
+ * ---------------------------------------------------------------- */
+
+func BoolToInt(cond bool) int {
+	if cond {
+		return 1
+	}
+	return 0
+}
+
+/* ---------------------------------------------------------------- *
+ * METHODS: for integer lists
+ * ---------------------------------------------------------------- */
+
 func Min2(x int, y int) int {
 	if x <= y {
 		return x
@@ -32,6 +47,61 @@ func Max2(x int, y int) int {
 	return y
 }
 
+func MinList(x []int) int {
+	if len(x) == 0 {
+		panic("Cannot compute the maximum of an empty array.")
+	}
+	var val int = x[0]
+	for i, val_ := range x {
+		if i > 0 {
+			val = Min2(val, val_)
+		}
+	}
+	return val
+}
+
+func MaxList(x []int) int {
+	if len(x) == 0 {
+		panic("Cannot compute the maximum of an empty array.")
+	}
+	var val int = x[0]
+	for i, val_ := range x {
+		if i > 0 {
+			val = Max2(val, val_)
+		}
+	}
+	return val
+}
+
+func SumList(x []int) int {
+	var val int = 0
+	for _, val_ := range x {
+		val += val_
+	}
+	return val
+}
+
+/* ---------------------------------------------------------------- *
+ * METHODS: for string lists
+ * ---------------------------------------------------------------- */
+
+func CopyStringList(list []string) []string {
+	var listCopy = make([]string, len(list))
+	for i, value := range list {
+		listCopy[i] = value
+	}
+	return listCopy
+}
+
+func StrListContains(list []string, x string) bool {
+	for _, obj := range list {
+		if obj == x {
+			return true
+		}
+	}
+	return false
+}
+
 func SortStrings(list *[]string) {
 	sort.Slice(*list, func(i int, j int) bool {
 		u := strings.ToLower((*list)[i])
@@ -68,7 +138,8 @@ func UnionStrings2(list1 []string, list2 []string) []string {
 	return list
 }
 
-func UnionStringsTo(listTo *[]string, listFrom []string) {
+// assumes that listTo contains no duplicates
+func UnionStringsInPlace(listTo *[]string, listFrom []string) {
 	var mark = make(map[string]bool)
 	for _, item := range listFrom {
 		mark[item] = true
@@ -82,3 +153,23 @@ func UnionStringsTo(listTo *[]string, listFrom []string) {
 		}
 	}
 }
+
+func UnionStringsList(lists [][]string) []string {
+	var list = []string{}
+	for _, list_ := range lists {
+		UnionStringsInPlace(&list, list_)
+	}
+	return list
+}
+
+/* ---------------------------------------------------------------- *
+ * METHODS: for maps
+ * ---------------------------------------------------------------- */
+
+func CopyMapStringBool(m map[string]bool) map[string]bool {
+	var mCopy = map[string]bool{}
+	for key, value := range m {
+		mCopy[key] = value
+	}
+	return mCopy
+}

codego/core/utils/utils_test.go

@@ -12,6 +12,60 @@ import (
 	"github.com/stretchr/testify/assert"
 )
 
+/* ---------------------------------------------------------------- *
+ * TESTCASE JsonToArrayOfStrings
+ * ---------------------------------------------------------------- */
+
+func TestJsonToArrayOfStrings(test *testing.T) {
+	var assert = assert.New(test)
+	var result []string
+	utils.JsonToArrayOfStrings("[]", &result)
+	assert.ElementsMatch([]string{}, result)
+	utils.JsonToArrayOfStrings("[ \"ganymed\" ]", &result)
+	assert.ElementsMatch([]string{"ganymed"}, result)
+	utils.JsonToArrayOfStrings("[ \"ganymed\", \"io\" ]", &result)
+	assert.ElementsMatch([]string{"ganymed", "io"}, result)
+	assert.Panics(func() { utils.JsonToArrayOfStrings("[ 178 ]", &result) }, "Should panic if converting not a JSON-encoded array of strings!")
+	assert.Panics(func() { utils.JsonToArrayOfStrings("true", &result) }, "Should panic if converting not a JSON-encoded array of strings!")
+	assert.Panics(func() { utils.JsonToArrayOfStrings("", &result) }, "Should panic if converting not a JSON-encoded array of strings!")
+	assert.Panics(func() { utils.JsonToArrayOfStrings("nil", &result) }, "Should panic if converting not a JSON-encoded array of strings!")
+	assert.Panics(func() { utils.JsonToArrayOfStrings("\"somestring\"", &result) }, "Should panic if converting not a JSON-encoded array of strings!")
+	assert.Panics(func() { utils.JsonToArrayOfStrings("'somestring'", &result) }, "Should panic if converting not a JSON-encoded array of strings!")
+}
+
+/* ---------------------------------------------------------------- *
+ * TESTCASE Min2, Max2, MinList, MaxList, SumList
+ * ---------------------------------------------------------------- */
+
+func TestMin(test *testing.T) {
+	var assert = assert.New(test)
+	assert.Equal(3, utils.Min2(3, 8))
+	assert.Equal(8, utils.Min2(100, 8))
+	assert.Equal(50, utils.MinList([]int{50}))
+	assert.Equal(1, utils.MinList([]int{50, 1}))
+	assert.Equal(2, utils.MinList([]int{50, 34, 10, 2, 8, 89}))
+	assert.Panics(func() { utils.MinList([]int{}) }, "Min of list should panic on empty list!")
+}
+
+func TestMax(test *testing.T) {
+	var assert = assert.New(test)
+	assert.Equal(8, utils.Max2(3, 8))
+	assert.Equal(100, utils.Max2(100, 8))
+	assert.Equal(50, utils.MaxList([]int{50}))
+	assert.Equal(50, utils.MaxList([]int{50, 1}))
+	assert.Equal(89, utils.MaxList([]int{50, 34, 10, 2, 8, 89}))
+	assert.Panics(func() { utils.MaxList([]int{}) }, "Max of list should panic on empty list!")
+}
+
+func TestSumList(test *testing.T) {
+	var assert = assert.New(test)
+	assert.Equal(0, utils.SumList([]int{}), "Sum of empty list should be 0.")
+	assert.Equal(2198, utils.SumList([]int{2198}))
+	assert.Equal(15, utils.SumList([]int{0, 1, 2, 3, 4, 5}))
+	assert.Equal(1038, utils.SumList([]int{1000, 1, 37}))
+	assert.Equal(237, utils.SumList([]int{1000, -800, 37}))
+}
+
 /* ---------------------------------------------------------------- *
  * TESTCASE SortStrings
  * ---------------------------------------------------------------- */
@@ -19,8 +73,9 @@ import (
 func TestSortStrings(test *testing.T) {
 	var assert = assert.New(test)
 	var list = []string{"katze", "Hund", "baby", "Pluto", "Saturn", "Mond"}
+	// NOTE: here use .Equal and not .ElementsMatch, since order important.
 	utils.SortStrings(&list)
-	assert.Equal(list, []string{"baby", "Hund", "katze", "Mond", "Pluto", "Saturn"})
+	assert.Equal([]string{"baby", "Hund", "katze", "Mond", "Pluto", "Saturn"}, list)
 }
 
