implements PR-08.2

prometeu-compiler/frontends/prometeu-frontend-pbs/src/main/java/p/studio/compiler/pbs/PbsFrontendCompiler.java

@@ -19,6 +19,7 @@ import p.studio.compiler.source.identifiers.CallableShapeId;
 import p.studio.compiler.source.identifiers.CallableId;
 import p.studio.compiler.source.identifiers.FileId;
 import p.studio.compiler.source.identifiers.IntrinsicId;
+import p.studio.compiler.source.identifiers.ModuleId;
 import p.studio.compiler.source.identifiers.NameId;
 import p.studio.compiler.source.identifiers.TypeSurfaceId;
 import p.studio.compiler.source.tables.CallableShapeTable;
@@ -26,6 +27,7 @@ import p.studio.compiler.source.tables.CallableSignatureRef;
 import p.studio.compiler.source.tables.CallableTable;
 import p.studio.compiler.source.tables.IntrinsicReference;
 import p.studio.compiler.source.tables.IntrinsicTable;
+import p.studio.compiler.source.tables.ModuleReference;
 import p.studio.compiler.source.tables.NameTable;
 import p.studio.compiler.source.tables.TypeSurfaceTable;
 import p.studio.utilities.structures.ReadOnlyList;
@@ -71,7 +73,16 @@ public final class PbsFrontendCompiler {
                 ? PbsParser.ParseMode.INTERFACE_MODULE
                 : PbsParser.ParseMode.ORDINARY;
         final var ast = PbsParser.parse(tokens, fileId, diagnostics, parseMode);
-        final var irBackendFile = compileParsedFile(fileId, ast, diagnostics, sourceKind, "", hostAdmissionContext, nameTable);
+        final var irBackendFile = compileParsedFile(
+                fileId,
+                ast,
+                diagnostics,
+                sourceKind,
+                ModuleId.none(),
+                "",
+                ReadOnlyList.empty(),
+                hostAdmissionContext,
+                nameTable);
         if (diagnostics.errorCount() > admissionBaseline) {
             return IRBackendFile.empty(fileId);
         }
@@ -99,7 +110,16 @@ public final class PbsFrontendCompiler {
             final DiagnosticSink diagnostics,
             final SourceKind sourceKind,
             final HostAdmissionContext hostAdmissionContext) {
-        return compileParsedFile(fileId, ast, diagnostics, sourceKind, "", hostAdmissionContext, new NameTable());
+        return compileParsedFile(
+                fileId,
+                ast,
+                diagnostics,
+                sourceKind,
+                ModuleId.none(),
+                "",
+                ReadOnlyList.empty(),
+                hostAdmissionContext,
+                new NameTable());
     }
 
     public IRBackendFile compileParsedFile(
@@ -109,7 +129,16 @@ public final class PbsFrontendCompiler {
             final SourceKind sourceKind,
             final String moduleKey,
             final HostAdmissionContext hostAdmissionContext) {
-        return compileParsedFile(fileId, ast, diagnostics, sourceKind, moduleKey, hostAdmissionContext, new NameTable());
+        return compileParsedFile(
+                fileId,
+                ast,
+                diagnostics,
+                sourceKind,
+                ModuleId.none(),
+                moduleKey,
+                ReadOnlyList.empty(),
+                hostAdmissionContext,
+                new NameTable());
     }
 
