1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
/*
* richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
* Copyright (C) 2026 Richard Qin
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*/
#pragma once
/// @file formula.h
/// @brief First-order logic formula AST (pre-clausification).
///
/// Design decision: atoms use TermId (interned), quantifier variables use
/// SymbolId (interned). The parser interns all symbols during parsing.
/// This avoids string→ID lookups during clausification and ensures
/// consistent variable identity across quantifier scopes.
#include "atp/core/types.h"
#include <memory>
#include <vector>
namespace atp {
/// AST node types for first-order logic formulas.
enum class FormulaKind : uint8_t {
kAtom, ///< Predicate application: P(t1, ..., tn)
kEquality, ///< Equality atom: t1 = t2 (distinguished for equality reasoning)
kNot, ///< Negation: ¬F
kAnd, ///< Conjunction: F ∧ G
kOr, ///< Disjunction: F ∨ G
kImplies, ///< Implication: F → G
kIff, ///< Biconditional: F ↔ G
kForall, ///< Universal: ∀x. F
kExists, ///< Existential: ∃x. F
};
/// A first-order logic formula node.
///
/// All identifiers are interned: atoms as TermIds, quantifier variables as
/// SymbolIds. No raw strings survive past the parser.
struct Formula {
FormulaKind kind;
/// For kAtom / kEquality: the predicate/equality term, already interned.
TermId atom = kInvalidId;
/// For kForall / kExists: the bound variable, as an interned SymbolId.
/// Using SymbolId (not string) so the clausifier can map bound variables
/// back to term-bank variables without string lookups.
SymbolId bound_var = kInvalidId;
/// Sub-formulas (1 for Not/Quantifiers, 2 for binary connectives).
std::vector<std::unique_ptr<Formula>> children;
// ── Factory methods ──
static std::unique_ptr<Formula> makeAtom(TermId atom);
static std::unique_ptr<Formula> makeEquality(TermId lhs, TermId rhs, TermId eq_atom);
static std::unique_ptr<Formula> makeNot(std::unique_ptr<Formula> child);
static std::unique_ptr<Formula> makeAnd(std::unique_ptr<Formula> lhs,
std::unique_ptr<Formula> rhs);
static std::unique_ptr<Formula> makeOr(std::unique_ptr<Formula> lhs,
std::unique_ptr<Formula> rhs);
static std::unique_ptr<Formula> makeImplies(std::unique_ptr<Formula> lhs,
std::unique_ptr<Formula> rhs);
static std::unique_ptr<Formula> makeIff(std::unique_ptr<Formula> lhs,
std::unique_ptr<Formula> rhs);
static std::unique_ptr<Formula> makeForall(SymbolId var,
std::unique_ptr<Formula> body);
static std::unique_ptr<Formula> makeExists(SymbolId var,
std::unique_ptr<Formula> body);
};
} // namespace atp
|