 /* ---------------------------------------------------------------- *
@@ -31,11 +86,11 @@ func TestFilterStrings(test *testing.T) {
 	var assert = assert.New(test)
 	var list = []string{"abram", "aaron", "aardvark", "aarhus", "alaska", "eel", "aal"}
 	var list2 = utils.FilterStrings(&list, func(x string) bool { return strings.HasPrefix(x, "aa") })
-	assert.Equal(list2, []string{"aaron", "aardvark", "aarhus", "aal"})
+	assert.ElementsMatch([]string{"aaron", "aardvark", "aarhus", "aal"}, list2)
 }
 
 /* ---------------------------------------------------------------- *
- * TESTCASE UnionStrings2, UnionStringsTo
+ * TESTCASE UnionStrings2, UnionStringsInPlace, UnionStringsList
  * ---------------------------------------------------------------- */
 
 func TestUnionStrings2(test *testing.T) {
@@ -43,15 +98,22 @@ func TestUnionStrings2(test *testing.T) {
 	var list1 = []string{"red", "blue", "blue", "green", "blue", "grey", "black", "green"}
 	var list2 = []string{"yellow", "orange", "lila", "red"}
 	var list = utils.UnionStrings2(list1, list2)
-	utils.SortStrings(&list)
-	assert.Equal(list, []string{"black", "blue", "green", "grey", "lila", "orange", "red", "yellow"})
+	assert.ElementsMatch([]string{"black", "blue", "green", "grey", "lila", "orange", "red", "yellow"}, list)
 }
 
-func UnionStringsTo(test *testing.T) {
+func TestUnionStringsInPlace(test *testing.T) {
 	var assert = assert.New(test)
-	var list1 = []string{"red", "blue", "blue", "green"}
-	var list2 = []string{"yellow", "red", "black"}
-	utils.UnionStringsTo(&list1, list2)
-	utils.SortStrings(&list1)
-	assert.Equal(list1, []string{"black", "blue", "green", "red", "yellow"})
+	var list1 = []string{"red", "blue", "green"}
+	var list2 = []string{"yellow", "red", "blue", "red", "black"}
+	utils.UnionStringsInPlace(&list1, list2)
+	assert.ElementsMatch([]string{"black", "blue", "green", "red", "yellow"}, list1)
+}
+
+func TestUnionStringsList(test *testing.T) {
+	var assert = assert.New(test)
+	var list []string
+	var lists [][]string
+	lists = [][]string{{"red", "blue", "blue", "green"}, {"yellow", "red", "black"}}
+	list = utils.UnionStringsList(lists)
+	assert.ElementsMatch([]string{"black", "blue", "green", "red", "yellow"}, list)
 }

