622 lines
18 KiB
Rust
622 lines
18 KiB
Rust
use super::terms::*;
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use super::tokens::*;
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pub fn formula(input: &str) -> Result<crate::Formula, crate::parse::Error>
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{
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let formula_str = FormulaStr::new(input);
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formula_str.parse(0)?;
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// TODO: implement correctly
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Ok(crate::Formula::true_())
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}
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pub(crate) fn predicate_name(identifier: &str) -> Option<(&str, &str)>
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{
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function_name(identifier)
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}
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#[derive(Clone, Copy, Eq, PartialEq)]
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enum LogicalConnective
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{
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And,
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IfAndOnlyIf,
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ImpliesLeftToRight,
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ImpliesRightToLeft,
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Or,
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}
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// TODO: rename to logic infix connective
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impl LogicalConnective
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{
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fn level(&self) -> usize
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{
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match self
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{
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Self::And => 1,
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Self::Or => 2,
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Self::ImpliesLeftToRight
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| Self::ImpliesRightToLeft => 3,
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Self::IfAndOnlyIf => 4,
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}
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}
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}
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impl std::fmt::Debug for LogicalConnective
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{
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fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
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{
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match &self
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{
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Self::And => write!(formatter, "and"),
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Self::IfAndOnlyIf => write!(formatter, "<->"),
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Self::ImpliesLeftToRight => write!(formatter, "->"),
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Self::ImpliesRightToLeft => write!(formatter, "<-"),
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Self::Or => write!(formatter, "or"),
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}
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}
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}
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struct FormulaStr<'i>
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{
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input: &'i str,
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}
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impl<'i> FormulaStr<'i>
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{
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pub fn new(input: &'i str) -> Self
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{
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Self
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{
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input,
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}
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}
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fn iter_tokens(&self) -> TokenIterator<'i>
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{
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TokenIterator::new(self.input)
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}
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fn filter_logical_connective(&self, logical_connective: LogicalConnective)
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-> std::iter::Filter<TokenIterator<'i>, impl FnMut(&Result<(usize, usize, Token<'i>), crate::parse::Error>) -> bool>
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{
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let token_selector = move |token: &_| match token
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{
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Ok((_, _, Token::Identifier(ref identifier))) => match *identifier
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{
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"and" => logical_connective == LogicalConnective::And,
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"or" => logical_connective == LogicalConnective::Or,
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_ => false,
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},
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Ok((_, _, Token::Symbol(ref symbol))) => match symbol
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{
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Symbol::ArrowLeft => logical_connective == LogicalConnective::ImpliesRightToLeft,
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Symbol::ArrowLeftAndRight => logical_connective == LogicalConnective::IfAndOnlyIf,
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Symbol::ArrowRight => logical_connective == LogicalConnective::ImpliesLeftToRight,
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_ => false,
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},
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_ => false,
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};
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self.iter_tokens().filter(token_selector)
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}
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pub fn top_level_logical_connective(&self)
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-> Result<Option<LogicalConnective>, crate::parse::Error>
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{
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let logical_connective = |token| match token
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{
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Token::Identifier(identifier) => match identifier
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{
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"and" => Some(LogicalConnective::And),
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"or" => Some(LogicalConnective::Or),
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_ => None,
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},
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Token::Symbol(symbol) => match symbol
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{
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Symbol::ArrowLeft => Some(LogicalConnective::ImpliesRightToLeft),
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Symbol::ArrowLeftAndRight => Some(LogicalConnective::IfAndOnlyIf),
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Symbol::ArrowRight => Some(LogicalConnective::ImpliesLeftToRight),
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_ => None,
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},
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_ => None,
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};
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let mut top_level_logical_connective = None;
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for token in self.iter_tokens()
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{
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let (_, _, token) = token?;
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let logical_connective = match logical_connective(token)
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{
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Some(logical_connective) => logical_connective,
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None => continue,
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};
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top_level_logical_connective = match top_level_logical_connective
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{
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None => Some(logical_connective),
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Some(top_level_logical_connective) =>
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{
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if (logical_connective == LogicalConnective::ImpliesLeftToRight
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&& top_level_logical_connective == LogicalConnective::ImpliesRightToLeft)
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|| (logical_connective == LogicalConnective::ImpliesRightToLeft
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&& top_level_logical_connective == LogicalConnective::ImpliesLeftToRight)
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{
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return Err(crate::parse::Error::new_mixed_implication_directions(
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crate::parse::error::Location::new(0, Some(0)),
