feat: implement substitution logic and unify/applySubstitution functions for term resolution

1 files changed, 337 insertions, 0 deletions

diff --git a/tests/test_unification.cc b/tests/test_unification.cc
index b62ffd0..3ee6f00 100644
--- a/tests/test_unification.cc
+++ b/tests/test_unification.cc
@@ -16,4 +16,341 @@
  * along with this program.  If not, see <https://www.gnu.org/licenses/>.
  */
 
+#include <gtest/gtest.h>
 
+#include "atp/core/symbol_table.h"
+#include "atp/core/term_bank.h"
+#include "atp/core/types.h"
+#include "atp/infer/substitution.h"
+#include "atp/infer/unification.h"
+
+namespace atp {
+namespace {
+
+// ═══════════════════════════════════════════════════════════════════════════
+// Test Fixture
+// ═══════════════════════════════════════════════════════════════════════════
+
+class UnificationTest : public ::testing::Test {
+  protected:
+    SymbolTable symbols;
+    TermBank bank{symbols};
+
+    // Symbols
+    SymbolId sym_a{}, sym_b{}, sym_c{};
+    SymbolId sym_f{}, sym_g{}, sym_h{};
+    SymbolId sym_P{};
+    SymbolId sym_X{}, sym_Y{}, sym_Z{};
+
+    // Terms (created in SetUp)
+    TermId a{}, b{}, c{};
+    TermId X{}, Y{}, Z{};
+
+    void SetUp() override {
+        sym_a = symbols.intern("a", SymbolKind::kConstant);
+        sym_b = symbols.intern("b", SymbolKind::kConstant);
+        sym_c = symbols.intern("c", SymbolKind::kConstant);
+        sym_f = symbols.intern("f", SymbolKind::kFunction, 1);
+        sym_g = symbols.intern("g", SymbolKind::kFunction, 2);
+        sym_h = symbols.intern("h", SymbolKind::kFunction, 1);
+        sym_P = symbols.intern("P", SymbolKind::kPredicate, 2);
+        sym_X = symbols.intern("X", SymbolKind::kVariable);
+        sym_Y = symbols.intern("Y", SymbolKind::kVariable);
+        sym_Z = symbols.intern("Z", SymbolKind::kVariable);
+
+        a = bank.makeTerm(sym_a, {});
+        b = bank.makeTerm(sym_b, {});
+        c = bank.makeTerm(sym_c, {});
+        X = bank.makeVar(sym_X);
+        Y = bank.makeVar(sym_Y);
+        Z = bank.makeVar(sym_Z);
+    }
+
+    // Helper: make f(arg)
+    TermId f(TermId arg) { return bank.makeTerm(sym_f, {{arg}}); }
+    // Helper: make g(arg1, arg2)
+    TermId g(TermId a1, TermId a2) { return bank.makeTerm(sym_g, {{a1, a2}}); }
+    // Helper: make h(arg)
+    TermId h(TermId arg) { return bank.makeTerm(sym_h, {{arg}}); }
+    // Helper: make P(arg1, arg2)
+    TermId P(TermId a1, TermId a2) { return bank.makeTerm(sym_P, {{a1, a2}}); }
+};
+
+// ═══════════════════════════════════════════════════════════════════════════
+// Substitution Tests
+// ═══════════════════════════════════════════════════════════════════════════
+
+TEST_F(UnificationTest, SubstBindAndLookup) {
+    Substitution subst;
+    EXPECT_TRUE(subst.bind(X, a));
+    EXPECT_EQ(subst.lookup(X), a);
+    EXPECT_EQ(subst.lookup(Y), kInvalidId);  // unbound
+}
+
+TEST_F(UnificationTest, SubstBindSameTermSucceeds) {
+    Substitution subst;
+    EXPECT_TRUE(subst.bind(X, a));
+    EXPECT_TRUE(subst.bind(X, a));  // same binding → OK
+}
+
+TEST_F(UnificationTest, SubstBindDifferentTermFails) {
+    Substitution subst;
+    EXPECT_TRUE(subst.bind(X, a));
+    EXPECT_FALSE(subst.bind(X, b));  // different binding → fail
+}
+
+TEST_F(UnificationTest, SubstResolveChain) {
+    // X → Y → a
+    Substitution subst;
+    subst.bind(X, Y);
+    subst.bind(Y, a);
+    EXPECT_EQ(subst.resolve(X, bank), a);
+}
+
+TEST_F(UnificationTest, SubstResolveUnbound) {
+    Substitution subst;
+    EXPECT_EQ(subst.resolve(X, bank), X);  // unbound → returns itself
+}
+
+TEST_F(UnificationTest, SubstResolveNonVariable) {
+    Substitution subst;
+    EXPECT_EQ(subst.resolve(a, bank), a);  // constant → returns itself
+}
+