codego/go.sum

@@ -12,25 +12,19 @@ github.com/stretchr/objx v0.1.0 h1:4G4v2dO3VZwixGIRoQ5Lfboy6nUhCyYzaqnIAPPhYs4=
 github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
 github.com/stretchr/testify v1.7.0 h1:nwc3DEeHmmLAfoZucVR881uASk0Mfjw8xYJ99tb5CcY=
 github.com/stretchr/testify v1.7.0/go.mod h1:6Fq8oRcR53rry900zMqJjRRixrwX3KX962/h/Wwjteg=
-github.com/yuin/goldmark v1.2.1/go.mod h1:3hX8gzYuyVAZsxl0MRgGTJEmQBFcNTphYh9decYSb74=
 github.com/yuin/goldmark v1.3.5/go.mod h1:mwnBkeHKe2W/ZEtQ+71ViKU8L12m81fl3OWwC1Zlc8k=
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2/go.mod h1:djNgcEr1/C05ACkg1iLfiJU5Ep61QUkGW8qpdssI0+w=
 golang.org/x/crypto v0.0.0-20191011191535-87dc89f01550/go.mod h1:yigFU9vqHzYiE8UmvKecakEJjdnWj3jj499lnFckfCI=
 golang.org/x/crypto v0.0.0-20200622213623-75b288015ac9/go.mod h1:LzIPMQfyMNhhGPhUkYOs5KpL4U8rLKemX1yGLhDgUto=
-golang.org/x/mod v0.3.0/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
 golang.org/x/mod v0.4.2/go.mod h1:s0Qsj1ACt9ePp/hMypM3fl4fZqREWJwdYDEqhRiZZUA=
 golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
 golang.org/x/net v0.0.0-20190620200207-3b0461eec859/go.mod h1:z5CRVTTTmAJ677TzLLGU+0bjPO0LkuOLi4/5GtJWs/s=
-golang.org/x/net v0.0.0-20201021035429-f5854403a974/go.mod h1:sp8m0HH+o8qH0wwXwYZr8TS3Oi6o0r6Gce1SSxlDquU=
 golang.org/x/net v0.0.0-20210405180319-a5a99cb37ef4/go.mod h1:p54w0d4576C0XHj96bSt6lcn1PtDYWL6XObtHCRCNQM=
 golang.org/x/sync v0.0.0-20190423024810-112230192c58/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
-golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20210220032951-036812b2e83c/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20190412213103-97732733099d/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/sys v0.0.0-20200930185726-fdedc70b468f/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20201119102817-f84b799fce68/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
-golang.org/x/sys v0.0.0-20210119212857-b64e53b001e4/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20210330210617-4fbd30eecc44/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
 golang.org/x/sys v0.0.0-20210510120138-977fb7262007/go.mod h1:oPkhp1MJrh7nUepCBck5+mAzfO9JrbApNNgaTdGDITg=
 golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
@@ -38,8 +32,6 @@ golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
 golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
 golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
 golang.org/x/tools v0.0.0-20191119224855-298f0cb1881e/go.mod h1:b+2E5dAYhXwXZwtnZ6UAqBI28+e2cm9otk0dWdXHAEo=
-golang.org/x/tools v0.1.0 h1:po9/4sTYwZU9lPhi1tOrb4hCv3qrhiQ77LZfGa2OjwY=
-golang.org/x/tools v0.1.0/go.mod h1:xkSsbof2nBLbhDlRMhhhyNLN/zl3eTqcnHD5viDpcZ0=
 golang.org/x/tools v0.1.1 h1:wGiQel/hW0NnEkJUk8lbzkX2gFJU6PFxf1v5OlCfuOs=
 golang.org/x/tools v0.1.1/go.mod h1:o0xws9oXOQQZyjljx8fwUC0k7L1pTE6eaCbjGeHmOkk=
 golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=

codego/grammars/aussagenlogik.g4

@@ -1,33 +1,37 @@
 grammar aussagenlogik;
 
 // Standardtokens:
-NUMBER: [0-9]+;
+NUMBER: [0-9];
+ZERO: ~[a-zA-Z0-9][0]; // negatives Look-Behind nötig, um konfliktierendes Lexing zu vermeiden
+ONE: ~[a-zA-Z0-9][1];  // ""
 WHITESPACE: [ \r\n\t]+ -> skip;
 LBRACE: '(';
 RBRACE: ')';
 LCURLYBRACE: '{';
 RCURLYBRACE: '}';
+TEXT: [a-zA-Z0-9\\_];
 
 // Symbole (erlaube mehrere Varianten)
 SYMB_NOT:  ('!'|'~'|'not');
 SYMB_AND:  ('&'+|'^'|'and');
 SYMB_OR:   ('|'+|'v'|'or');
-SYMB_IMPL: ('->'|'=>');
+SYMB_IFF:  ([<][-]+[>]|[<][=]+[>]|'iff');
+SYMB_IMPL: (~[<][-]+[>]|~[<][=]+[>]);
 
 // Rules
 start: open <EOF> | closed <EOF>;
 
 closed: atomic | not | LBRACE open RBRACE;
-open: and2 | and | or2 | or | implies;
+open: and2 | and | or2 | or | implies | iff;
 
 // Schemata für atomische Ausdrücke
-atomic: taut | contradiction | atom; //| generic;
-taut:  ('1'|'true');
-contradiction: ('0'|'false');
-atom: 'A0' | 'A1' | 'A' NUMBER; // muss A0, A1 wegen falsum/verum extra auflisten
-// // als 'generische' Formeln schreibe bspw. {F}, {G}, {F1}, usw.
-// // generic: LCURLYBRACE (.*?) RCURLYBRACE;
-// FIXME: dieses Schema führt zu Konflikten
+atomic: taut | contradiction | atom | generic;
+taut:  (ONE|'true');
+contradiction: (ZERO|'false');
+atom: 'A' NUMBER+;
+// als 'generische' Formeln schreibe bspw. {F}, {G}, usw.
+generic: LCURLYBRACE TEXT+ RCURLYBRACE | LCURLYBRACE TEXT* ( generic TEXT* )+ RCURLYBRACE;
+// FIXME: liest Zahlen schlecht ein
 
