[{"name":"Formula","comment":" This library exports and parses formulas.\n\n\n# Definitions\n\n@docs Formula, Signed, Substitution, Term\n\n\n# Parsers\n\n@docs parse, parseSigned, parseTerm\n\n\n# Strings\n\n@docs strFormula, strSigned, strTerm, strSubstitution, errorString\n\n\n# Tableau helpers\n\n@docs substitute, isAlpha, isBeta, isGamma, isDelta, freeFormula, removeQuantifierAndSubstitute, isSignedComplementary, isSignedSubformulaOf, signedGetFormula, signedSubformulas, isSubformulaOf\n\n","unions":[{"name":"Formula","comment":" Formula\n","args":[],"cases":[["Atom",["String.String","List.List Formula.Term"]],["Neg",["Formula.Formula"]],["Disj",["Formula.Formula","Formula.Formula"]],["Conj",["Formula.Formula","Formula.Formula"]],["Impl",["Formula.Formula","Formula.Formula"]],["ForAll",["String.String","Formula.Formula"]],["Exists",["String.String","Formula.Formula"]],["FF",[]],["FT",[]]]},{"name":"Signed","comment":" Signed with T[rue] or F[alse]\n","args":["a"],"cases":[["T",["a"]],["F",["a"]]]},{"name":"Term","comment":" Term\n","args":[],"cases":[["Var",["String.String"]],["Fun",["String.String","List.List Formula.Term"]]]}],"aliases":[{"name":"Substitution","comment":" Type alias for substitution\n","args":[],"type":"Dict.Dict String.String Formula.Term"}],"values":[{"name":"errorString","comment":" Format parsing error\n","type":"List.List Parser.DeadEnd -> String.String"},{"name":"freeFormula","comment":" Returns set of all free variables in given formula\n","type":"Formula.Formula -> Set.Set String.String"},{"name":"isAlpha","comment":" Is the signed formula of type Alpha\n","type":"Formula.Signed Formula.Formula -> Basics.Bool"},{"name":"isBeta","comment":" Is the signed formula of type Beta\n","type":"Formula.Signed Formula.Formula -> Basics.Bool"},{"name":"isDelta","comment":" Is the signed formula of type Delta\n","type":"Formula.Signed Formula.Formula -> Basics.Bool"},{"name":"isGamma","comment":" Is the signed formula of type Gamma\n","type":"Formula.Signed Formula.Formula -> Basics.Bool"},{"name":"isSignedComplementary","comment":" Is the first Signed Formula complementary of the second Signed Formula\n","type":"Formula.Signed Formula.Formula -> Formula.Signed Formula.Formula -> Basics.Bool"},{"name":"isSignedSubformulaOf","comment":" Is the first a Signed subformula of the second\n","type":"Formula.Signed Formula.Formula -> Formula.Signed Formula.Formula -> Basics.Bool"},{"name":"isSubformulaOf","comment":" Is the first a subformula of the second\n","type":"Formula.Formula -> Formula.Formula -> Basics.Bool"},{"name":"parse","comment":" Parse string to Formula\n","type":"String.String -> Result.Result (List.List Parser.DeadEnd) Formula.Formula"},{"name":"parseSigned","comment":" Parse string to Signed Formula\n","type":"String.String -> Result.Result (List.List Parser.DeadEnd) (Formula.Signed Formula.Formula)"},{"name":"parseTerm","comment":" Parses string to Term\n","type":"String.String -> Result.Result (List.List Parser.DeadEnd) Formula.Term"},{"name":"removeQuantifierAndSubstitute","comment":" Removes quantifier from given signed formula and returns formula after substitution or error\n","type":"Formula.Substitution -> Formula.Formula -> Result.Result String.String Formula.Formula"},{"name":"signedGetFormula","comment":" Get Formula out of Signed Formula\n","type":"Formula.Signed Formula.Formula -> Formula.Formula"},{"name":"signedSubformulas","comment":" Get signed subformulas as a list of signed formulas\n","type":"Formula.Signed Formula.Formula -> List.List (Formula.Signed Formula.Formula)"},{"name":"strFormula","comment":" String representation of a Formula\n","type":"Formula.Formula -> String.String"},{"name":"strSigned","comment":" String representation of a Signed Formula\n","type":"Formula.Signed Formula.Formula -> String.String"},{"name":"strSubstitution","comment":" String representation of a Substitution\n","type":"Formula.Substitution -> String.String"},{"name":"strTerm","comment":" String representation of a Term\n","type":"Formula.Term -> String.String"},{"name":"substitute","comment":" Checks if substitution is applicable and substitutes if yes. Returns Result.\nErrMessage or Formula after substitution\n","type":"Formula.Substitution -> Formula.Formula -> Result.Result String.String Formula.Formula"}],"binops":[]}]