     public IRBackendFile compileParsedFile(
@@ -117,7 +146,9 @@ public final class PbsFrontendCompiler {
             final PbsAst.File ast,
             final DiagnosticSink diagnostics,
             final SourceKind sourceKind,
+            final ModuleId moduleId,
             final String moduleKey,
+            final ReadOnlyList<ModuleReference> modulePool,
             final HostAdmissionContext hostAdmissionContext,
             final NameTable nameTable) {
         return compileParsedFile(
@@ -125,7 +156,9 @@ public final class PbsFrontendCompiler {
                 ast,
                 diagnostics,
                 sourceKind,
+                moduleId,
                 moduleKey,
+                modulePool,
                 hostAdmissionContext,
                 nameTable,
                 ReadOnlyList.empty(),
@@ -138,12 +171,16 @@ public final class PbsFrontendCompiler {
             final PbsAst.File ast,
             final DiagnosticSink diagnostics,
             final SourceKind sourceKind,
+            final ModuleId moduleId,
             final String moduleKey,
+            final ReadOnlyList<ModuleReference> modulePool,
             final HostAdmissionContext hostAdmissionContext,
             final NameTable nameTable,
             final ReadOnlyList<PbsAst.TopDecl> supplementalTopDecls,
             final ReadOnlyList<ImportedCallableSurface> importedCallables,
             final IRReservedMetadata importedReservedMetadata) {
+        final var effectiveModuleId = moduleId == null ? ModuleId.none() : moduleId;
+        final var effectiveModulePool = modulePool == null ? ReadOnlyList.<ModuleReference>empty() : modulePool;
         final var effectiveNameTable = nameTable == null ? new NameTable() : nameTable;
         final var effectiveSupplementalTopDecls = supplementalTopDecls == null
                 ? ReadOnlyList.<PbsAst.TopDecl>empty()
@@ -187,6 +224,7 @@ public final class PbsFrontendCompiler {
                 fileId,
                 ast,
                 effectiveSupplementalTopDecls,
+                effectiveModuleId,
                 moduleKey,
                 effectiveReservedMetadata,
                 effectiveNameTable,
@@ -200,6 +238,7 @@ public final class PbsFrontendCompiler {
                 functions,
                 executableLowering.executableFunctions(),
                 reservedMetadata,
+                effectiveModulePool,
                 executableLowering.callableSignatures(),
                 executableLowering.intrinsicPool());
     }
@@ -221,12 +260,14 @@ public final class PbsFrontendCompiler {
             final FileId fileId,
             final PbsAst.File ast,
             final ReadOnlyList<PbsAst.TopDecl> supplementalTopDecls,
+            final ModuleId moduleId,
             final String moduleKey,
             final IRReservedMetadata reservedMetadata,
             final NameTable nameTable,
             final DiagnosticSink diagnostics,
             final ReadOnlyList<ImportedCallableSurface> importedCallables) {
         final var normalizedModuleKey = moduleKey == null ? "" : moduleKey;
+        final var normalizedModuleId = moduleId == null ? ModuleId.none() : moduleId;
         final var hostByMethodName = new HashMap<NameId, List<IRReservedMetadata.HostMethodBinding>>();
         for (final var hostBinding : reservedMetadata.hostMethodBindings()) {
             hostByMethodName
@@ -318,6 +359,7 @@ public final class PbsFrontendCompiler {
             final var declaredFn = declaredCallable.functionDecl();
             final var callableShapeId = callableShapeId(declaredFn, typeSurfaceTable, callableShapeTable);
             final var callableId = callableIdTable.register(
+                    normalizedModuleId,
                     normalizedModuleKey,
                     declaredCallable.callableName(),
                     declaredFn.parameters().size(),
@@ -333,6 +375,7 @@ public final class PbsFrontendCompiler {
         }
         for (final var importedCallable : importedCallables) {
             final var callableId = callableIdTable.register(
+                    importedCallable.moduleId(),
                     importedCallable.moduleKey(),
                     importedCallable.callableName(),
                     importedCallable.arity(),
@@ -359,6 +402,7 @@ public final class PbsFrontendCompiler {
                 localSlotByNameId.put(nameTable.register(fn.parameters().get(paramIndex).name()), paramIndex);
             }
             final var loweringContext = new ExecutableLoweringContext(
+                    normalizedModuleId,
                     normalizedModuleKey,
                     diagnostics,
                     nameTable,
@@ -401,6 +445,7 @@ public final class PbsFrontendCompiler {
             final var end = safeToInt(fn.span().getEnd());
             executableFunctions.add(new IRBackendExecutableFunction(
                     fileId,
+                    normalizedModuleId,
                     normalizedModuleKey,
                     callable.callableName(),
                     functionCallableId,
@@ -921,6 +966,7 @@ public final class PbsFrontendCompiler {
         final var calleeCallableId = callableCandidates.getFirst();
         context.instructions().add(new IRBackendExecutableFunction.Instruction(
                 IRBackendExecutableFunction.InstructionKind.CALL_FUNC,
+                context.moduleId(),
                 context.moduleKey(),
                 calleeIdentity.primaryCallableDisplayName(),
                 calleeCallableId,
@@ -1292,6 +1338,7 @@ public final class PbsFrontendCompiler {
     }
 