 // Schema für Negation: ¬ F
 not:                symb=SYMB_NOT  closed;
@@ -39,3 +43,5 @@ or2:       closed   symb=SYMB_OR   closed;
 or:      ( closed ( symb=SYMB_OR   closed )+ );
 // Schema für Implikation: F1 ⟶ F2
 implies:   closed   symb=SYMB_IMPL closed;
+// Schema für Implikation: F1 ⟷ F2
+iff:       closed   symb=SYMB_IFF  closed;

codego/main.go

@@ -1,12 +1,12 @@
 package main
 
 import (
-	"encoding/json"
 	"fmt"
-	"logik/aussagenlogik/rekursion"
+	"logik/aussagenlogik/formulae"
+	"logik/aussagenlogik/recursion"
 	"logik/aussagenlogik/schema"
-	"logik/aussagenlogik/syntaxbaum"
 	env "logik/core/environment"
+	"logik/core/utils"
 	"strings"
 
 	"github.com/lithammer/dedent"
@@ -21,6 +21,7 @@ type dataType struct {
 
 type resultsType struct {
 	eval         int
+	nnf          formulae.Formula
 	atoms        []string
 	depth        int
 	length       int
@@ -31,23 +32,10 @@ var data dataType
 
 func main() {
 	// Extrahiere Daten
-	err := getData()
-	if err != nil {
-		return
-	}
+	getData()
 	// Ausdruck -> Syntaxbaum
-	tree, err := schema.ParseExpr(data.expr)
-	if err != nil {
-		return
-	}
-	// Methoden ausführen:
-	results := resultsType{
-		eval:         rekursion.RekursivEval(tree, data.interpretation),
-		atoms:        rekursion.RekursivAtoms(tree),
-		depth:        rekursion.RekursivDepth(tree),
-		length:       rekursion.RekursivLength(tree),
-		nParentheses: rekursion.RekursivParentheses(tree),
-	}
+	tree := schema.ParseExpr(data.expr)
+	results := getResults(tree)
 	// Resultate anzeigen:
 	displayResults(tree, results)
 }
@@ -56,15 +44,25 @@ func main() {
 // SONSTIGE METHODEN
 // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-func getData() error {
+func getData() {
 	env.ENV_FILE_NAME = DATA_ENV
 	data.expr = env.ReadEnvKey("expr")
 	s := env.ReadEnvKey("interpretation")
-	err := json.Unmarshal([]byte(s), &data.interpretation)
-	return err
+	utils.JsonToArrayOfStrings(s, &data.interpretation)
 }
 
-func displayResults(tree syntaxbaum.SyntaxBaum, results resultsType) {
+func getResults(tree formulae.Formula) resultsType {
+	return resultsType{
+		eval:         recursion.Eval(tree, data.interpretation),
+		nnf:          recursion.NNF(tree),
+		atoms:        recursion.Atoms(tree),
+		depth:        recursion.FmlDepth(tree),
+		length:       recursion.FmlLength(tree),
+		nParentheses: recursion.NrParentheses(tree),
+	}
+}
+
+func displayResults(tree formulae.Formula, results resultsType) {
 	fmt.Println(fmt.Sprintf(
 		dedent.Dedent(`
 		Syntaxbaum von
@@ -74,18 +72,20 @@ func displayResults(tree syntaxbaum.SyntaxBaum, results resultsType) {
 
 		Für I = {%[3]s} und F wie oben gilt
 		eval(F, I)      = %[4]d;
-		atoms(F)        = {%[5]s};  <- *
-		depth(F)        = %[6]d;  <- *
-		length(F)       = %[7]d;  <- *
-		#parentheses(F) = %[8]d;  <- *
+		F^NNF           = %[5]s;
+		atoms(F)        = {%[6]s};  <- *
+		depth(F)        = %[7]d;  <- *
+		length(F)       = %[8]d;  <- *
+		#parentheses(F) = %[9]d;  <- *
 
 		* noch nicht implementiert!
 		Challenge: schreibe diese Methoden! (siehe README.md)
 		`),
-		tree.Expr,
+		tree.GetExpr(),
 		tree.Pretty("    "),
 		strings.Join(data.interpretation, ", "),
 		results.eval,
+		results.nnf.GetExpr(),
 		// string(results.atoms),
 		strings.Join(results.atoms, ", "),
 		results.depth,

codego/scripts/build.sh

@@ -47,12 +47,10 @@ function precompile_grammars() {
 }
 
 function compile_programme() {
-    [ -f "main" ] && rm "main";
+    [ -f "dist/main" ] && rm "dist/main";
     echo -e "\033[92;1mGO\033[0m kompiliert \033[1mmain.go\033[0m";
-    call_go build "main.go";
-    ! [ -f "main" ] && exit 1;
-    ! [ -d "dist" ] && mkdir "dist";
-    mv "main" "dist";
+    call_go build -o dist/main "main.go";
+    ! [ -f "dist/main" ] && exit 1;
 }
 
