chop-logic-core/lib/index.cjs

Core classes, methods and functions for calculating logical formulas and constructing proofs within the Chop Logic project.

"use strict";
var __defProp = Object.defineProperty;
var __getOwnPropDesc = Object.getOwnPropertyDescriptor;
var __getOwnPropNames = Object.getOwnPropertyNames;
var __hasOwnProp = Object.prototype.hasOwnProperty;
var __export = (target, all) => {
  for (var name in all)
    __defProp(target, name, { get: all[name], enumerable: true });
};
var __copyProps = (to, from, except, desc) => {
  if (from && typeof from === "object" || typeof from === "function") {
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      if (!__hasOwnProp.call(to, key) && key !== except)
        __defProp(to, key, { get: () => from[key], enumerable: !(desc = __getOwnPropDesc(from, key)) || desc.enumerable });
  }
  return to;
};
var __toCommonJS = (mod) => __copyProps(__defProp({}, "__esModule", { value: true }), mod);

// src/index.ts
var index_exports = {};
__export(index_exports, {
  Glyph: () => Glyph,
  GlyphType: () => GlyphType,
  GlyphUnicode: () => GlyphUnicode,
  HilbertAxioms: () => HilbertAxioms,
  HilbertCalculusRule: () => HilbertCalculusRule,
  HilbertCalculusSchema: () => HilbertCalculusSchema,
  HilbertProof: () => HilbertProof,
  HilbertProofBuilder: () => HilbertProofBuilder,
  HilbertRules: () => HilbertRules,
  NaturalCalculusRule: () => NaturalCalculusRule,
  NaturalProof: () => NaturalProof,
  NaturalProofBuilder: () => NaturalProofBuilder,
  NaturalRules: () => NaturalRules,
  Operator: () => Operator,
  PropFormulaCheck: () => PropFormulaCheck,
  Step: () => Step,
  arePropFormulasStructurallyEqual: () => arePropFormulasStructurallyEqual,
  buildHilbertProof: () => buildHilbertProof,
  buildNaturalProof: () => buildNaturalProof,
  calculatePropFormula: () => calculatePropFormula,
  composeHilbertProof: () => composeHilbertProof,
  composeNaturalProof: () => composeNaturalProof,
  convertPropFormulaToExpression: () => convertPropFormulaToExpression,
  convertPropFormulaToString: () => convertPropFormulaToString,
  createOperator: () => createOperator,
  createPropExpression: () => createPropExpression,
  createPropFormula: () => createPropFormula,
  createPropSymbol: () => createPropSymbol,
  extractPropSubFormulas: () => extractPropSubFormulas,
  extractPropVariables: () => extractPropVariables,
  generateHilbertProofSteps: () => generateHilbertProofSteps,
  generateNaturalProofSteps: () => generateNaturalProofSteps,
  generatePropTruthTable: () => generatePropTruthTable,
  generateTruthAssignments: () => generateTruthAssignments,
  getBinaryOperationValue: () => getBinaryOperationValue,
  getGlyphUnicode: () => getGlyphUnicode,
  getOperatorGlyph: () => getOperatorGlyph,
  getUnaryOperationValue: () => getUnaryOperationValue,
  isConjunctionEliminationApplicable: () => isConjunctionEliminationApplicable,
  isConjunctionIntroductionApplicable: () => isConjunctionIntroductionApplicable,
  isDisjunctionEliminationApplicable: () => isDisjunctionEliminationApplicable,
  isDisjunctionIntroductionApplicable: () => isDisjunctionIntroductionApplicable,
  isEquivalenceEliminationApplicable: () => isEquivalenceEliminationApplicable,
  isEquivalenceIntroductionApplicable: () => isEquivalenceIntroductionApplicable,
  isImplicationDistributionApplicable: () => isImplicationDistributionApplicable,
  isImplicationEliminationApplicable: () => isImplicationEliminationApplicable,
  isImplicationIntroductionApplicable: () => isImplicationIntroductionApplicable,
  isImplicationReversalApplicable: () => isImplicationReversalApplicable,
  isNegationEliminationApplicable: () => isNegationEliminationApplicable,
  isNegationIntroductionApplicable: () => isNegationIntroductionApplicable,
  isWellFormedFormula: () => isWellFormedFormula,
  replaceAtomInFormula: () => replaceAtomInFormula,
  tokenizeString: () => tokenizeString,
  validatePropFormulas: () => validatePropFormulas
});
module.exports = __toCommonJS(index_exports);

// src/enums/proof.ts
var Step = /* @__PURE__ */ ((Step2) => {
  Step2["Premise"] = "Premise";
  Step2["Assumption"] = "Assumption";
  Step2["Shortcut"] = "Shortcut";
  Step2["Reiteration"] = "Reiteration";
  Step2["Derivation"] = "Derivation";
  Step2["Axiom"] = "Axiom";
  return Step2;
})(Step || {});
var HilbertCalculusSchema = /* @__PURE__ */ ((HilbertCalculusSchema2) => {
  HilbertCalculusSchema2["II"] = "II";
  HilbertCalculusSchema2["ID"] = "ID";
  HilbertCalculusSchema2["IR"] = "IR";
  return HilbertCalculusSchema2;
})(HilbertCalculusSchema || {});
var HilbertCalculusRule = /* @__PURE__ */ ((HilbertCalculusRule2) => {
  HilbertCalculusRule2["II"] = "II";
  HilbertCalculusRule2["ID"] = "ID";
  HilbertCalculusRule2["IR"] = "IR";
  HilbertCalculusRule2["IE"] = "IE";
  return HilbertCalculusRule2;
})(HilbertCalculusRule || {});
var NaturalCalculusRule = /* @__PURE__ */ ((NaturalCalculusRule2) => {
  NaturalCalculusRule2["NI"] = "NI";
  NaturalCalculusRule2["CI"] = "CI";
  NaturalCalculusRule2["DI"] = "DI";
  NaturalCalculusRule2["II"] = "II";
  NaturalCalculusRule2["EI"] = "EI";
  NaturalCalculusRule2["NE"] = "NE";
  NaturalCalculusRule2["CE"] = "CE";
  NaturalCalculusRule2["DE"] = "DE";
  NaturalCalculusRule2["IE"] = "IE";
  NaturalCalculusRule2["EE"] = "EE";
  return NaturalCalculusRule2;
})(NaturalCalculusRule || {});
var PropFormulaCheck = /* @__PURE__ */ ((PropFormulaCheck2) => {
  PropFormulaCheck2["areEqual"] = "areEqual";
  PropFormulaCheck2["isIE"] = "isIE";
  PropFormulaCheck2["isDE"] = "isDE";
  PropFormulaCheck2["isCE"] = "isCE";
  PropFormulaCheck2["isEE"] = "isEE";
  PropFormulaCheck2["isNE"] = "isNE";
  PropFormulaCheck2["isDI"] = "isDI";
  PropFormulaCheck2["isCI"] = "isCI";
  PropFormulaCheck2["isEI"] = "isEI";
  PropFormulaCheck2["isNI"] = "isNI";
  PropFormulaCheck2["isII"] = "isII";
  PropFormulaCheck2["isID"] = "isID";
  PropFormulaCheck2["isIR"] = "isIR";
  return PropFormulaCheck2;
})(PropFormulaCheck || {});

