Implement proof mechanism
This commit is contained in:
245
src/problem.rs
245
src/problem.rs
@@ -6,6 +6,7 @@ pub enum StatementKind
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Assertion,
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}
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#[derive(Copy, Clone, Eq, PartialEq)]
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enum ProofStatus
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{
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AssumedProven,
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@@ -151,10 +152,86 @@ impl Problem
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drop(statements);
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self.display(crate::output::Format::HumanReadable);
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self.prove_unproven_statements();
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log::info!("finished forward proof");
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}
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if proof_direction == crate::ProofDirection::Backward
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|| proof_direction == crate::ProofDirection::Both
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{
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log::info!("performing backward proof");
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let mut statements = self.statements.borrow_mut();
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// Initially reset all proof statuses
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for (_, statements) in statements.iter_mut()
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{
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for statement in statements.iter_mut()
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{
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match statement.kind
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{
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StatementKind::Axiom
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| StatementKind::Assertion
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=> statement.proof_status = ProofStatus::AssumedProven,
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_ => statement.proof_status = ProofStatus::ToProve,
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}
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}
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}
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drop(statements);
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self.prove_unproven_statements();
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log::info!("finished backward proof");
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}
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}
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fn prove_unproven_statements(&self) -> Result<(), crate::Error>
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{
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while self.statements.borrow()
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.iter()
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.find(|section|
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section.1.iter().find(|x| x.proof_status == ProofStatus::ToProve).is_some())
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.is_some()
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{
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let mut tptp_problem_to_prove_next_statement = "".to_string();
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self.write_tptp_problem_to_prove_next_statement(
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&mut tptp_problem_to_prove_next_statement)
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.map_err(|error| crate::Error::new_write_tptp_program(error))?;
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log::info!("proving program:\n{}", &tptp_problem_to_prove_next_statement);
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// TODO: refactor
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let mut conjecture_found = false;
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for section in self.statements.borrow_mut().iter_mut()
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{
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for statement in section.1.iter_mut()
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{
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if statement.proof_status == ProofStatus::ToProve
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{
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conjecture_found = true;
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statement.proof_status = ProofStatus::AssumedProven;
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}
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if conjecture_found
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{
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break;
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}
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}
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if conjecture_found
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{
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break;
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}
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}
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log::info!("program proven!");
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}
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Ok(())
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}
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fn display(&self, output_format: crate::output::Format)
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@@ -306,7 +383,8 @@ impl Problem
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if output_format == crate::output::Format::TPTP
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{
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print!("tff({}, <TODO>, ", name);
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// TODO: add proper statement type
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print!("tff({}, axiom, ", name);
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}
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print_formula(&statement.formula);
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@@ -320,6 +398,169 @@ impl Problem
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}
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}
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}
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fn write_tptp_problem_to_prove_next_statement(&self, formatter: &mut String) -> std::fmt::Result
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{
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use std::fmt::Write as _;
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use std::io::Write as _;
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let format_context = FormatContext
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{
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program_variable_declaration_ids:
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std::cell::RefCell::new(VariableDeclarationIDs::new()),
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integer_variable_declaration_ids:
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std::cell::RefCell::new(VariableDeclarationIDs::new()),
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input_constant_declaration_domains: &self.input_constant_declaration_domains.borrow(),
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variable_declaration_domains: &self.variable_declaration_domains.borrow(),
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};
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let write_title = |formatter: &mut String, title, section_separator| -> std::fmt::Result
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{
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write!(formatter, "{}{}", section_separator, "%".repeat(72))?;
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write!(formatter, "\n% {}", title)?;
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writeln!(formatter, "\n{}", "%".repeat(72))
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};
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let mut section_separator = "";
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write_title(formatter, "anthem types", section_separator)?;
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section_separator = "\n";
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let tptp_preamble_anthem_types
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= include_str!("output/tptp/preamble_types.tptp").trim_end();
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writeln!(formatter, "{}", tptp_preamble_anthem_types)?;
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write_title(formatter, "anthem axioms", section_separator)?;
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let tptp_preamble_anthem_types
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= include_str!("output/tptp/preamble_axioms.tptp").trim_end();
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writeln!(formatter, "{}", tptp_preamble_anthem_types)?;
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if !self.predicate_declarations.borrow().is_empty()
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|| !self.function_declarations.borrow().is_empty()
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{
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write_title(formatter, "types", section_separator)?;
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if !self.predicate_declarations.borrow().is_empty()
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{
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writeln!(formatter, "% predicate types")?;
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}
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for predicate_declaration in self.predicate_declarations.borrow().iter()
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{
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writeln!(formatter, "tff(type, type, {}).",
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crate::output::tptp::display_predicate_declaration(predicate_declaration))?;
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}
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if !self.function_declarations.borrow().is_empty()
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{
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writeln!(formatter, "% function types")?;
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}
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for function_declaration in self.function_declarations.borrow().iter()
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{
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writeln!(formatter, "tff(type, type, {}).",
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crate::output::tptp::display_function_declaration(function_declaration,
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&format_context))?;
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}
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}
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let function_declarations = self.function_declarations.borrow();
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let symbolic_constants = function_declarations.iter().filter(
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|x| !self.input_constant_declaration_domains.borrow().contains_key(*x));
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let mut last_symbolic_constant: Option<std::rc::Rc<foliage::FunctionDeclaration>> =
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None;
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for (i, symbolic_constant) in symbolic_constants.enumerate()
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{
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// Order axioms are only necessary with two or more symbolic constants
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if i == 1
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{
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writeln!(formatter, "% axioms for order of symbolic constants")?;
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}
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if symbolic_constant.arity > 0
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{
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// TODO: refactor
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unimplemented!("n-ary function declarations aren’t supported");
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}
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if let Some(last_symbolic_constant) = last_symbolic_constant
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{
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writeln!(formatter, "tff(symbolic_constant_order, axiom, p__less__({}, {})).",
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last_symbolic_constant.name, symbolic_constant.name)?;
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}
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last_symbolic_constant = Some(std::rc::Rc::clone(symbolic_constant));
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}
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let mut conjecture_found = false;
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for (section_kind, statements) in self.statements.borrow().iter()
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{
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if statements.is_empty()
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{
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continue;
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}
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let title = match section_kind
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{
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SectionKind::CompletedDefinitions => "completed definitions",
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SectionKind::IntegrityConstraints => "integrity constraints",
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SectionKind::Axioms => "axioms",
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SectionKind::Assumptions => "assumptions",
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SectionKind::Lemmas => "lemmas",
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SectionKind::Assertions => "assertions",
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};
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write_title(formatter, title, section_separator)?;
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section_separator = "\n";
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let mut i = 0;
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for statement in statements.iter()
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{
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// Only prove one statement at a time
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if conjecture_found && statement.proof_status == ProofStatus::ToProve
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{
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continue;
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}
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if let Some(ref description) = statement.description
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{
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writeln!(formatter, "% {}", description)?;
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}
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let name = match &statement.name
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{
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// TODO: refactor
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Some(name) => name.clone(),
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None =>
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{
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i += 1;
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format!("statement_{}", i)
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},
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};
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let statement_type = match statement.proof_status
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{
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ProofStatus::AssumedProven => "axiom",
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ProofStatus::ToProve =>
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{
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conjecture_found = true;
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"conjecture"
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},
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};
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// TODO: add proper statement type
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writeln!(formatter, "tff({}, {}, {}).", name, statement_type,
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crate::output::tptp::display_formula(&statement.formula, &format_context))?;
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}
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}
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Ok(())
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}
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}
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impl foliage::FindOrCreateFunctionDeclaration for Problem
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