 function run_programme() {

codego/scripts/test.sh

@@ -9,14 +9,13 @@
 ################################
 
 export TEST_VERBOSE=false # <- true: unittest mit verbose output
-export TEST_TIMEOUT="60s"
+export TEST_TIMEOUT="10s"
 
 function call_go() {
     go $@;
 }
 
 function check_requirements() {
-    [ -f "go.sum" ] && rm "go.sum";
     call_go get "$( cat scripts/requirements )";
 }
 

notes/.gitignore

@@ -1,4 +0,0 @@
-*
-!/.gitignore
-
-!/*.pdf

notes/glossar.md

@@ -0,0 +1,69 @@
+<style>
+    table tbody tr td {
+        vertical-align: top;
+    }
+    table tbody tr td:nth-child(1) {
+        font-size: 10pt;
+    }
+    table tbody tr td:nth-child(2), table tbody tr td:nth-child(3) {
+        font-size: 8pt;
+    }
+</style>
+
+# Glossar #
+
+| Symbol | Referenz (im Skript) | Kurze Beschreibung |
+| :----- | :------------------- | :----------------- |
+| `¬` | §8 Definition, VL2, Seite 8 | Negationsjunktor („nicht“) |
+| `⋀` | §8 Definition, VL2, Seite 8 | Konjunktionsjunktor („und“) |
+| `⋁` | §8 Definition, VL2, Seite 8 | Disunktionsjunktor („oder“) |
+| `⟶` | VL2, Seite 47 | **Abkürzung** für Implikation |
+| `⟷` | VL2, Seite 47 | **Abkürzung** für Doppeltimplikation |
+| `⊨` | §9 Definition, VL2, Seite 34 | Erfüllbarkeitsbeziehung: `I ⊨ F` gdw. `I` erf. `F` |
+| `=` | — | `F = G` gdw. `F` und `G` _dieselbe_ Formel sind |
+| `≡` | §13 Definition, VL3, Seite 11 | `F ≡ G` gdw. `F`, `G` **semantisch** äquivalent |
+| `{...}_⋀` | §39 Definition, VL5, Seite 108 | Mengendarstellung von Disjunktionsglied |
+| ~~-`𝒜`-~~ | — | (**Eintrag ignorieren**: kommt in VL nicht vor!) |
+| AL | (VL2–VL6) | Aussagenlogik |
+| `Aᵢ` | §8 Definition, VL2, Seite 8 | das _i_-te Atom in der AL-Sprache |
+| `Atome(·)` | §5 Definition, V2, Seite 14 | `Atome(F) =` Menge aller Atome in `F` |
+| bereinigt | §76 Definition, VL10, Seite 21 | äqv. Formel, Variablensubstitution, so dass jede Var nur gebunden od. frei vorkommt |
+| `𝔠` | §88+§89 Definition, VL11, Seiten 9+14 | (Fraktur c) die Herbrand-Konstante („out of bounds“) |
+| DNF | §22 Definition, VL3, Seite 55 | disjunktive Normalform für AL und PL |
+| erfüllbar | §10 Definition, VL2, Seite 68 | Die „klassischen“ Probleme |
+| `eval(·,·)` | §16 Algorithmus, VL3, Seite 30 | Evaluation: `eval(F,I)=1` gdw. `I ⊨ F` |
+| `ℱ` | §8 Definition, VL2, Seite 8 | Die „AL-Sprache“, Menge aller AL-Formeln |
+| `Fun(t)` | §63 Definition, VL9, Seite 18 | alle Variablen, Konstanten, Fktsymbole in Term `t` |
+| `FV(F)` | §57 Definition, VL8, Seite 27 | Menge freier Variablen in `F` (für Terme siehe `var(t)`) |
+| `g`, `g´`, `g´´`, ... | | Skolemisierung: ∃-Eliminierung mittels Funktionen, die Abhängigkeiten ausdrücken |
+| `GV(F)` | §75 Definition, VL10, Seite 17 | Menge gebundener Variablen in `F`|
+| `H,H(F)` | §88 Definition, VL11, Seite 9 | Herbrand-Symbole, Herbrand-Universum |
+| Herbrand-Interpretation | §89 Definition, VL11, Seite 14 | Interpretation für ein Herbrand-Modell. Alle H-M haben die gleiche Interpretationen von Termen. Nur Relationen können anders interpretiert werden. |
+| KNF | §22 Definition (AL), VL3, Seite 55; §85 Definition (PL), VL10, Seite 89 | konjunktive Normalform für AL und PL |
+| `ℒ` | §8 Definition, VL2, Seite 8 | Die Menge der Literale |
+| PL | (ab VL7) | Prädikatenlogik |
+| NNF | §18 Definition (AL), VL3, Seite 39; §73 Definition (PL), VL10, Seite 8 | Negationsnormalform - Negation nur bei Literalen |
+| PNF | §78 Definition, VL10, Seite 37 | Pränexnormalform - Kette von Quantoren um einen Q-freien Teil |
+| `ℛ,ℛ⁽ᵏ⁾`| §52 Definition, VL7, Seite 72 | Menge der (`k`-stelligen) Relationssymbole, `k≥0`. |
+| `res(·)` | §41–43 Definition, VL6, Seiten 37–43 | `res(F) =` Menge aller Resolventen aus Disjunktionsgliedern aus `F` |
+| `Res(·)` | §43 Definition, VL6, Seite 43 | `Res(F) = F ∪ res(F)` |
+| `Res⁽ⁿ⁾(·)` | §43 Definition, VL6, Seite 43 | `Res(Res(···Res(F)···))`, _n_ Mal |
+| `Res*(·)` | §43 Definition, VL6, Seite 43 | Resolutionshülle |
+| `𝒮,𝒮⁽ᵏ⁾`| §52 Definition, VL7, Seite 72 | Menge der (`k`-stelligen) Funktionssymbole, `k≥0`. **Beachte:** für `k=0` sind dies die Konstanten! |
+| Skolemform | §81, VL10, Seite 62 | äqv. Formel, in der alle Existenzquantoren eliminiert wurden |
+| strukturelle Ind | §6 Theorem, VL2, Seite 24 | allgemeine Induktion über die Teilformelbeziehung |
+| strukturelle Rek | §4 Theorem, VL2, Seite 12 | rekursive Konstruktionschemata über die Teilformelbeziehung |
+| `Sym(F)` | §64 Definition, VL9, Seite 20 | alle „relevanten“ Symbole in `F`: alle **freien** Vars, alle Konstanten, Fktsymbole, Relnsymbole |
+| `𝒯` | §53 Definition, VL7, Seite 74 | Menge der Terme in PL |
+| tautologisch | §10 Definition, VL2, Seite 68 | Die „klassischen“ Probleme |
+| `TF(·)` | §35 Definition, VL5, Seite 56 | `TF(F) =` Menge aller Teilformeln in `F` (inkl. `F` selbst) |
+| `tᵥ` | §37 Definition, VL5, Seite 64 | Abbildung, die Teilformeln auf Literale abbildet |
+| `tseiᵥ` | §37 Definition, VL5, Seite 64 | Tseitin-Transformation |
+| unerfüllbar | §10 Definition, VL2, Seite 68 | Die „klassischen“ Probleme |
+| `𝒱` | §52 Definition, VL7, Seite 72 | Menge der Variablen in PL |
+| `var(t)` | §55 Definition, VL8, Seite 20 | Menge der Variablen in `t` (für Fml siehe `FV(F)`) |
+| widerlegbar | §10 Definition, VL2, Seite 68 | Die „klassischen“ Probleme |
+
+... (wird fortgesetzt)
+
+**ACHTUNG:** Seitennr können abweichen.