     private static final class ExecutableLoweringContext {
+        private final ModuleId moduleId;
         private final String moduleKey;
         private final DiagnosticSink diagnostics;
         private final NameTable nameTable;
@@ -1308,6 +1355,7 @@ public final class PbsFrontendCompiler {
         private int nextLabelId = 0;
 
         private ExecutableLoweringContext(
+                final ModuleId moduleId,
                 final String moduleKey,
                 final DiagnosticSink diagnostics,
                 final NameTable nameTable,
@@ -1319,6 +1367,7 @@ public final class PbsFrontendCompiler {
                 final Map<CallableId, Integer> returnSlotsByCallableId,
                 final IntrinsicTable intrinsicIdTable,
                 final Map<NameId, Integer> localSlotByNameId) {
+            this.moduleId = moduleId == null ? ModuleId.none() : moduleId;
             this.moduleKey = moduleKey;
             this.diagnostics = diagnostics;
             this.nameTable = nameTable;
@@ -1332,6 +1381,10 @@ public final class PbsFrontendCompiler {
             this.localSlotByNameId = localSlotByNameId == null ? Map.of() : localSlotByNameId;
         }
 
+        private ModuleId moduleId() {
+            return moduleId;
+        }
+
         private String moduleKey() {
             return moduleKey;
         }
@@ -1440,11 +1493,15 @@ public final class PbsFrontendCompiler {
     }
 
     public record ImportedCallableSurface(
+            ModuleId moduleId,
             String moduleKey,
             String callableName,
             int arity,
             int returnSlots,
             String shapeSurface) {
+        public ImportedCallableSurface {
+            moduleId = moduleId == null ? ModuleId.none() : moduleId;
+        }
     }
 
     private static final class ExecutableLoweringAnalysisException extends RuntimeException {

prometeu-compiler/frontends/prometeu-frontend-pbs/src/main/java/p/studio/compiler/services/PBSFrontendPhaseService.java

@@ -159,6 +159,7 @@ public class PBSFrontendPhaseService implements FrontendPhaseService {
         markModulesWithLinkingErrors(diagnostics, moduleIdByFile, failedModuleIds);
         final var moduleDependencyGraph = buildModuleDependencyGraph(parsedSourceFiles, moduleTable);
         final var importedSemanticContexts = buildImportedSemanticContexts(parsedSourceFiles, moduleTable);
+        final var canonicalModulePool = emitModulePool(moduleTable);
 
         final var compiledSourceFiles = new ArrayList<CompiledSourceFile>(parsedSourceFiles.size());
         for (final var parsedSource : parsedSourceFiles) {
@@ -175,7 +176,9 @@ public class PBSFrontendPhaseService implements FrontendPhaseService {
                     parsedSource.ast(),
                     diagnostics,
                     parsedSource.sourceKind(),
+                    parsedSource.moduleId(),
                     renderModuleKey(moduleTable, parsedSource.moduleId()),
+                    canonicalModulePool,
                     ctx.hostAdmissionContext(),
                     nameTable,
                     importedSemanticContext.supplementalTopDecls(),
@@ -431,6 +434,7 @@ public class PBSFrontendPhaseService implements FrontendPhaseService {
                                         importedCallables,
                                         importedCallableKeys,
                                         new PbsFrontendCompiler.ImportedCallableSurface(
+                                                importedModuleId,
                                                 importedModuleKey,
                                                 localName + "." + method.name(),
                                                 method.parameters().size(),
@@ -444,6 +448,7 @@ public class PBSFrontendPhaseService implements FrontendPhaseService {
                                     importedCallables,
                                     importedCallableKeys,
                                     new PbsFrontendCompiler.ImportedCallableSurface(
+                                            importedModuleId,
                                             importedModuleKey,
                                             localName,
                                             functionDecl.parameters().size(),
@@ -793,6 +798,14 @@ public class PBSFrontendPhaseService implements FrontendPhaseService {
         return moduleReference.project() + ":" + String.join("/", moduleReference.pathSegments().asList());
     }
 