+TEST_F(UnificationTest, SubstApplySimple) {
+    // σ = {X → a}    apply to f(X) → f(a)
+    Substitution subst;
+    subst.bind(X, a);
+    TermId fx = f(X);
+    TermId result = subst.apply(fx, bank);
+    TermId expected = f(a);
+    EXPECT_EQ(result, expected);
+}
+
+TEST_F(UnificationTest, SubstApplyLeavesUnbound) {
+    // σ = {X → a}    apply to g(X, Y) → g(a, Y)
+    Substitution subst;
+    subst.bind(X, a);
+    TermId gxy = g(X, Y);
+    TermId result = subst.apply(gxy, bank);
+    TermId expected = g(a, Y);
+    EXPECT_EQ(result, expected);
+}
+
+TEST_F(UnificationTest, SubstApplyNested) {
+    // σ = {X → f(a)}    apply to g(X, b) → g(f(a), b)
+    Substitution subst;
+    subst.bind(X, f(a));
+    TermId result = subst.apply(g(X, b), bank);
+    EXPECT_EQ(result, g(f(a), b));
+}
+
+TEST_F(UnificationTest, SubstOccursIn) {
+    Substitution subst;
+    // X occurs in f(X)
+    EXPECT_TRUE(subst.occursIn(X, f(X), bank));
+    // X occurs in g(a, f(X))
+    EXPECT_TRUE(subst.occursIn(X, g(a, f(X)), bank));
+    // X does NOT occur in f(a)
+    EXPECT_FALSE(subst.occursIn(X, f(a), bank));
+    // X does NOT occur in Y (different variable)
+    EXPECT_FALSE(subst.occursIn(X, Y, bank));
+}
+
+TEST_F(UnificationTest, SubstClearAndSize) {
+    Substitution subst;
+    EXPECT_TRUE(subst.empty());
+    subst.bind(X, a);
+    subst.bind(Y, b);
+    EXPECT_EQ(subst.size(), 2);
+    subst.clear();
+    EXPECT_TRUE(subst.empty());
+    EXPECT_EQ(subst.lookup(X), kInvalidId);
+}
+
+// ═══════════════════════════════════════════════════════════════════════════
+// Unification Tests
+// ═══════════════════════════════════════════════════════════════════════════
+
+TEST_F(UnificationTest, UnifyIdenticalConstants) {
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, a, a, subst));
+    EXPECT_TRUE(subst.empty());
+}
+
+TEST_F(UnificationTest, UnifyDifferentConstants) {
+    Substitution subst;
+    EXPECT_FALSE(unify(bank, a, b, subst));
+}
+
+TEST_F(UnificationTest, UnifyVarWithConstant) {
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, X, a, subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+}
+
+TEST_F(UnificationTest, UnifyConstantWithVar) {
+    // Symmetric: unify(a, X) should also work
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, a, X, subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+}
+
+TEST_F(UnificationTest, UnifyTwoVariables) {
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, X, Y, subst));
+    // One should be bound to the other
+    TermId rx = subst.resolve(X, bank);
+    TermId ry = subst.resolve(Y, bank);
+    EXPECT_EQ(rx, ry);
+}
+
+TEST_F(UnificationTest, UnifyCompoundTerms) {
+    // f(X) =? f(a)  → {X → a}
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, f(X), f(a), subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+}
+
+TEST_F(UnificationTest, UnifyMultipleArgs) {
+    // g(X, Y) =? g(a, b)  → {X → a, Y → b}
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, g(X, Y), g(a, b), subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+    EXPECT_EQ(subst.resolve(Y, bank), b);
+}
+
+TEST_F(UnificationTest, UnifyConflictingBindings) {
+    // g(X, X) =? g(a, b)  → fails (X can't be both a and b)
+    Substitution subst;
+    EXPECT_FALSE(unify(bank, g(X, X), g(a, b), subst));
+}
+
+TEST_F(UnificationTest, UnifyConsistentRepeatedVar) {
+    // g(X, X) =? g(a, a)  → {X → a}
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, g(X, X), g(a, a), subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+}
+
+TEST_F(UnificationTest, UnifyDifferentHeadSymbols) {
+    // f(X) =? h(X) → fails
+    Substitution subst;
+    EXPECT_FALSE(unify(bank, f(X), h(X), subst));
+}
+
+TEST_F(UnificationTest, UnifyDifferentArity) {
+    // f(X) =? g(X, Y) → fails (arity 1 vs 2)