protocol/README.md

@@ -2,9 +2,30 @@
 
 Inhaltsverzeichnis
 
-- [Vorlesungswoche 1](./woche1.md)
-- [Vorlesungswoche 2](./woche2.md) Erste Übung: Organisatorisches
-- [Vorlesungswoche 3](./woche3.md) Seminaraufgaben aus Blatt 1
-- [Vorlesungswoche 4](./woche4.md) ~~Hausaufgaben aus Blatt ??~~ Spezielle Themen
-- [Vorlesungswoche 5](./woche5.md) Seminaraufgaben aus Blatt 2
-- [Vorlesungswoche 6](./woche6.md) Hausaufgaben aus Blatt 1
+- [Vorlesungswoche 1](./woche1.md) (_keine Übung_)
+- [Vorlesungswoche 2](./woche2.md) Erste Übung: Organisatorisches.
+- [Vorlesungswoche 3](./woche3.md) Semaufg Blatt 1; [BBB Aufzeichnung](https://t1p.de/tjiu).
+- [Vorlesungswoche 4](./woche4.md) Spezielle Themen; [Zoom Aufzeichnung](https://t1p.de/91vz).
+- [Vorlesungswoche 5](./woche5.md) Semaufg Blatt 2; [Zoom Aufzeichnung](https://t1p.de/ny7n).
+- [Vorlesungswoche 6](./woche6.md) HA Blatt 1; [Zoom Aufzeichnung](https://t1p.de/m431).
+- [Vorlesungswoche 7](./woche7.md) (_keine Übung: ...Pfingsten..._)
+- [Vorlesungswoche 8](./woche8.md) Semaufg Blatt 3; [Zoom Aufzeichnung](https://t1p.de/fmok).
+- [Vorlesungswoche 9](./woche9.md) HA Blatt 2; [Zoom Aufzeichnung](https://t1p.de/8vmh).
+- [Vorlesungswoche 10](./woche10.md) Semaufg Blatt 4; [Zoom Aufzeichnung](https://t1p.de/fpv5).
+- [Vorlesungswoche 11](./woche11.md) HA Blatt 3; [Zoom Aufzeichnung](https://t1p.de/626y).
+- [Vorlesungswoche 12](./woche12.md) Semaufg Blatt 5; [Zoom Aufzeichnung](https://t1p.de/n4bt).
+  - (Zusatz) Seminaraufgabe 5.5 [Zoom Aufzeichnung](https://t1p.de/bnlj).
+- [Vorlesungswoche 13](./woche13.md) HA Blatt 4; [Zoom Aufzeichnung](https://t1p.de/76qo).
+- [Vorlesungswoche 14](./woche14.md) Semaufg Blatt 6; [Zoom Aufzeichnung](https://t1p.de/slya).
+- [Vorlesungswoche 15](./woche15.md) HA Blatt 5; [Zoom Aufzeichnung](https://t1p.de/3xsm).
+
+**Notizen**
+
+- Für den BBB-Raum bzw. die Zoom-Aufzeichnungen braucht man einen **Code** (siehe Moodle).
+- Klausurdatum wird noch angekündigt.
+  Je nachdem können wir ggf. 1–2 Stunden für Vorklausurfragen organisieren.
+- In [**Vorlesungswoche 16**](./woche16.md) wird eine zusätzliche Übung angeboten:
+  <br/>
+  allgemeine Fragestellung von Studierenden.
+  - Zoom-Raum mit dem üblichen Code.
+  - Dies wird _nicht_ aufgezeichnet werden!