// src/enums/symbols.ts
var Glyph = /* @__PURE__ */ ((Glyph2) => {
  Glyph2["Implication"] = "=>";
  Glyph2["ReversedImplication"] = "<=";
  Glyph2["Conjunction"] = "&";
  Glyph2["Disjunction"] = "|";
  Glyph2["Negation"] = "~";
  Glyph2["Equivalence"] = "<=>";
  Glyph2["ExclusiveConjunction"] = "^";
  Glyph2["ShefferStroke"] = "!&";
  Glyph2["WebbOperation"] = "!|";
  Glyph2["AntiImplication"] = "!=>";
  Glyph2["ReversedAntiImplication"] = "!<=";
  Glyph2["Contradiction"] = "#";
  Glyph2["Tautology"] = "@";
  Glyph2["OpenParenthesis"] = "(";
  Glyph2["CloseParenthesis"] = ")";
  return Glyph2;
})(Glyph || {});
var GlyphType = /* @__PURE__ */ ((GlyphType2) => {
  GlyphType2["Variable"] = "variable";
  GlyphType2["Operator"] = "operator";
  GlyphType2["Parenthesis"] = "parenthesis";
  return GlyphType2;
})(GlyphType || {});
var GlyphUnicode = /* @__PURE__ */ ((GlyphUnicode2) => {
  GlyphUnicode2["Implication"] = "\u2192";
  GlyphUnicode2["ReversedImplication"] = "\u2190";
  GlyphUnicode2["Conjunction"] = "\u2227";
  GlyphUnicode2["Disjunction"] = "\u2228";
  GlyphUnicode2["Negation"] = "\xAC";
  GlyphUnicode2["Equivalence"] = "\u2261";
  GlyphUnicode2["ExclusiveConjunction"] = "\u2295";
  GlyphUnicode2["ShefferStroke"] = "\u2191";
  GlyphUnicode2["WebbOperation"] = "\u2193";
  GlyphUnicode2["AntiImplication"] = "\u219B";
  GlyphUnicode2["ReversedAntiImplication"] = "\u219A";
  GlyphUnicode2["Contradiction"] = "\u22A5";
  GlyphUnicode2["Tautology"] = "\u22A4";
  GlyphUnicode2["OpenParenthesis"] = "(";
  GlyphUnicode2["CloseParenthesis"] = ")";
  return GlyphUnicode2;
})(GlyphUnicode || {});
var Operator = /* @__PURE__ */ ((Operator2) => {
  Operator2["Var"] = "VAR";
  Operator2["Not"] = "NOT";
  Operator2["And"] = "AND";
  Operator2["Or"] = "OR";
  Operator2["Implies"] = "IMPLIES";
  Operator2["ReversedImplies"] = "REVERSED_IMPLIES";
  Operator2["Equiv"] = "EQUIV";
  Operator2["Xor"] = "XOR";
  Operator2["Nand"] = "NAND";
  Operator2["Nor"] = "NOR";
  Operator2["AntiImplies"] = "ANTI_IMPLIES";
  Operator2["ReversedAntiImplies"] = "REVERSED_ANTI_IMPLIES";
  Operator2["Contradiction"] = "CONTRADICTION";
  Operator2["Tautology"] = "TAUTOLOGY";
  return Operator2;
})(Operator || {});

// src/propositional/builders/create-operator.ts
function createOperator(symbol) {
  switch (symbol.atom[0]) {
    case "~" /* Negation */:
      return "NOT" /* Not */;
    case "&" /* Conjunction */:
      return "AND" /* And */;
    case "|" /* Disjunction */:
      return "OR" /* Or */;
    case "=>" /* Implication */:
      return "IMPLIES" /* Implies */;
    case "<=" /* ReversedImplication */:
      return "REVERSED_IMPLIES" /* ReversedImplies */;
    case "<=>" /* Equivalence */:
      return "EQUIV" /* Equiv */;
    case "^" /* ExclusiveConjunction */:
      return "XOR" /* Xor */;
    case "!&" /* ShefferStroke */:
      return "NAND" /* Nand */;
    case "!|" /* WebbOperation */:
      return "NOR" /* Nor */;
    case "!=>" /* AntiImplication */:
      return "ANTI_IMPLIES" /* AntiImplies */;
    case "!<=" /* ReversedAntiImplication */:
      return "REVERSED_ANTI_IMPLIES" /* ReversedAntiImplies */;
    case "#" /* Contradiction */:
      return "CONTRADICTION" /* Contradiction */;
    case "@" /* Tautology */:
      return "TAUTOLOGY" /* Tautology */;
    default:
      if (symbol.type === "variable" /* Variable */) {
        return "VAR" /* Var */;
      }
      throw new Error(
        `Cannot create an operator from symbol "${symbol.atom[0]}".`
      );
  }
}

// src/tokenizer/get-glyph-unicode.ts
var GlyphsDictionary = {
  ["=>" /* Implication */]: "\u2192" /* Implication */,
  ["<=" /* ReversedImplication */]: "\u2190" /* ReversedImplication */,
  ["&" /* Conjunction */]: "\u2227" /* Conjunction */,
  ["|" /* Disjunction */]: "\u2228" /* Disjunction */,
  ["~" /* Negation */]: "\xAC" /* Negation */,
  ["<=>" /* Equivalence */]: "\u2261" /* Equivalence */,
  ["^" /* ExclusiveConjunction */]: "\u2295" /* ExclusiveConjunction */,
  ["!&" /* ShefferStroke */]: "\u2191" /* ShefferStroke */,
  ["!|" /* WebbOperation */]: "\u2193" /* WebbOperation */,
  ["!=>" /* AntiImplication */]: "\u219B" /* AntiImplication */,
  ["!<=" /* ReversedAntiImplication */]: "\u219A" /* ReversedAntiImplication */,
  ["#" /* Contradiction */]: "\u22A5" /* Contradiction */,
  ["@" /* Tautology */]: "\u22A4" /* Tautology */,
  ["(" /* OpenParenthesis */]: "(" /* OpenParenthesis */,
  [")" /* CloseParenthesis */]: ")" /* CloseParenthesis */
};
function getGlyphUnicode(char) {
  if (char in GlyphsDictionary) {
    return GlyphsDictionary[char];
  } else {
    throw new Error(`Cannot get a GlyphUnicode for the character "${char}".`);
  }
}