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crate::parse::error::Location::new(0, Some(0))));
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}
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if logical_connective.level() > top_level_logical_connective.level()
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{
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Some(logical_connective)
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}
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else
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{
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Some(top_level_logical_connective)
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}
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},
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}
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}
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Ok(top_level_logical_connective)
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}
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fn filter_comparison_operators(&self)
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-> std::iter::FilterMap<TokenIterator<'i>, impl FnMut(Result<(usize, usize, Token<'i>), crate::parse::Error>)
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-> Option<Result<(usize, usize, crate::ComparisonOperator), crate::parse::Error>>>
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{
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let token_functor = |token| match token
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{
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Ok((input_left, remaining_input, Token::Symbol(symbol))) => match symbol
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{
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Symbol::Greater =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::Greater))),
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Symbol::GreaterOrEqual =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::GreaterOrEqual))),
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Symbol::Less =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::Less))),
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Symbol::LessOrEqual =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::LessOrEqual))),
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Symbol::Equal =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::Equal))),
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Symbol::NotEqual =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::NotEqual))),
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_ => None,
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},
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Err(error) => Some(Err(error)),
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_ => None,
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};
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self.iter_tokens().filter_map(token_functor)
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}
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pub fn parse(&self, level: usize) -> Result<crate::Formula, crate::parse::Error>
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{
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let indentation = " ".repeat(level);
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let input = self.input.trim_start();
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println!("{}- parsing formula: {}", indentation, input);
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match input.chars().next()
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{
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Some(')') => return Err(crate::parse::Error::new_unmatched_parenthesis(
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crate::parse::error::Location::new(0, Some(0)))),
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None => return Err(crate::parse::Error::new_empty_input(
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crate::parse::error::Location::new(0, Some(0)))),
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_ => (),
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}
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// Parse logical infix connectives
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if let Some(top_level_logical_connective) = self.top_level_logical_connective()?
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{
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println!("{} parsing “{:?}” infix formula", indentation, top_level_logical_connective);
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// Parse arguments of n-ary logical infix connectives
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let arguments_n_ary = ||
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{
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// TODO: improve error handling if the formulas between the operators are invalid
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TokenSplit::new(self.filter_logical_connective(top_level_logical_connective),
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self.input)
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.map(|subformula| FormulaStr::new(subformula?).parse(level + 1))
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.collect::<Result<Vec<_>, _>>()
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};
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match top_level_logical_connective
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{
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LogicalConnective::And => return Ok(crate::Formula::and(arguments_n_ary()?)),
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LogicalConnective::Or => return Ok(crate::Formula::or(arguments_n_ary()?)),
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LogicalConnective::IfAndOnlyIf =>
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return Ok(crate::Formula::if_and_only_if(arguments_n_ary()?)),
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LogicalConnective::ImpliesLeftToRight =>
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return implication_left_to_right(
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TokenSplit::new(
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self.filter_logical_connective(top_level_logical_connective),
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self.input),
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level + 1),
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/*LogicalConnective::ImpliesRightToLeft => unimplemented!(),*/
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_ =>
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{
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println!("{} TODO: parse implication", indentation);
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// TODO: implement correctly
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return Ok(crate::Formula::true_());
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}
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}
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}
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// Parse quantified formulas
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if let Some((identifier, input)) = identifier(input)
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{
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let quantifier = match identifier
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{
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"exists" => Some(Quantifier::Existential),
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"forall" => Some(Quantifier::Universal),
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_ => None,
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};
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if let Some(quantifier) = quantifier
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{
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let input = input.trim_start();
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println!("{} parsing “{:?}” formula body: {}", indentation, quantifier, input);
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return quantified_formula(input, quantifier, level + 1);
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}
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}
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let mut comparison_operators = self.filter_comparison_operators();
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// Parse comparisons
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if let Some(comparison_operator) = comparison_operators.next()
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{
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let (_, _, comparison_operator) = comparison_operator?;
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// Comparisons with more than one comparison operator aren’t supported
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if let Some(next_comparison_operator) = comparison_operators.next()
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{
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let (_, _, next_comparison_operator) = next_comparison_operator?;
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return Err(crate::parse::Error::new_multiple_comparison_operators(
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comparison_operator, next_comparison_operator,
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crate::parse::error::Location::new(0, Some(0))));
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}
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println!("{} parsing “{:?}” comparison: {}", indentation, comparison_operator, input);
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let mut comparison_operator_split =
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TokenSplit::new(self.filter_comparison_operators(), self.input);
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// There’s exactly one comparison operator in this formula, as we have verified above.