protocol/woche10.md

@@ -0,0 +1,23 @@
+# Vorlesungswoche 10 (14.–20. Juni) #
+
+Handnotizen findet man unter [notes/woche10.pdf](./../notes/woche10.pdf).
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+- [x] Serie 4, Seminaraufgaben besprechen
+    - [x] SemA 4.1
+    - [x] SemA 4.2
+    - [x] SemA 4.3
+    - [x] SemA 4.4
+    - [x] SemA 4.5
+    - Anmerkungen zu HA
+- [x] restliche Zeit für allg. Fragen
+
+## Nächste Woche ##
+
+- HA aus Blatt 3.
+
+### TODOs (Studierende) ###
+
+- am ÜB 4 weiter arbeiten.

protocol/woche11.md

@@ -0,0 +1,20 @@
+# Vorlesungswoche 11 (21.–27. Juni) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+- [x] Serie 3, Hausaufgaben besprechen
+    - [x] allgemeines Feedback
+    - [x] HA 3.1
+    - [x] HA 3.2
+    - [x] HA 3.3
+- [x] restliche Zeit für allg. Fragen
+    - Frage über VPN Zugang bis nächste Woche zu klären.
+
+## Nächste Woche ##
+
+- Seminaraufgaben aus Blatt 5.
+
+### TODOs (Studierende) ###
+
+- ÜB 4 bis **Do 24.06.** um 22:00 abgeben!

protocol/woche12.md

@@ -0,0 +1,43 @@
+# Vorlesungswoche 12 (28. Juni – 4. Juli) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+- [x] Serie 5, Seminaraufgaben besprechen
+    - [x] SemA 5.1
+    - [x] SemA 5.2
+    - [x] SemA 5.3
+    - [x] SemA 5.4
+    - ~~[ ] (Zusatz) SemA 5.5~~ ---> siehe Aufzeichnung
+- [x] restliche Zeit für allg. Fragen
+    - Alternativer Beweis von (d) durch Argument:
+
+        ```
+        »Sonst wären F und F^skol sem. äquivalent,
+        aber das ist nicht i. A. der Fall.«
+        ```
+
+        Da wir aber uns aber auf einer Instanz beschränken,
+        passt dieser Ansatz nicht.
+        Wir müssen im Einzelfall prüfen.
+        Vgl. Unterschied zw.
+
+        ```
+        1. Es ist nicht so, dass (F ≡ F^skol) für alle F
+        ```
+        und
+
+        ```
+        2. Für alle F, es ist nicht so dass (F ≡ F^skol).
+        ```
+
+        Wir haben nur 1 und damit kann es durchaus sein,
+        dass für einzelne Fälle F, F^skol schon sem. äqv. sind.
+
+## Nächste Woche ##
+
+- HA aus Blatt 4.
+
+### TODOs (Studierende) ###
+
+- am ÜB 5 weiter arbeiten.

protocol/woche13.md

@@ -0,0 +1,21 @@
+# Vorlesungswoche 13 (5.–11. Juli) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+- [x] Serie 4, Hausaufgaben besprechen
+    - [x] allgemeines Feedback
+    - [x] HA 4.1
+    - [x] HA 4.2
+    - [x] HA 4.3
+    - [x] HA 4.4
+    - [x] HA 4.5
+- [x] restliche Zeit für allg. Fragen
+
+## Nächste Woche ##
+
+- Seminaraufgaben aus Blatt 6.
+
+### TODOs (Studierende) ###
+
+- ÜB 5 bis **Do 08.07.** um 22:00 abgeben!

protocol/woche14.md

@@ -0,0 +1,23 @@
+# Vorlesungswoche 14 (12.–18. Juli) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+    - **Beachte:** HA zu Serie 6 werden leider nicht besprochen!
+    - Notenstand in Moodle, Schwellwert 59 Pkt
+    - Zusatzübung
+- [x] Serie 6, Seminaraufgaben besprechen
+    - [x] SemA 6.1
+    - [x] SemA 6.2
+    - [x] SemA 6.3
+    - [x] SemA 6.4
+    - ~~[ ] (Zusatz) SemA 6.5~~ ---> siehe Aufzeichnung in Moodle
+- [x] restliche Zeit für allg. Fragen
+
+## Nächste Woche ##
+
+- HA aus Blatt 5.
+
+### TODOs (Studierende) ###
+
+- am ÜB 6 weiter arbeiten.