// src/tokenizer/get-operator-glyph.ts
function getOperatorGlyph(operator) {
  switch (operator) {
    case "NOT" /* Not */:
      return "~" /* Negation */;
    case "AND" /* And */:
      return "&" /* Conjunction */;
    case "OR" /* Or */:
      return "|" /* Disjunction */;
    case "IMPLIES" /* Implies */:
      return "=>" /* Implication */;
    case "REVERSED_IMPLIES" /* ReversedImplies */:
      return "<=" /* ReversedImplication */;
    case "EQUIV" /* Equiv */:
      return "<=>" /* Equivalence */;
    case "XOR" /* Xor */:
      return "^" /* ExclusiveConjunction */;
    case "NAND" /* Nand */:
      return "!&" /* ShefferStroke */;
    case "NOR" /* Nor */:
      return "!|" /* WebbOperation */;
    case "ANTI_IMPLIES" /* AntiImplies */:
      return "!=>" /* AntiImplication */;
    case "REVERSED_ANTI_IMPLIES" /* ReversedAntiImplies */:
      return "!<=" /* ReversedAntiImplication */;
    case "CONTRADICTION" /* Contradiction */:
      return "#" /* Contradiction */;
    case "TAUTOLOGY" /* Tautology */:
      return "@" /* Tautology */;
    default:
      throw new Error(`Cannot convert operator "${operator}" to a glyph.`);
  }
}

// src/tokenizer/tokenize-string.ts
function tokenizeString(input) {
  if (!input.length) return [];
  const glyphs = Object.values(Glyph).sort((a, b) => b.length - a.length);
  const glyphPattern = glyphs.map((g) => g.replaceAll(/[.*+?^${}()|[\]\\]/g, String.raw`\$&`)).join("|");
  const variablePattern = "[a-zA-Z]+";
  const tokenizer = new RegExp(`(${glyphPattern})|(${variablePattern})`, "g");
  const tokens = [];
  let match = tokenizer.exec(input);
  while (match !== null) {
    tokens.push(match[0]);
    match = tokenizer.exec(input);
  }
  if (!tokens.length || tokens.join("") !== input.replaceAll(/\s+/g, "")) {
    throw new Error(`Invalid character(s) found in input: "${input}".`);
  }
  return tokens;
}

// src/propositional/builders/create-prop-symbol.ts
function createPropSymbol(char, position) {
  const knownGlyphs = Object.values(Glyph);
  const onlyLatinLetters = /^[a-zA-Z]+$/;
  if (char === "(" /* OpenParenthesis */ || char === ")" /* CloseParenthesis */) {
    return {
      position,
      atom: [char],
      type: "parenthesis" /* Parenthesis */,
      view: getGlyphUnicode(char)
    };
  } else if (knownGlyphs.includes(char)) {
    return {
      position,
      atom: [char],
      type: "operator" /* Operator */,
      view: getGlyphUnicode(char)
    };
  } else if (onlyLatinLetters.test(char)) {
    const firstLetter = char[0].toLowerCase();
    return {
      position,
      atom: [char],
      type: "variable" /* Variable */,
      view: firstLetter
    };
  } else {
    throw new Error(
      `Cannot create a propositional symbol from the character "${char}".`
    );
  }
}

// src/propositional/builders/create-prop-expression.ts
function createPropExpression(input) {
  const tokens = tokenizeString(input);
  return tokens.map((token, index) => createPropSymbol(token, index));
}

// src/propositional/validators/is-well-formed-formula.ts
function isWellFormedFormula(expression) {
  if (expression.length === 0) return false;
  let index = 0;
  function parseWFF() {
    if (isEndOfExpression()) return false;
    if (isVariable(expression[index])) {
      return parseVariable2();
    }
    if (isNegation(expression[index])) {
      return parseNegation2();
    }
    if (isParenthesizedExpression(expression[index])) {
      return parseParenthesizedExpression();
    }
    return false;
  }
  function parseVariable2() {
    index++;
    return true;
  }
  function parseNegation2() {
    index++;
    return parseWFF();
  }
  function parseParenthesizedExpression() {
    index++;
    if (!parseWFF()) return false;
    if (isEndOfExpression() || !isBinaryOperator(expression[index]))
      return false;
    index++;
    if (!parseWFF()) return false;
    if (isEndOfExpression() || !isClosingParenthesis(expression[index]))
      return false;
    index++;
    return true;
  }
  function isEndOfExpression() {
    return index >= expression.length;
  }
  const result = parseWFF();
  return result && index === expression.length;
}
function isVariable(symbol) {
  return symbol.type === "variable" /* Variable */;
}
function isNegation(symbol) {
  return symbol.atom[0] === "~" /* Negation */;
}
function isParenthesizedExpression(symbol) {
  return symbol.atom[0] === "(" /* OpenParenthesis */;
}
function isBinaryOperator(symbol) {
  return symbol.type === "operator" /* Operator */ && symbol.atom[0] !== "~" /* Negation */;
}
function isClosingParenthesis(symbol) {
  return symbol.atom[0] === ")" /* CloseParenthesis */;
}

// src/propositional/builders/create-prop-formula.ts
function createPropFormula(expression) {
  if (!isWellFormedFormula(expression)) {
    throw new Error(
      "Invalid propositional expression: Not a well-formed formula (WFF)."
    );
  }
  return parseExpression({ expression, start: 0, end: expression.length - 1 });
}
function parseExpression({
  expression,
  start,
  end
}) {
  if (start > end) {
    throw new Error(
      `Unexpected expression boundaries: start=${start}, end=${end}`
    );
  }
  if (isSingleVariable(expression, start, end)) {
    return parseVariable(expression[start]);
  }
  if (isNegation2(expression, start)) {
    return parseNegation(expression, start, end);
  }
  if (isParenthesized(expression, start, end)) {
    return parseBinaryExpression(expression, start, end);
  }
  throw new Error("Invalid formula structure.");
}
function isSingleVariable(expression, start, end) {
  return start === end && expression[start].type === "variable" /* Variable */;
}
function parseVariable(symbol) {
  return { operator: "VAR" /* Var */, values: symbol.atom };
}
function isNegation2(expression, start) {
  return expression[start].atom[0] === "~" /* Negation */;
}
function parseNegation(expression, start, end) {
  return {
    operator: "NOT" /* Not */,
    values: [parseExpression({ expression, start: start + 1, end })]
  };
}
function isParenthesized(expression, start, end) {
  return expression[start].atom[0] === "(" /* OpenParenthesis */ && expression[end].atom[0] === ")" /* CloseParenthesis */;
}
function parseBinaryExpression(expression, start, end) {
  const mainOperatorIndex = findMainOperator(expression, start, end);
  if (mainOperatorIndex === -1) {
    throw new Error("Could not determine the main operator.");
  }
  return {
    operator: createOperator(expression[mainOperatorIndex]),
    values: [
      parseExpression({
        expression,
        start: start + 1,
        end: mainOperatorIndex - 1
      }),
      parseExpression({
        expression,
        start: mainOperatorIndex + 1,
        end: end - 1
      })
    ]
  };
}
function findMainOperator(expression, start, end) {
  let balance = 0;
  for (let i = start; i <= end; i++) {
    const symbol = expression[i];
    if (symbol.atom[0] === "(" /* OpenParenthesis */) balance++;
    if (symbol.atom[0] === ")" /* CloseParenthesis */) balance--;
    if (balance === 1 && symbol.type === "operator" /* Operator */ && symbol.atom[0] !== "~" /* Negation */) {
      return i;
    }
  }
  return -1;
}