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// Hence, the split is guaranteed to generate exactly these two elements
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let input_left = comparison_operator_split.next().unwrap()?;
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let input_right = comparison_operator_split.next().unwrap()?;
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let argument_left = TermStr::new(input_left).parse(level + 1)?;
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let argument_right = TermStr::new(input_right).parse(level + 1)?;
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return Ok(crate::Formula::compare(comparison_operator, Box::new(argument_left),
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Box::new(argument_right)));
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}
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// Parse predicates
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if let Some((predicate_name, input)) = predicate_name(input)
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{
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println!("{} TODO: parse predicate {}", indentation, predicate_name);
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let input = input.trim_start();
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// Parse arguments if there are any
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/*let arguments = match parenthesized_expression(input)?
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{
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Some((parenthesized_expression, remaining_input)) =>
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{
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unimplemented!();
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}
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None => unimplemented!(),
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};*/
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// TODO: implement correctly
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return Ok(crate::Formula::true_());
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}
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// Parse parenthesized formulas
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if let Some('(') = input.chars().next()
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{
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match parenthesized_expression(input)?
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{
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Some((parenthesized_expression, remaining_input)) =>
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{
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if !remaining_input.trim().is_empty()
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{
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return Err(crate::parse::Error::new_unexpected_token(
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crate::parse::error::Location::new(0, Some(0))));
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}
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return FormulaStr::new(parenthesized_expression).parse(level);
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},
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None => unreachable!(),
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}
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};
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println!("{} can’t break down formula any further: {}", indentation, input);
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// TODO: implement correctly
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Ok(crate::Formula::true_())
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}
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}
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#[derive(Clone, Copy, Eq, PartialEq)]
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pub(crate) enum Quantifier
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{
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Existential,
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Universal,
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}
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impl std::fmt::Debug for Quantifier
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{
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fn fmt(&self, formatter: &mut std::fmt::Formatter) -> std::fmt::Result
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{
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match &self
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{
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Self::Existential => write!(formatter, "exists"),
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Self::Universal => write!(formatter, "forall"),
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}
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}
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}
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// TODO: refactor
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fn implication_left_to_right_inner<'i, T>(
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mut split_formula_at_logical_connective: TokenSplit<'i, T, Token<'i>>, level: usize)
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-> Result<Option<crate::Formula>, crate::parse::Error>
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where
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T: std::iter::Iterator<Item = Result<(usize, usize, Token<'i>), crate::parse::Error>>
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{
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match split_formula_at_logical_connective.next()
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{
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Some(argument) =>
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{
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// TODO: improve error handling if antecedent cannot be parsed
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let argument = FormulaStr::new(argument?).parse(level)?;
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match implication_left_to_right_inner(split_formula_at_logical_connective, level)?
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{
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Some(next_argument) => Ok(Some(crate::Formula::implies(
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crate::ImplicationDirection::LeftToRight, Box::new(argument),
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Box::new(next_argument)))),
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None => Ok(Some(argument)),
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}
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},
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None => Ok(None),
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}
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}
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fn implication_left_to_right<'i, T>(
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mut split_formula_at_logical_connective: TokenSplit<'i, T, Token<'i>>, level: usize)
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-> Result<crate::Formula, crate::parse::Error>
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where
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T: std::iter::Iterator<Item = Result<(usize, usize, Token<'i>), crate::parse::Error>>
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{
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match split_formula_at_logical_connective.next()
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{
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Some(argument) =>
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{
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// TODO: improve error handling if antecedent cannot be parsed
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let argument = FormulaStr::new(argument?).parse(level)?;
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match implication_left_to_right_inner(split_formula_at_logical_connective, level)?