protocol/woche15.md

@@ -0,0 +1,23 @@
+# Vorlesungswoche 15 (19.–25. Juli) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+    - [x] Anfragen, ob Vorklausurübung erwünscht wird.
+- [x] Serie 5, Hausaufgaben besprechen
+    - ~~[ ] allgemeines Feedback~~
+    - [x] HA 5.1
+    - [x] HA 5.2
+    - [x] HA 5.3
+    - [x] HA 5.4
+    - [x] HA 5.5
+- ~~[ ] restliche Zeit für allg. Fragen~~
+
+## Nächste Woche ##
+
+- Studierende bringen **eigene Fragen** mit und wir diskutieren diese.
+
+### TODOs (Studierende) ###
+
+- ÜB 6 bis **Do 22.07.** um 22:00 abgeben!
+- Klausurvorbereitung!

protocol/woche16.md

@@ -0,0 +1,15 @@
+# Woche 16 (26. Juli – 1. Aug) #
+
+Diese Woche wird nicht aufgezeichnet.
+
+## Agenda ##
+
+[x] allgemeine ganzen Stoff betreffende Fragen von Studierenden
+
+## Nächste Woche ##
+
+- Klausur.
+
+### TODOs (Studierende) ###
+
+- Klausurvorbereitung!

protocol/woche3.md

@@ -1,5 +1,7 @@
 # Vorlesungswoche 3 (26. April – 2. Mai) #
 
+## Agenda ##
+
 - [x] Organisatorisches (max. 5 min)
     - Erinnerung über Abgabe: Matrikelnr., 1 PDF.
 - [x] Serie 1, Seminaraufgaben

protocol/woche4.md

@@ -1,4 +1,8 @@
-# Vorlesungswoche 4 (3. April – 9. Mai) #
+# Vorlesungswoche 4 (3. Mai – 9. Mai) #
+
+Handnotizen findet man unter [notes/woche4.pdf](./../notes/woche4.pdf).
+
+## Agenda ##
 
 - [x] Organisatorisches (max. 5 min)
     - Hochladen = Abgeben
@@ -43,7 +47,6 @@
         -> „gelöst“ durch wohlfundiert/Wohlordnung
         -> R keine Menge
 
-
 ## Nächste Woche ##
 
 - Seminaraufgaben für Serie 2:

protocol/woche5.md

@@ -1,6 +1,9 @@
 # Vorlesungswoche 5 (10.–16. Mai) #
 
+Handnotizen findet man unter [notes/woche5.pdf](./../notes/woche5.pdf).
+
 ## Agenda ##
+
 - [x] 2–5 min Organisatorisches (max. 5 min)
 - [x] Serie 2, Seminaraufgaben
     - [x] 7,5 min SA 2.1 Modelle

protocol/woche6.md

@@ -0,0 +1,20 @@
+# Vorlesungswoche 6 (17.–23. Mai) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+- [x] Serie 1, Hausaufgaben besprechen (inkl. Feedbacknotizen von SHK)
+    - [x] HA 1.1
+    - [x] HA 1.2
+    - [x] HA 1.3
+    - [x] HA 1.4
+- [x] restliche Zeit für allg. Fragen
+    - Fragen zu strukturelle Induktion
+
+## Nächste Woche ##
+
+- nach Anfrage kann ggf. etwas aufgezeichnet werden
+
+### TODOs (Studierende) ###
+
+- ÜB 2 bis **Do 20.05.** um 22:00 abgeben!

protocol/woche7.md

@@ -0,0 +1,3 @@
+# Vorlesungswoche 7 (24.–30. Mai) #
+
+(keine VL od. ÜG diese Woche)

protocol/woche8.md

@@ -0,0 +1,23 @@
+# Vorlesungswoche 8 (31. Mai – 6. Juni) #
+
+Handnotizen findet man unter [notes/woche8.pdf](./../notes/woche8.pdf).
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+    - Feedback zu HA 1
+    - Symbolverzeichnis findet man in [notes/glossar.md](./../notes/glossar.md).
+- [x] Serie 3, Seminaraufgaben besprechen
+    - [x] SemA 3.1
+    - [x] SemA 3.2
+    - [x] SemA 3.3
+- [ ] restliche Zeit für allg. Fragen
+
+## Nächste Woche ##
+
+- HA aus Blatt 2.
+
+### TODOs (Studierende) ###
+
+– VL Wochen 5+6 wieder durchlesen, VL Woche 7 für Vorlesung durchlesen.
+- am ÜB 3 weiter arbeiten.

protocol/woche9.md

@@ -0,0 +1,24 @@
+# Vorlesungswoche 9 (7.–13. Juni) #
+
+## Agenda ##
+
+- [x] 2–5 min Organisatorisches
+- [x] Serie 2, Hausaufgaben besprechen
+    - [x] allgemeines Feedback
+    - [x] SemA 2.1
+    - [x] SemA 2.2
+    - [x] SemA 2.3
+    - [x] SemA 2.4
+    - [x] SemA 2.5
+- [x] restliche Zeit für allg. Fragen
+
+## Nächste Woche ##
+
+- Seminaraufgaben aus Blatt 4.
+- Allg.: bitte überlegen, was vor der Klausur erwünscht wäre, bspw. interaktive Sprechstunden/Fragerunde,
+    oder ob ihr (selbstverständlich Pandemie-Maßnahmen beachtend) unter euch euch treffen wollt,
+    durch den Stoff + die Übungen gemeinsam geht.
+
+### TODOs (Studierende) ###
+
+- ÜB 3 bis **Do 10.06.** um 22:00 abgeben!