// src/propositional/converters/convert-prop-formula-to-expression.ts
function convertPropFormulaToExpression(formula) {
  const expression = [];
  let position = 0;
  function traverse(node) {
    const { operator, values } = node;
    if (operator === "VAR" /* Var */) {
      expression.push(createPropSymbol(values[0], position++));
      return;
    }
    expression.push(createPropSymbol("(", position++));
    if (operator === "NOT" /* Not */) {
      expression.push(createPropSymbol(getOperatorGlyph(operator), position++));
      traverse(values[0]);
    } else {
      const [left, right] = values;
      traverse(left);
      expression.push(createPropSymbol(getOperatorGlyph(operator), position++));
      traverse(right);
    }
    expression.push(createPropSymbol(")", position++));
  }
  traverse(formula);
  return expression;
}

// src/propositional/converters/convert-prop-formula-to-string.ts
function convertPropFormulaToString(formula) {
  if (formula.operator === "VAR" /* Var */) {
    return formula.values[0];
  }
  const glyph = getGlyphUnicode(getOperatorGlyph(formula.operator));
  const subFormulas = formula.values;
  const values = subFormulas.map(convertPropFormulaToString);
  if (formula.operator === "NOT" /* Not */) {
    return `${glyph}${values[0]}`;
  }
  const glyphSpace = ` ${glyph} `;
  return `(${values.join(glyphSpace)})`;
}

// src/propositional/converters/extract-prop-sub-formulas.ts
function extractPropSubFormulas(formula) {
  if (formula.operator === "VAR" /* Var */) return [];
  const subFormulas = /* @__PURE__ */ new Set();
  const result = [];
  function traverse(subFormula) {
    if (subFormula.operator === "VAR" /* Var */) {
      return;
    }
    const key = JSON.stringify(subFormula);
    if (!subFormulas.has(key)) {
      subFormulas.add(key);
      result.push(subFormula);
    }
    if (Array.isArray(subFormula.values)) {
      for (const value of subFormula.values) {
        traverse(value);
      }
    }
  }
  if (Array.isArray(formula.values)) {
    for (const value of formula.values) {
      traverse(value);
    }
  }
  return result;
}

// src/propositional/converters/extract-prop-variables.ts
function extractPropVariables(formula) {
  const variablesSet = /* @__PURE__ */ new Set();
  function traverse(node) {
    if (node.operator === "VAR" /* Var */) {
      variablesSet.add(node.values[0]);
      return;
    }
    if (Array.isArray(node.values)) {
      const subFormulas = node.values;
      for (const subFormula of subFormulas) {
        traverse(subFormula);
      }
    }
  }
  traverse(formula);
  const sortedVariables = Array.from(variablesSet).sort(
    (a, b) => a.localeCompare(b)
  );
  return new Map(sortedVariables.map((varName, index) => [index, [varName]]));
}

// src/propositional/converters/replace-atom-in-formula.ts
function replaceAtomInFormula({
  formula,
  atom,
  substitute
}) {
  function traverse(node) {
    if (node.operator === "VAR" /* Var */) {
      const nodeAtom = node.values;
      if (nodeAtom[0] === atom[0]) {
        if (Array.isArray(substitute) && substitute.length === 1 && typeof substitute[0] === "string") {
          return {
            operator: "VAR" /* Var */,
            values: substitute
          };
        } else {
          return substitute;
        }
      }
      return node;
    }
    if (Array.isArray(node.values)) {
      const subFormulas = node.values;
      const newValues = subFormulas.map((subFormula) => traverse(subFormula));
      return {
        operator: node.operator,
        values: newValues
      };
    }
    return node;
  }
  return traverse(formula);
}

// src/propositional/evaluators/get-binary-operation-value.ts
function getBinaryOperationValue({
  operator,
  leftOperand,
  rightOperand
}) {
  switch (operator) {
    case "AND" /* And */:
      return leftOperand && rightOperand;
    case "OR" /* Or */:
      return leftOperand || rightOperand;
    case "IMPLIES" /* Implies */:
      return !leftOperand || rightOperand;
    case "REVERSED_IMPLIES" /* ReversedImplies */:
      return !rightOperand || leftOperand;
    case "EQUIV" /* Equiv */:
      return leftOperand === rightOperand;
    case "XOR" /* Xor */:
      return leftOperand !== rightOperand;
    case "NAND" /* Nand */:
      return !(leftOperand && rightOperand);
    case "NOR" /* Nor */:
      return !(leftOperand || rightOperand);
    case "ANTI_IMPLIES" /* AntiImplies */:
      return leftOperand && !rightOperand;
    case "REVERSED_ANTI_IMPLIES" /* ReversedAntiImplies */:
      return rightOperand && !leftOperand;
    case "CONTRADICTION" /* Contradiction */:
      return false;
    case "TAUTOLOGY" /* Tautology */:
      return true;
    case "VAR" /* Var */:
    case "NOT" /* Not */:
      throw new Error(`Operator "${operator}" is not a binary operator.`);
    default:
      throw new Error(`Unknown operator: "${operator}".`);
  }
}

// src/propositional/evaluators/get-unary-operation-value.ts
function getUnaryOperationValue({
  operator,
  operand
}) {
  switch (operator) {
    case "VAR" /* Var */:
      return operand;
    // A variable simply retains its boolean value.
    case "NOT" /* Not */:
      return !operand;
    // Logical negation.
    default:
      throw new Error(`Operator "${operator}" is not a valid unary operator.`);
  }
}