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{
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Some(next_argument) => Ok(crate::Formula::implies(
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crate::ImplicationDirection::LeftToRight, Box::new(argument),
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Box::new(next_argument))),
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None => Err(crate::parse::Error::new_expected_logical_connective_argument(
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"left-to-right implication".to_string(),
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crate::parse::error::Location::new(0, Some(0)))),
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}
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},
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None => Err(crate::parse::Error::new_expected_logical_connective_argument(
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"left-to-right implication".to_string(),
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crate::parse::error::Location::new(0, Some(0)))),
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}
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}
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fn quantified_formula(input: &str, quantifier: Quantifier, level: usize)
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-> Result<crate::Formula, crate::parse::Error>
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{
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let (parameters, input) = match variable_declarations(input)?
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{
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Some(variable_declarations) => variable_declarations,
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None => return Err(crate::parse::Error::new_expected_variable_declaration(
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crate::parse::error::Location::new(0, Some(0)))),
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};
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let parameters = std::rc::Rc::new(parameters);
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let formula_str = FormulaStr::new(input.trim());
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let formula = Box::new(formula_str.parse(level)?);
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// TODO: push variable stack layer
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let formula = match quantifier
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{
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Quantifier::Existential => crate::Formula::exists(parameters, formula),
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Quantifier::Universal => crate::Formula::for_all(parameters, formula),
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};
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Ok(formula)
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}
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/*struct ComparisonOperatorIterator<'i>
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{
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original_input: &'i str,
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input: &'i str,
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}
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impl<'i> ComparisonOperatorIterator<'i>
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{
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pub fn new(input: &'i str) -> Self
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{
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Self
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{
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original_input: input,
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input,
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}
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}
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}
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// TODO: refactor
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impl<'i> std::iter::Iterator for ComparisonOperatorIterator<'i>
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{
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type Item = Result<(&'i str, &'i str, crate::ComparisonOperator), crate::parse::Error>;
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fn next(&mut self) -> Option<Self::Item>
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{
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loop
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{
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self.input = self.input.trim_start();
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let first_character = match self.input.chars().next()
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{
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None => return None,
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Some(first_character) => first_character,
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};
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if self.input.starts_with(")")
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{
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return Some(Err(crate::parse::Error::new_unmatched_parenthesis(
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crate::parse::error::Location::new(0, Some(1)))));
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}
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match parenthesized_expression(self.input)
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{
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Ok(Some((_, remaining_input))) =>
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{
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self.input = remaining_input;