+    private ReadOnlyList<ModuleReference> emitModulePool(final ModuleTable moduleTable) {
+        final var pool = new ArrayList<ModuleReference>(moduleTable.size());
+        for (final var moduleId : moduleTable.identifiers()) {
+            pool.add(moduleTable.get(moduleId));
+        }
+        return ReadOnlyList.wrap(pool);
+    }
+
     private static final class MutableModuleUnit {
         private final ArrayList<PbsModuleVisibilityValidator.SourceFile> sources = new ArrayList<>();
         private final ArrayList<PbsModuleVisibilityValidator.BarrelFile> barrels = new ArrayList<>();

prometeu-compiler/prometeu-build-pipeline/src/main/java/p/studio/compiler/backend/irvm/LowerToIRVMService.java

@@ -6,19 +6,15 @@ import p.studio.compiler.models.IRBackend;
 import p.studio.compiler.models.IRBackendExecutableFunction;
 import p.studio.compiler.source.Span;
 import p.studio.compiler.source.identifiers.CallableId;
+import p.studio.compiler.source.identifiers.ModuleId;
+import p.studio.compiler.source.tables.ModuleReference;
 import p.studio.utilities.structures.ReadOnlyList;
 
 import java.util.ArrayList;
-import java.util.Comparator;
 import java.util.HashMap;
+import java.util.StringJoiner;
 
 public class LowerToIRVMService {
-    private static final Comparator<IRBackendExecutableFunction> FUNCTION_ORDER = Comparator
-            .comparing(IRBackendExecutableFunction::moduleKey)
-            .thenComparing(IRBackendExecutableFunction::callableName)
-            .thenComparingInt(function -> function.callableId().getIndex())
-            .thenComparingInt(IRBackendExecutableFunction::sourceStart);
-
     private final IRVMValidator validator;
 
     public LowerToIRVMService() {
@@ -301,7 +297,23 @@ public class LowerToIRVMService {
                     "frontend IRBackend entrypoint declaration is missing");
         }
         final var sorted = new ArrayList<>(backend.getExecutableFunctions().asList());
-        sorted.sort(FUNCTION_ORDER);
+        sorted.sort((left, right) -> {
+            final var leftModuleKey = moduleSortKey(backend, left.moduleId(), left.moduleKey());
+            final var rightModuleKey = moduleSortKey(backend, right.moduleId(), right.moduleKey());
+            final var moduleCmp = leftModuleKey.compareTo(rightModuleKey);
+            if (moduleCmp != 0) {
+                return moduleCmp;
+            }
+            final var nameCmp = left.callableName().compareTo(right.callableName());
+            if (nameCmp != 0) {
+                return nameCmp;
+            }
+            final var idCmp = Integer.compare(left.callableId().getIndex(), right.callableId().getIndex());
+            if (idCmp != 0) {
+                return idCmp;
+            }
+            return Integer.compare(left.sourceStart(), right.sourceStart());
+        });
         final var entrypoints = sorted.stream()
                 .filter(candidate -> entryPointCallableName.equals(candidate.callableName()))
                 .toList();
@@ -328,6 +340,27 @@ public class LowerToIRVMService {
         return ReadOnlyList.wrap(ordered);
     }
 