// src/propositional/evaluators/calculate-prop-formula.ts
function calculatePropFormula({
  formula,
  assignment,
  variablesMap
}) {
  const variables = variablesMap ?? extractPropVariables(formula);
  if (variables.size !== assignment.length) {
    throw new Error(
      `Mismatch between formula variables (${variables.size}) and assignment length (${assignment.length}).`
    );
  }
  const variableValues = /* @__PURE__ */ new Map();
  variables.forEach((atom, index) => {
    variableValues.set(atom[0], assignment[index]);
  });
  function evaluate(node) {
    if (node.operator === "VAR" /* Var */) {
      return !!variableValues.get(node.values[0]);
    }
    if (node.operator === "NOT" /* Not */) {
      const operand = node.values[0];
      return getUnaryOperationValue({
        operator: node.operator,
        operand: evaluate(operand)
      });
    }
    const [left, right] = node.values;
    return getBinaryOperationValue({
      operator: node.operator,
      leftOperand: evaluate(left),
      rightOperand: evaluate(right)
    });
  }
  return evaluate(formula);
}

// src/propositional/hilbert-calculus/axioms/implication-distribution.ts
function implicationDistributionSchema(formulas) {
  const [A, B, C] = formulas;
  return {
    operator: "IMPLIES" /* Implies */,
    values: [
      {
        operator: "IMPLIES" /* Implies */,
        values: [A, { operator: "IMPLIES" /* Implies */, values: [B, C] }]
      },
      {
        operator: "IMPLIES" /* Implies */,
        values: [
          { operator: "IMPLIES" /* Implies */, values: [A, B] },
          { operator: "IMPLIES" /* Implies */, values: [A, C] }
        ]
      }
    ]
  };
}

// src/propositional/hilbert-calculus/axioms/implication-introduction.ts
function implicationIntroductionSchema(formulas) {
  const [A, B] = formulas;
  return {
    operator: "IMPLIES" /* Implies */,
    values: [
      A,
      {
        operator: "IMPLIES" /* Implies */,
        values: [B, A]
      }
    ]
  };
}

// src/propositional/hilbert-calculus/axioms/implication-reversal.ts
function implicationReversalSchema(formulas) {
  const [A, B] = formulas;
  return {
    operator: "IMPLIES" /* Implies */,
    values: [
      {
        operator: "IMPLIES" /* Implies */,
        values: [
          { operator: "NOT" /* Not */, values: [A] },
          { operator: "NOT" /* Not */, values: [B] }
        ]
      },
      {
        operator: "IMPLIES" /* Implies */,
        values: [B, A]
      }
    ]
  };
}

// src/propositional/hilbert-calculus/axioms/index.ts
var HilbertAxioms = Object.freeze({
  II: implicationIntroductionSchema,
  ID: implicationDistributionSchema,
  IR: implicationReversalSchema
});

// src/propositional/validators/are-prop-formulas-structurally-equal.ts
function arePropFormulasStructurallyEqual(formulas) {
  if (!formulas.length) return false;
  const strings = formulas.map((formula) => JSON.stringify(formula));
  return strings.every((item) => item === strings[0]);
}

// src/propositional/validators/is-conjunction-elimination-applicable.ts
function isConjunctionEliminationApplicable(formulas) {
  if (formulas.length === 0) {
    return false;
  }
  return formulas.every((formula) => formula.operator === "AND" /* And */);
}

// src/propositional/validators/is-conjunction-introduction-applicable.ts
function isConjunctionIntroductionApplicable(formulas) {
  return formulas.length === 2;
}

// src/propositional/validators/is-disjunction-elimination-applicable.ts
function isDisjunctionEliminationApplicable(formulas) {
  if (formulas.length !== 3) return false;
  const [formula1, formula2, formula3] = formulas;
  let disjunction = null;
  let implication1 = null;
  let implication2 = null;
  for (const formula of [formula1, formula2, formula3]) {
    const isValidDisjunction = formula.operator === "OR" /* Or */ && Array.isArray(formula.values) && formula.values.length === 2;
    const isValidImplication = formula.operator === "IMPLIES" /* Implies */ && Array.isArray(formula.values) && formula.values.length === 2;
    const isImplication1Missing = !implication1;
    if (isValidDisjunction) {
      disjunction = formula;
    } else if (isValidImplication) {
      if (isImplication1Missing) {
        implication1 = formula;
      } else {
        implication2 = formula;
      }
    }
  }
  if (!disjunction || !implication1 || !implication2) {
    return false;
  }
  const [disjunct1, disjunct2] = disjunction.values;
  const [antecedent1, consequent1] = implication1.values;
  const [antecedent2, consequent2] = implication2.values;
  if (!arePropFormulasStructurallyEqual([consequent1, consequent2])) {
    return false;
  }
  return arePropFormulasStructurallyEqual([disjunct1, antecedent1]) && arePropFormulasStructurallyEqual([disjunct2, antecedent2]) || arePropFormulasStructurallyEqual([disjunct1, antecedent2]) && arePropFormulasStructurallyEqual([disjunct2, antecedent1]);
}

// src/propositional/validators/is-disjunction-introduction-applicable.ts
function isDisjunctionIntroductionApplicable(formulas) {
  return formulas.length === 2;
}

// src/propositional/validators/is-equivalence-elimination-applicable.ts
function isEquivalenceEliminationApplicable(formulas) {
  if (formulas.length === 0) {
    return false;
  }
  return formulas.every((formula) => formula.operator === "EQUIV" /* Equiv */);
}

// src/propositional/validators/is-equivalence-introduction-applicable.ts
function isEquivalenceIntroductionApplicable(formulas) {
  if (formulas.length !== 2) {
    return false;
  }
  const [formula1, formula2] = formulas;
  if (formula1.operator !== "IMPLIES" /* Implies */ || formula2.operator !== "IMPLIES" /* Implies */) {
    return false;
  }
  const [antecedent1, consequent1] = formula1.values;
  const [antecedent2, consequent2] = formula2.values;
  return arePropFormulasStructurallyEqual([antecedent1, consequent2]) && arePropFormulasStructurallyEqual([antecedent2, consequent1]);
}

// src/propositional/validators/is-implication-distribution-applicable.ts
function isImplicationDistributionSchema(formula) {
  if (formula.operator !== "IMPLIES" /* Implies */) {
    return false;
  }
  if (!Array.isArray(formula.values) || formula.values.length !== 2) {
    return false;
  }
  const consequent = formula.values[1];
  if (!Array.isArray(consequent.values) || consequent.operator !== "IMPLIES" /* Implies */ || consequent.values.length !== 2) {
    return false;
  }
  return true;
}
function isImplicationDistributionApplicable(formulas) {
  if (formulas.length === 0) {
    return false;
  }
  return formulas.every(isImplicationDistributionSchema);
}

// src/propositional/validators/is-implication-elimination-applicable.ts
function isImplicationEliminationApplicable(formulas) {
  if (formulas.length !== 2) return false;
  const [formula1, formula2] = formulas;
  const checkImplication = (implication, antecedent) => implication.operator === "IMPLIES" /* Implies */ && Array.isArray(implication.values) && implication.values.length === 2 && arePropFormulasStructurallyEqual([implication.values[0], antecedent]);
  return checkImplication(formula1, formula2) || checkImplication(formula2, formula1);
}