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continue;
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},
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Ok(None) => (),
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Err(error) => return Some(Err(error)),
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}
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match number(self.input)
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{
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Ok(Some((_, remaining_input))) =>
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{
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self.input = remaining_input;
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continue;
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}
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Ok(None) => (),
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Err(error) => return Some(Err(error)),
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}
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let index_left = self.input.as_ptr() as usize - self.original_input.as_ptr() as usize;
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let input_left = self.original_input.split_at(index_left).0.trim_end();
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if let Some((symbol, remaining_input)) = symbol(self.input)
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{
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self.input = remaining_input;
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match symbol
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{
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Symbol::Greater =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::Greater))),
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Symbol::GreaterOrEqual =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::GreaterOrEqual))),
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Symbol::Less =>
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return Some(Ok((input_left, remaining_input,
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crate::ComparisonOperator::Less))),
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Symbol::LessOrEqual =>
|
||
return Some(Ok((input_left, remaining_input,
|
||
crate::ComparisonOperator::LessOrEqual))),
|
||
Symbol::Equal =>
|
||
return Some(Ok((input_left, remaining_input,
|
||
crate::ComparisonOperator::Equal))),
|
||
Symbol::NotEqual =>
|
||
return Some(Ok((input_left, remaining_input,
|
||
crate::ComparisonOperator::NotEqual))),
|
||
_ => continue,
|
||
}
|
||
}
|
||
|
||
match identifier(self.input)
|
||
{
|
||
Some((_, remaining_input)) =>
|
||
{
|
||
self.input = remaining_input;
|
||
continue;
|
||
}
|
||
None => (),
|
||
}
|
||
|
||
return Some(Err(crate::parse::Error::new_character_not_allowed(first_character,
|
||
crate::parse::error::Location::new(0, Some(0)))));
|
||
}
|
||
}
|
||
}*/
|
||
|
||
#[cfg(test)]
|
||
mod tests
|
||
{
|
||
use super::*;
|
||
|
||
#[test]
|
||
fn tokenize_formula_infix_operators()
|
||
{
|
||
let f = FormulaStr::new("((forall X exists Y (p(X) -> q(Y)) and false) or p) -> false");
|
||
assert_eq!(f.top_level_infix_operator().unwrap(),
|
||
Some(FormulaInfixOperator::ImpliesLeftToRight));
|
||
let mut i = f.iter_infix_operators();
|
||
assert_eq!(i.next().unwrap().unwrap().2, FormulaInfixOperator::ImpliesLeftToRight);
|
||
assert!(i.next().is_none());
|
||
|
||
let f = FormulaStr::new("forall X exists Y (p(X) -> q(Y)) and false or p -> false");
|
||
assert_eq!(f.top_level_infix_operator().unwrap(),
|
||
Some(FormulaInfixOperator::ImpliesLeftToRight));
|
||
let mut i = f.iter_infix_operators();
|
||
assert_eq!(i.next().unwrap().unwrap().2, FormulaInfixOperator::And);
|
||
assert_eq!(i.next().unwrap().unwrap().2, FormulaInfixOperator::Or);
|
||
assert_eq!(i.next().unwrap().unwrap().2, FormulaInfixOperator::ImpliesLeftToRight);
|
||
assert!(i.next().is_none());
|
||
|
||
let f = FormulaStr::new(" p -> forall X exists Y (p(X) -> q(Y)) and false or p -> false ");
|
||
assert_eq!(f.top_level_infix_operator().unwrap(),
|
||
Some(FormulaInfixOperator::ImpliesLeftToRight));
|
||
let mut i = f.split_at_infix_operator(FormulaInfixOperator::ImpliesLeftToRight);
|
||
assert_eq!(i.next().unwrap().unwrap(), "p");
|
||
assert_eq!(i.next().unwrap().unwrap(), "forall X exists Y (p(X) -> q(Y)) and false or p");
|
||
assert_eq!(i.next().unwrap().unwrap(), "false");
|
||
assert!(i.next().is_none());
|
||
|
||
let f = FormulaStr::new(" p -> forall X exists Y (p(X) -> q(Y)) and false or p -> false ");
|
||
assert_eq!(f.top_level_infix_operator().unwrap(),
|
||
Some(FormulaInfixOperator::ImpliesLeftToRight));
|
||
let mut i = f.split_at_infix_operator(FormulaInfixOperator::And);
|
||
assert_eq!(i.next().unwrap().unwrap(), "p -> forall X exists Y (p(X) -> q(Y))");
|
||
assert_eq!(i.next().unwrap().unwrap(), "false or p -> false");
|
||
assert!(i.next().is_none());
|
||
|
||
let f = FormulaStr::new(" p and forall X exists Y (p(X) -> q(Y)) and false or p or false ");
|
||
assert_eq!(f.top_level_infix_operator().unwrap(), Some(FormulaInfixOperator::Or));
|
||
let mut i = f.split_at_infix_operator(FormulaInfixOperator::Or);
|
||
assert_eq!(i.next().unwrap().unwrap(), "p and forall X exists Y (p(X) -> q(Y)) and false");
|
||
assert_eq!(i.next().unwrap().unwrap(), "p");
|
||
assert_eq!(i.next().unwrap().unwrap(), "false");
|
||
assert!(i.next().is_none());
|
||
|
||
let f = FormulaStr::new(" (p and q) ");
|
||
assert!(f.top_level_infix_operator().unwrap().is_none());
|
||
let mut i = f.split_at_infix_operator(FormulaInfixOperator::And);
|
||
assert_eq!(i.next().unwrap().unwrap(), "(p and q)");
|
||
assert!(i.next().is_none());
|
||
|
||
assert!(FormulaStr::new(" a -> b -> c ").parse(0).is_ok());
|
||
assert!(FormulaStr::new(" a -> b <- c ").parse(0).is_err());
|
||
|
||
assert!(!FormulaStr::new(" p -> forall X exists Y (p(X) -> q(Y)) and false or p -> false ")
|
||
.parse(0).is_ok());
|
||
}
|
||
}
|