+    private String moduleSortKey(
+            final IRBackend backend,
+            final ModuleId moduleId,
+            final String fallbackModuleKey) {
+        if (moduleId != null && !moduleId.isNone()) {
+            final var index = moduleId.getIndex();
+            if (index >= 0 && index < backend.getModulePool().size()) {
+                return canonicalModuleSortKey(backend.getModulePool().get(index));
+            }
+        }
+        return fallbackModuleKey == null ? "" : fallbackModuleKey;
+    }
+
+    private String canonicalModuleSortKey(final ModuleReference reference) {
+        final var joiner = new StringJoiner("/", reference.project() + ":", "");
+        for (final var segment : reference.pathSegments()) {
+            joiner.add(segment);
+        }
+        return joiner.toString();
+    }
+
     private BytecodeModule.SourceSpan toBytecodeSpan(
             final int fallbackFileId,
             final Span span) {

prometeu-compiler/prometeu-build-pipeline/src/test/java/p/studio/compiler/backend/irvm/LowerToIRVMServiceTest.java

@@ -7,7 +7,9 @@ import p.studio.compiler.source.Span;
 import p.studio.compiler.source.identifiers.CallableId;
 import p.studio.compiler.source.identifiers.FileId;
 import p.studio.compiler.source.identifiers.IntrinsicId;
+import p.studio.compiler.source.identifiers.ModuleId;
 import p.studio.compiler.source.tables.IntrinsicReference;
+import p.studio.compiler.source.tables.ModuleReference;
 import p.studio.utilities.structures.ReadOnlyList;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
@@ -199,6 +201,27 @@ class LowerToIRVMServiceTest {
         assertEquals(IRVMLoweringErrorCode.LOWER_IRVM_ENTRYPOINT_AMBIGUOUS, thrown.code());
     }
 
+    @Test
+    void lowerMustUseModulePoolCanonicalIdentityForNonEntrypointOrdering() {
+        final var backend = IRBackend.builder()
+                .entryPointCallableName("frame")
+                .modulePool(ReadOnlyList.from(
+                        new ModuleReference("app", ReadOnlyList.from("alpha")),
+                        new ModuleReference("app", ReadOnlyList.from("zeta"))))
+                .executableFunctions(ReadOnlyList.from(
+                        fnWithModule("helper_in_zeta", "legacy/zeta", 1, 21, ReadOnlyList.from(ret())),
+                        fnWithModule("frame", "legacy/zeta", 1, 20, ReadOnlyList.from(ret())),
+                        fnWithModule("helper_in_alpha", "legacy/alpha", 0, 22, ReadOnlyList.from(ret()))))
+                .build();
+
+        final var lowered = new LowerToIRVMService().lower(backend);
+
+        assertEquals(3, lowered.module().functions().size());
+        assertEquals("frame", lowered.module().functions().get(0).name());
+        assertEquals("helper_in_alpha", lowered.module().functions().get(1).name());
+        assertEquals("helper_in_zeta", lowered.module().functions().get(2).name());
+    }
+
     private static IRBackendExecutableFunction fn(
             final String name,
             final String moduleKey,
@@ -219,6 +242,28 @@ class LowerToIRVMServiceTest {
                 Span.none());
     }
 
+    private static IRBackendExecutableFunction fnWithModule(
+            final String name,
+            final String moduleKey,
+            final int moduleId,
+            final int callableId,
+            final ReadOnlyList<IRBackendExecutableFunction.Instruction> instructions) {
+        return new IRBackendExecutableFunction(
+                new FileId(0),
+                new ModuleId(moduleId),
+                moduleKey,
+                name,
+                new CallableId(callableId),
+                0,
+                10,
+                0,
+                0,
+                0,
+                4,
+                instructions,
+                Span.none());
+    }
+
     private static IRBackendExecutableFunction.Instruction ret() {
         return new IRBackendExecutableFunction.Instruction(
                 IRBackendExecutableFunction.InstructionKind.RET,

prometeu-compiler/prometeu-compiler-core/src/main/java/p/studio/compiler/source/identifiers/ModuleId.java

@@ -1,7 +1,17 @@
 package p.studio.compiler.source.identifiers;
 
 public class ModuleId extends SourceIdentifier {
+    public static final ModuleId NONE = new ModuleId(-1);
+
     public ModuleId(int id) {
         super(id);
     }
+
+    public static ModuleId none() {
+        return NONE;
+    }
+
+    public boolean isNone() {
+        return this == NONE;
+    }
 }

prometeu-compiler/prometeu-compiler-core/src/main/java/p/studio/compiler/source/tables/CallableSignatureRef.java