// src/propositional/validators/is-implication-introduction-applicable.ts
function isImplicationIntroductionApplicable(formulas) {
  return formulas.length === 2;
}

// src/propositional/validators/is-implication-reversal-applicable.ts
function isImplicationReversalSchema(formula) {
  if (formula.operator !== "IMPLIES" /* Implies */) {
    return false;
  }
  if (!Array.isArray(formula.values) || formula.values.length !== 2) {
    return false;
  }
  const antecedent = formula.values[0];
  const consequent = formula.values[1];
  if (!Array.isArray(antecedent.values) || antecedent.operator !== "NOT" /* Not */ || antecedent.values.length !== 1) {
    return false;
  }
  if (!Array.isArray(consequent.values) || consequent.operator !== "NOT" /* Not */ || consequent.values.length !== 1) {
    return false;
  }
  return true;
}
function isImplicationReversalApplicable(formulas) {
  if (formulas.length === 0) {
    return false;
  }
  return formulas.every(isImplicationReversalSchema);
}

// src/propositional/validators/is-negation-elimination-applicable.ts
function isNegationEliminationApplicable(formulas) {
  if (formulas.length === 0) {
    return false;
  }
  return formulas.every(
    (formula) => formula.operator === "NOT" /* Not */ && Array.isArray(formula.values) && formula.values.length === 1 && formula.values[0].operator === "NOT" /* Not */
  );
}

// src/propositional/validators/is-negation-introduction-applicable.ts
function isNegationIntroductionApplicable(formulas) {
  if (formulas.length !== 2) {
    return false;
  }
  const [formula1, formula2] = formulas;
  if (formula1.operator !== "IMPLIES" /* Implies */ || formula2.operator !== "IMPLIES" /* Implies */) {
    return false;
  }
  const [antecedent1, consequent1] = formula1.values;
  const [antecedent2, consequent2] = formula2.values;
  if (!arePropFormulasStructurallyEqual([antecedent1, antecedent2])) {
    return false;
  }
  return consequent1.operator === "NOT" /* Not */ && arePropFormulasStructurallyEqual([
    consequent1.values[0],
    consequent2
  ]) || consequent2.operator === "NOT" /* Not */ && arePropFormulasStructurallyEqual([
    consequent2.values[0],
    consequent1
  ]);
}

// src/propositional/validators/validate-prop-formulas.ts
var PROP_FORMULA_CHECKS = {
  ["areEqual" /* areEqual */]: arePropFormulasStructurallyEqual,
  // Elimination rules
  ["isIE" /* isIE */]: isImplicationEliminationApplicable,
  ["isDE" /* isDE */]: isDisjunctionEliminationApplicable,
  ["isCE" /* isCE */]: isConjunctionEliminationApplicable,
  ["isEE" /* isEE */]: isEquivalenceEliminationApplicable,
  ["isNE" /* isNE */]: isNegationEliminationApplicable,
  // Introduction rules
  ["isDI" /* isDI */]: isDisjunctionIntroductionApplicable,
  ["isCI" /* isCI */]: isConjunctionIntroductionApplicable,
  ["isEI" /* isEI */]: isEquivalenceIntroductionApplicable,
  ["isNI" /* isNI */]: isNegationIntroductionApplicable,
  ["isII" /* isII */]: isImplicationIntroductionApplicable,
  // Other rules
  ["isID" /* isID */]: isImplicationDistributionApplicable,
  ["isIR" /* isIR */]: isImplicationReversalApplicable
};
function validatePropFormulas(formulas, checks = Object.keys(
  PropFormulaCheck
)) {
  return checks.reduce((results, checkName) => {
    const checkFunction = PROP_FORMULA_CHECKS[checkName];
    results[checkName] = checkFunction ? checkFunction(formulas) : false;
    return results;
  }, {});
}

// src/propositional/hilbert-calculus/rules/implication-distribution.ts
function implicationDistributionRule(formulas) {
  if (!isImplicationDistributionApplicable(formulas)) {
    throw new Error(
      "Implication distribution requires each formula to have the form F => (G => H)."
    );
  }
  return formulas.map((formula) => {
    const F = formula.values[0];
    const consequent = formula.values[1];
    const G = consequent.values[0];
    const H = consequent.values[1];
    return {
      operator: "IMPLIES" /* Implies */,
      values: [
        {
          operator: "IMPLIES" /* Implies */,
          values: [F, G]
        },
        {
          operator: "IMPLIES" /* Implies */,
          values: [F, H]
        }
      ]
    };
  });
}

// src/propositional/hilbert-calculus/rules/implication-elimination.ts
function implicationEliminationRule(formulas) {
  if (!isImplicationEliminationApplicable(formulas)) {
    throw new Error(
      "Implication elimination is not applicable to the given formulas."
    );
  }
  const [formula1, formula2] = formulas;
  let implicationFormula;
  if (formula1.operator === "IMPLIES" /* Implies */ && Array.isArray(formula1.values) && formula1.values.length === 2 && arePropFormulasStructurallyEqual([formula1.values[0], formula2])) {
    implicationFormula = formula1;
  } else if (formula2.operator === "IMPLIES" /* Implies */ && Array.isArray(formula2.values) && formula2.values.length === 2 && arePropFormulasStructurallyEqual([formula2.values[0], formula1])) {
    implicationFormula = formula2;
  }
  return [implicationFormula?.values[1]];
}

// src/propositional/hilbert-calculus/rules/implication-introduction.ts
function implicationIntroductionRule(formulas) {
  if (!isImplicationIntroductionApplicable(formulas)) {
    throw new Error(
      "Implication introduction requires exactly two formulas: the proven formula and the new antecedent formula."
    );
  }
  const [provenFormula, newFormula] = formulas;
  return [
    {
      operator: "IMPLIES" /* Implies */,
      values: [newFormula, provenFormula]
    }
  ];
}

// src/propositional/hilbert-calculus/rules/implication-reversal.ts
function implicationReversalRule(formulas) {
  if (!isImplicationReversalApplicable(formulas)) {
    throw new Error(
      "Implication reversal requires each formula to have the form \xACF => \xACG."
    );
  }
  return formulas.map((formula) => {
    const antecedent = formula.values[0];
    const consequent = formula.values[1];
    const F = antecedent.values[0];
    const G = consequent.values[0];
    return {
      operator: "IMPLIES" /* Implies */,
      values: [G, F]
    };
  });
}