+    Substitution subst;
+    EXPECT_FALSE(unify(bank, f(X), g(X, Y), subst));
+}
+
+TEST_F(UnificationTest, UnifyNestedTerms) {
+    // f(g(X, a)) =? f(Y)  → {Y → g(X, a)}
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, f(g(X, a)), f(Y), subst));
+    EXPECT_EQ(subst.resolve(Y, bank), g(X, a));
+}
+
+TEST_F(UnificationTest, UnifyVarWithCompound) {
+    // X =? f(a) → {X → f(a)}
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, X, f(a), subst));
+    EXPECT_EQ(subst.resolve(X, bank), f(a));
+}
+
+TEST_F(UnificationTest, UnifyDeepNesting) {
+    // f(f(f(X))) =? f(f(f(a))) → {X → a}
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, f(f(f(X))), f(f(f(a))), subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+}
+
+TEST_F(UnificationTest, UnifyChainedVariables) {
+    // g(X, Y) =? g(Y, a) → {X → Y, Y → a} effectively X → a
+    Substitution subst;
+    EXPECT_TRUE(unify(bank, g(X, Y), g(Y, a), subst));
+    EXPECT_EQ(subst.resolve(X, bank), a);
+    EXPECT_EQ(subst.resolve(Y, bank), a);
+}
+
+// ═══════════════════════════════════════════════════════════════════════════
+// Occurs Check Tests
+// ═══════════════════════════════════════════════════════════════════════════
+
+TEST_F(UnificationTest, OccursCheckBlocks) {
+    // X =? f(X) with occurs check → fails
+    Substitution subst;
+    UnificationConfig config{.enable_occurs_check = true};
+    EXPECT_FALSE(unify(bank, X, f(X), subst, config));
+}
+
+TEST_F(UnificationTest, OccursCheckDisabledAllows) {
+    // X =? f(X) without occurs check → succeeds (unsound but fast)
+    Substitution subst;
+    UnificationConfig config{.enable_occurs_check = false};
+    EXPECT_TRUE(unify(bank, X, f(X), subst, config));
+}
+
+TEST_F(UnificationTest, OccursCheckDeep) {
+    // X =? f(g(X, a)) with occurs check → fails
+    Substitution subst;
+    UnificationConfig config{.enable_occurs_check = true};
+    EXPECT_FALSE(unify(bank, X, f(g(X, a)), subst, config));
+}
+
+// ═══════════════════════════════════════════════════════════════════════════
+// applySubstitution Tests
+// ═══════════════════════════════════════════════════════════════════════════
+
+TEST_F(UnificationTest, ApplySubstitutionSimple) {
+    Substitution subst;
+    subst.bind(X, a);
+    EXPECT_EQ(applySubstitution(subst, f(X), bank), f(a));
+}
+
+TEST_F(UnificationTest, ApplySubstitutionNested) {
+    Substitution subst;
+    subst.bind(X, a);
+    subst.bind(Y, b);
+    EXPECT_EQ(applySubstitution(subst, g(f(X), Y), bank), g(f(a), b));
+}
+
+TEST_F(UnificationTest, ApplySubstitutionPreservesUnbound) {
+    Substitution subst;
+    subst.bind(X, a);
+    // Y is unbound → stays as Y
+    EXPECT_EQ(applySubstitution(subst, g(X, Y), bank), g(a, Y));
+}
+
+TEST_F(UnificationTest, ApplySubstitutionToConstant) {
+    Substitution subst;
+    subst.bind(X, a);
+    // Constant is unchanged
+    EXPECT_EQ(applySubstitution(subst, b, bank), b);
+}
+
+TEST_F(UnificationTest, ApplySubstitutionChain) {
+    // σ = {X → Y, Y → a}   apply to f(X) → f(a)
+    Substitution subst;
+    subst.bind(X, Y);
+    subst.bind(Y, a);
+    EXPECT_EQ(applySubstitution(subst, f(X), bank), f(a));
+}
+
+TEST_F(UnificationTest, UnifyThenApply) {
+    // Full round-trip: unify P(X, f(Y)) with P(a, f(b)), then apply
+    Substitution subst;
+    TermId lhs = P(X, f(Y));
+    TermId rhs = P(a, f(b));
+    ASSERT_TRUE(unify(bank, lhs, rhs, subst));
+
+    EXPECT_EQ(applySubstitution(subst, lhs, bank), P(a, f(b)));
+    EXPECT_EQ(applySubstitution(subst, rhs, bank), P(a, f(b)));
+    // Both sides should produce the same term after applying the MGU
+    EXPECT_EQ(applySubstitution(subst, lhs, bank),
+              applySubstitution(subst, rhs, bank));
+}
+
+}  // namespace
+}  // namespace atp