@@ -1,14 +1,29 @@
 package p.studio.compiler.source.tables;
 
+import p.studio.compiler.source.identifiers.ModuleId;
+
 import java.util.Objects;
 
 public record CallableSignatureRef(
+        ModuleId moduleId,
         String moduleKey,
         String callableName,
         int arity,
         String typeShape) {
 
+    public CallableSignatureRef(
+            final String moduleKey,
+            final String callableName,
+            final int arity,
+            final String typeShape) {
+        this(ModuleId.none(), moduleKey, callableName, arity, typeShape);
+    }
+
     public CallableSignatureRef {
+        moduleId = moduleId == null ? ModuleId.none() : moduleId;
+        if (!moduleId.isNone()) {
+            moduleId.getIndex();
+        }
         moduleKey = moduleKey == null ? "" : moduleKey;
         callableName = Objects.requireNonNull(callableName, "callableName");
         typeShape = typeShape == null ? "" : typeShape;

prometeu-compiler/prometeu-compiler-core/src/main/java/p/studio/compiler/source/tables/CallableTable.java

@@ -1,6 +1,7 @@
 package p.studio.compiler.source.tables;
 
 import p.studio.compiler.source.identifiers.CallableId;
+import p.studio.compiler.source.identifiers.ModuleId;
 
 public class CallableTable extends InternTable<CallableId, CallableSignatureRef> implements CallableTableReader {
 
@@ -13,6 +14,15 @@ public class CallableTable extends InternTable<CallableId, CallableSignatureRef>
             final String callableName,
             final int arity,
             final String typeShape) {
-        return register(new CallableSignatureRef(moduleKey, callableName, arity, typeShape));
+        return register(new CallableSignatureRef(ModuleId.none(), moduleKey, callableName, arity, typeShape));
+    }
+
+    public CallableId register(
+            final ModuleId moduleId,
+            final String moduleKey,
+            final String callableName,
+            final int arity,
+            final String typeShape) {
+        return register(new CallableSignatureRef(moduleId, moduleKey, callableName, arity, typeShape));
     }
 }

prometeu-compiler/prometeu-frontend-api/src/main/java/p/studio/compiler/models/IRBackend.java

@@ -4,14 +4,18 @@ import lombok.Builder;
 import lombok.Getter;
 import p.studio.compiler.source.identifiers.CallableId;
 import p.studio.compiler.source.identifiers.IntrinsicId;
+import p.studio.compiler.source.identifiers.ModuleId;
 import p.studio.compiler.source.tables.CallableSignatureRef;
 import p.studio.compiler.source.tables.CallableTable;
 import p.studio.compiler.source.tables.IntrinsicReference;
 import p.studio.compiler.source.tables.IntrinsicTable;
+import p.studio.compiler.source.tables.ModuleReference;
+import p.studio.compiler.source.tables.ModuleTable;
 import p.studio.utilities.structures.ReadOnlyList;
 
 import java.util.ArrayList;
 import java.util.LinkedHashSet;
+import java.util.List;
 