// src/propositional/hilbert-calculus/generators/generate-hilbert-proof-steps.ts
function generateHilbertProofSteps(input) {
  const { index, step } = input;
  if (step === "Derivation" /* Derivation */) {
    return buildDerivedSteps(index, input.payload);
  }
  if (step === "Axiom" /* Axiom */) {
    return buildAxiomStep(index, input.payload);
  }
  return buildBaseStep(index, step, input.payload);
}
function buildDerivedSteps(index, payload) {
  const { formulas, rule, derivedFrom } = payload;
  const derivedFormulas = getRuleFunction(rule)(formulas);
  return derivedFormulas.map((formula, derivedIndex) => {
    return {
      index: index + derivedIndex,
      step: "Derivation" /* Derivation */,
      formula,
      stringView: convertPropFormulaToString(formula),
      expression: convertPropFormulaToExpression(formula),
      comment: `${rule}: ${derivedFrom.join(", ")}`,
      derivedFrom
    };
  });
}
function buildAxiomStep(index, payload) {
  const { formulas, schema } = payload;
  const formula = getSchemaFunction(schema)(formulas);
  return [
    {
      index,
      step: "Axiom" /* Axiom */,
      formula,
      stringView: convertPropFormulaToString(formula),
      expression: convertPropFormulaToExpression(formula),
      comment: `${schema}`
    }
  ];
}
function buildBaseStep(index, step, payload) {
  return [
    {
      index,
      step,
      formula: payload.formula,
      stringView: convertPropFormulaToString(payload.formula),
      expression: convertPropFormulaToExpression(payload.formula),
      comment: `${step}`
    }
  ];
}
function getSchemaFunction(schema) {
  switch (schema) {
    case "II" /* II */:
      return implicationIntroductionSchema;
    case "ID" /* ID */:
      return implicationDistributionSchema;
    case "IR" /* IR */:
      return implicationReversalSchema;
  }
}
function getRuleFunction(rule) {
  switch (rule) {
    case "II" /* II */:
      return implicationIntroductionRule;
    case "ID" /* ID */:
      return implicationDistributionRule;
    case "IR" /* IR */:
      return implicationReversalRule;
    case "IE" /* IE */:
      return implicationEliminationRule;
  }
}

// src/propositional/hilbert-calculus/classes/hilbert-proof.ts
var HilbertProof = class {
  /**
   * Creates a new Hilbert proof with a goal formula.
   * @param goal - The target formula to prove
   */
  constructor(goal) {
    this.steps = [];
    this.goal = goal;
  }
  /**
   * Gets all proof steps in order.
   * @returns Array of proof steps
   */
  getSteps() {
    return Object.freeze([...this.steps]);
  }
  /**
   * Gets the goal formula of this proof.
   * @returns The target formula
   */
  getGoal() {
    return this.goal;
  }
  /**
   * Gets the number of steps in the proof.
   * @returns The current step count
   */
  getStepCount() {
    return this.steps.length;
  }
  /**
   * Gets a specific step by index (1-based).
   * @param index - The step number (1-based)
   * @returns The proof step, or undefined if not found
   */
  getStep(index) {
    return this.steps[index - 1];
  }
  /**
   * Adds a premise (given assumption) to the proof.
   * @param formula - The premise formula
   * @param comment - Optional explanation for the premise
   * @returns The added proof step
   */
  addPremise(formula, comment) {
    const steps = generateHilbertProofSteps({
      index: this.steps.length + 1,
      step: "Premise" /* Premise */,
      payload: { formula }
    });
    const step = steps[0];
    if (comment) {
      step.comment = comment;
    }
    this.steps.push(step);
    return step;
  }
  /**
   * Adds an axiom step to the proof.
   * @param payload - The axiom payload containing formulas and schema
   * @param comment - Optional explanation for the axiom
   * @returns The added proof step
   */
  addAxiom(payload, comment) {
    const steps = generateHilbertProofSteps({
      index: this.steps.length + 1,
      step: "Axiom" /* Axiom */,
      payload
    });
    const step = steps[0];
    if (comment) {
      step.comment = comment;
    }
    this.steps.push(step);
    return step;
  }
  /**
   * Adds a derived step to the proof using a Hilbert calculus rule.
   * @param payload - The derived step payload containing formulas, schema, and step references
   * @param comment - Optional explanation for the derivation
   * @returns The added proof step
   */
  addDerivedStep(payload, comment) {
    const newSteps = generateHilbertProofSteps({
      index: this.steps.length + 1,
      step: "Derivation" /* Derivation */,
      payload
    });
    newSteps.forEach((step) => {
      if (comment) {
        step.comment = comment;
      }
      this.steps.push(step);
    });
    return newSteps;
  }
  /**
   * Checks if the proof is complete (last step matches the goal).
   * @returns True if the last step's formula matches the goal
   */
  isComplete() {
    if (this.steps.length === 0) {
      return false;
    }
    if (this.steps.every((step) => step.step === "Premise" /* Premise */)) {
      return false;
    }
    const lastStep = this.getLastStep();
    return arePropFormulasStructurallyEqual([lastStep.formula, this.goal]);
  }
  /**
   * Gets the last step in the proof (which should be the goal).
   * @returns The final proof step, or undefined if no steps exist
   */
  getLastStep() {
    return this.steps.at(-1);
  }
  /**
   * Reiterates (repeats) a previously proved step.
   * Allows referring to a formula from an earlier step in the proof.
   * @param fromIndex - The index of the step to reiterate (1-based)
   * @param comment - Optional explanation for the reiteration
   * @returns The added reiteration step
   * @throws {Error} if the step index is invalid
   */
  reiterateStep(fromIndex, comment) {
    const sourceStep = this.getStep(fromIndex);
    if (!sourceStep) {
      throw new Error(`Cannot reiterate: step ${fromIndex} not found in proof`);
    }
    const steps = generateHilbertProofSteps({
      index: this.steps.length + 1,
      step: "Reiteration" /* Reiteration */,
      payload: { formula: sourceStep.formula }
    });
    const step = steps[0];
    if (comment) {
      step.comment = comment;
    } else {
      step.comment = `Reiteration: ${fromIndex}`;
    }
    step.derivedFrom = [fromIndex];
    this.steps.push(step);
    return step;
  }
  /**
   * Clears all steps from the proof.
   */
  clear() {
    this.steps = [];
  }
  /**
   * Replaces all occurrences of an atom with a formula or atom in all proof steps.
   * The goal formula is not modified.
   *
   * @param atom - The atomic proposition to replace
   * @param substitute - The formula or atom to substitute
   */
  replace(atom, substitute) {
    this.steps.forEach((step) => {
      const newFormula = replaceAtomInFormula({
        formula: step.formula,
        atom,
        substitute
      });
      step.formula = newFormula;
      step.expression = convertPropFormulaToExpression(newFormula);
      step.stringView = convertPropFormulaToString(newFormula);
    });
  }
};