 @Builder
 @Getter
@@ -23,6 +27,8 @@ public class IRBackend {
     @Builder.Default
     private final ReadOnlyList<IRBackendExecutableFunction> executableFunctions = ReadOnlyList.empty();
     @Builder.Default
+    private final ReadOnlyList<ModuleReference> modulePool = ReadOnlyList.empty();
+    @Builder.Default
     private final ReadOnlyList<CallableSignatureRef> callableSignatures = ReadOnlyList.empty();
     @Builder.Default
     private final ReadOnlyList<IntrinsicReference> intrinsicPool = ReadOnlyList.empty();
@@ -37,6 +43,7 @@ public class IRBackend {
         private String entryPointCallableName;
         private final ArrayList<IRFunction> functions = new ArrayList<>();
         private final ArrayList<IRBackendExecutableFunction> executableFunctions = new ArrayList<>();
+        private final ModuleTable moduleTable = new ModuleTable();
         private final CallableTable callableTable = new CallableTable();
         private final IntrinsicTable intrinsicTable = new IntrinsicTable();
         private final ArrayList<IRReservedMetadata.HostMethodBinding> hostMethodBindings = new ArrayList<>();
@@ -49,10 +56,11 @@ public class IRBackend {
                 return;
             }
             functions.addAll(backendFile.functions().asList());
-            final var callableRemap = reindexCallables(backendFile.callableSignatures());
+            final var moduleRemap = reindexModules(backendFile.modulePool());
+            final var callableRemap = reindexCallables(backendFile.callableSignatures(), moduleRemap);
             final var intrinsicRemap = reindexIntrinsics(backendFile.intrinsicPool());
             for (final var function : backendFile.executableFunctions()) {
-                executableFunctions.add(remapExecutableFunction(function, callableRemap, intrinsicRemap));
+                executableFunctions.add(remapExecutableFunction(function, moduleRemap, callableRemap, intrinsicRemap));
             }
             final var metadata = backendFile.reservedMetadata();
             hostMethodBindings.addAll(metadata.hostMethodBindings().asList());
@@ -68,22 +76,52 @@ public class IRBackend {
             return this;
         }
 
-        private CallableId[] reindexCallables(final ReadOnlyList<CallableSignatureRef> localCallableSignatures) {
+        private ModuleId[] reindexModules(final ReadOnlyList<ModuleReference> localModulePool) {
+            if (localModulePool == null || localModulePool.isEmpty()) {
+                return new ModuleId[0];
+            }
+            final var remap = new ModuleId[localModulePool.size()];
+            for (var i = 0; i < localModulePool.size(); i++) {
+                remap[i] = moduleTable.register(localModulePool.get(i));
+            }
+            return remap;
+        }
+
+        private CallableId[] reindexCallables(
+                final ReadOnlyList<CallableSignatureRef> localCallableSignatures,
+                final ModuleId[] moduleRemap) {
             if (localCallableSignatures == null || localCallableSignatures.isEmpty()) {
                 return new CallableId[0];
             }
             final var remap = new CallableId[localCallableSignatures.size()];
             for (var i = 0; i < localCallableSignatures.size(); i++) {
-                remap[i] = callableTable.register(localCallableSignatures.get(i));
+                final var signature = localCallableSignatures.get(i);
+                final var remappedModuleId = remapModuleId(
+                        signature.moduleId(),
+                        signature.moduleKey(),
+                        moduleRemap,
+                        "callable signature");
+                remap[i] = callableTable.register(
+                        remappedModuleId,
+                        signature.moduleKey(),
+                        signature.callableName(),
+                        signature.arity(),
+                        signature.typeShape());
             }
             return remap;
         }
 
         private IRBackendExecutableFunction remapExecutableFunction(
                 final IRBackendExecutableFunction function,
+                final ModuleId[] moduleRemap,
                 final CallableId[] callableRemap,
                 final IntrinsicId[] intrinsicRemap) {
             final var remappedInstructions = new ArrayList<IRBackendExecutableFunction.Instruction>(function.instructions().size());
+            final var remappedFunctionModuleId = remapModuleId(
+                    function.moduleId(),
+                    function.moduleKey(),
+                    moduleRemap,
+                    "function");
             for (final var instruction : function.instructions()) {
                 final CallableId remappedCallee;
                 if (instruction.calleeCallableId() == null) {
@@ -101,8 +139,14 @@ public class IRBackend {
                 } else {
                     remappedIntrinsic = instruction.intrinsicCall();
                 }
+                final var remappedCalleeModuleId = remapModuleId(
+                        instruction.calleeModuleId(),
+                        instruction.calleeModuleKey(),
+                        moduleRemap,
+                        "callee");
                 remappedInstructions.add(new IRBackendExecutableFunction.Instruction(
                         instruction.kind(),
+                        remappedCalleeModuleId,
                         instruction.calleeModuleKey(),
                         instruction.calleeCallableName(),
                         remappedCallee,
@@ -116,6 +160,7 @@ public class IRBackend {
             }
             return new IRBackendExecutableFunction(
                     function.fileId(),
+                    remappedFunctionModuleId,
                     function.moduleKey(),
                     function.callableName(),
                     remapCallableId(function.callableId(), callableRemap, "function"),
@@ -129,6 +174,45 @@ public class IRBackend {
                     function.span());
         }
 