// src/propositional/hilbert-calculus/classes/hilbert-proof-builder.ts
var HilbertProofBuilder = class {
  /**
   * Creates a new proof builder with a goal formula.
   * @param goal - The target formula to prove
   */
  constructor(goal) {
    this.proof = new HilbertProof(goal);
  }
  /**
   * Adds a premise (given assumption) to the proof.
   * @param formula - The premise formula
   * @param comment - Optional explanation for the premise
   * @returns This builder instance for chaining
   */
  addPremise(formula, comment) {
    this.proof.addPremise(formula, comment);
    return this;
  }
  /**
   * Adds an axiom step to the proof.
   * @param payload - The axiom payload containing formulas and schema
   * @param comment - Optional explanation for the axiom
   * @returns This builder instance for chaining
   */
  addAxiom(payload, comment) {
    this.proof.addAxiom(payload, comment);
    return this;
  }
  /**
   * Adds a derived step to the proof using a Hilbert calculus rule.
   * @param payload - The derived step payload containing formulas, schema, and step references
   * @param comment - Optional explanation for the derivation
   * @returns This builder instance for chaining
   */
  addDerivedStep(payload, comment) {
    this.proof.addDerivedStep(payload, comment);
    return this;
  }
  /**
   * Reiterates (repeats) a previously proved step.
   * Allows referring to a formula from an earlier step in the proof.
   * @param fromIndex - The index of the step to reiterate (1-based)
   * @param comment - Optional explanation for the reiteration
   * @returns This builder instance for chaining
   */
  reiterateStep(fromIndex, comment) {
    this.proof.reiterateStep(fromIndex, comment);
    return this;
  }
  /**
   * Replaces all occurrences of an atom with a formula or atom in all proof steps.
   * The goal formula is not modified.
   *
   * @param atom - The atomic proposition to replace
   * @param substitute - The formula or atom to substitute
   * @returns This builder instance for chaining
   */
  replace(atom, substitute) {
    this.proof.replace(atom, substitute);
    return this;
  }
  /**
   * Constructs the proof and returns it.
   * @returns The completed HilbertProof instance
   */
  build() {
    return this.proof;
  }
  /**
   * Adds multiple steps in sequence using a callback function.
   * Useful for building complex proofs programmatically.
   *
   * @param stepsFn - A callback that receives the current builder and adds steps
   * @returns This builder instance for chaining
   *
   * @example
   * ```typescript
   * proof.buildSteps((builder) => {
   *   builder.addPremise(p);
   *   builder.addAxiom(axiom1);
   *   builder.addDerivedStep(derived1);
   * });
   * ```
   */
  buildSteps(stepsFn) {
    stepsFn(this);
    return this;
  }
  /**
   * Gets the current state of the proof without building.
   * Useful for inspection during construction.
   * @returns The current HilbertProof instance
   */
  preview() {
    return this.proof;
  }
};

// src/propositional/hilbert-calculus/generators/build-hilbert-proof.ts
function buildHilbertProof(goal) {
  return new HilbertProofBuilder(goal);
}

// src/propositional/hilbert-calculus/generators/compose-hilbert-proof.ts
function composeHilbertProof(goal, ...stepGenerators) {
  const builder = buildHilbertProof(goal);
  for (const generator of stepGenerators) {
    generator(builder);
  }
  return builder.build();
}

// src/propositional/hilbert-calculus/rules/index.ts
var HilbertRules = Object.freeze({
  II: implicationIntroductionRule,
  ID: implicationDistributionRule,
  IE: implicationEliminationRule,
  IR: implicationReversalRule
});

// src/propositional/natural-calculus/rules/conjunction-elimination.ts
function conjunctionElimination(formulas) {
  if (!isConjunctionEliminationApplicable(formulas)) {
    throw new Error(
      "Conjunction Elimination is not applicable for the given formulas."
    );
  }
  return formulas.flatMap((formula) => {
    const conjunct1 = formula.values[0];
    const conjunct2 = formula.values[1];
    return [conjunct1, conjunct2];
  });
}

// src/propositional/natural-calculus/rules/conjunction-introduction.ts
function conjunctionIntroduction(formulas) {
  if (!isConjunctionIntroductionApplicable(formulas)) {
    throw new Error(
      "Conjunction introduction is not applicable to the given formulas."
    );
  }
  const conjunct1 = formulas[0];
  const conjunct2 = formulas[1];
  return [
    {
      operator: "AND" /* And */,
      values: [conjunct1, conjunct2]
    },
    {
      operator: "AND" /* And */,
      values: [conjunct2, conjunct1]
    }
  ];
}

// src/propositional/natural-calculus/rules/disjunction-elimination.ts
function disjunctionElimination(formulas) {
  if (!isDisjunctionEliminationApplicable(formulas)) {
    throw new Error(
      "Disjunction elimination is not applicable to the given formulas."
    );
  }
  const implication1 = formulas.find(
    (formula) => formula.operator === "IMPLIES" /* Implies */
  );
  return [implication1?.values[1]];
}

// src/propositional/natural-calculus/rules/disjunction-introduction.ts
function disjunctionIntroduction(formulas) {
  if (!isDisjunctionIntroductionApplicable(formulas)) {
    throw new Error(
      "Disjunction introduction is not applicable to the given formulas."
    );
  }
  const disjunct1 = formulas[0];
  const disjunct2 = formulas[1];
  return [
    { operator: "OR" /* Or */, values: [disjunct1, disjunct2] },
    { operator: "OR" /* Or */, values: [disjunct2, disjunct1] }
  ];
}

// src/propositional/natural-calculus/rules/equivalence-elimination.ts
function equivalenceElimination(formulas) {
  if (!isEquivalenceEliminationApplicable(formulas)) {
    throw new Error(
      "Equivalence elimination is not applicable. All formulas must be equivalences."
    );
  }
  return formulas.flatMap((formula) => {
    const [A, B] = formula.values;
    return [
      { operator: "IMPLIES" /* Implies */, values: [A, B] },
      { operator: "IMPLIES" /* Implies */, values: [B, A] }
    ];
  });
}

// src/propositional/natural-calculus/rules/equivalence-introduction.ts
function equivalenceIntroduction(formulas) {
  if (!isEquivalenceIntroductionApplicable(formulas)) {
    throw new Error(
      "Equivalence introduction is not applicable to the given formulas."
    );
  }
  const [implication1, implication2] = formulas;
  const firstAntecedent = implication1.values[0];
  const secondAntecedent = implication2.values[0];
  return [
    {
      operator: "EQUIV" /* Equiv */,
      values: [firstAntecedent, secondAntecedent]
    }
  ];
}

// src/propositional/natural-calculus/rules/implication-elimination.ts
functio