+        private ModuleId remapModuleId(
+                final ModuleId localModuleId,
+                final String moduleKey,
+                final ModuleId[] moduleRemap,
+                final String label) {
+            if (localModuleId != null && !localModuleId.isNone()) {
+                final var localIndex = localModuleId.getIndex();
+                if (localIndex < 0 || localIndex >= moduleRemap.length) {
+                    throw new IllegalArgumentException("invalid local " + label + " module id: " + localModuleId);
+                }
+                return moduleRemap[localIndex];
+            }
+            final var fallbackReference = moduleReferenceFromKey(moduleKey);
+            if (fallbackReference != null) {
+                return moduleTable.register(fallbackReference);
+            }
+            return ModuleId.none();
+        }
+
+        private ModuleReference moduleReferenceFromKey(final String moduleKey) {
+            if (moduleKey == null || moduleKey.isBlank()) {
+                return null;
+            }
+            final var separator = moduleKey.indexOf(':');
+            if (separator <= 0) {
+                return null;
+            }
+            final var project = moduleKey.substring(0, separator).trim();
+            final var rawPath = moduleKey.substring(separator + 1).trim();
+            if (project.isBlank()) {
+                return null;
+            }
+            if (rawPath.isBlank()) {
+                return new ModuleReference(project, ReadOnlyList.empty());
+            }
+            final var segments = List.of(rawPath.split("/"));
+            return new ModuleReference(project, ReadOnlyList.wrap(segments));
+        }
+
         private CallableId remapCallableId(
                 final CallableId localCallableId,
                 final CallableId[] callableRemap,
@@ -169,6 +253,14 @@ public class IRBackend {
             return ReadOnlyList.wrap(signatures);
         }
 
+        private ReadOnlyList<ModuleReference> emitModulePool() {
+            final var modules = new ArrayList<ModuleReference>(moduleTable.size());
+            for (final var moduleId : moduleTable.identifiers()) {
+                modules.add(moduleTable.get(moduleId));
+            }
+            return ReadOnlyList.wrap(modules);
+        }
+
         private ReadOnlyList<IntrinsicReference> emitIntrinsicPool() {
             final var pool = new ArrayList<IntrinsicReference>(intrinsicTable.size());
             for (final var intrinsicId : intrinsicTable.identifiers()) {
@@ -183,6 +275,7 @@ public class IRBackend {
                     .entryPointCallableName(resolveEntryPointCallableName())
                     .functions(ReadOnlyList.wrap(functions))
                     .executableFunctions(ReadOnlyList.wrap(executableFunctions))
+                    .modulePool(emitModulePool())
                     .callableSignatures(emitCallableSignatures())
                     .intrinsicPool(emitIntrinsicPool())
                     .reservedMetadata(new IRReservedMetadata(
@@ -206,6 +299,7 @@ public class IRBackend {
         sb.append("IRBackend{entrypoint=").append(entryPointCallableName)
                 .append(", functions=").append(functions.size())
                 .append(", executableFunctions=").append(executableFunctions.size())
+                .append(", modulePool=").append(modulePool.size())
                 .append(", callableSignatures=").append(callableSignatures.size())
                 .append(", intrinsicPool=").append(intrinsicPool.size())
                 .append(", hostBindings=").append(reservedMetadata.hostMethodBindings().size())

prometeu-compiler/prometeu-frontend-api/src/main/java/p/studio/compiler/models/IRBackendExecutableFunction.java

@@ -4,12 +4,14 @@ import p.studio.compiler.source.Span;
 import p.studio.compiler.source.identifiers.CallableId;
 import p.studio.compiler.source.identifiers.FileId;
 import p.studio.compiler.source.identifiers.IntrinsicId;
+import p.studio.compiler.source.identifiers.ModuleId;
 import p.studio.utilities.structures.ReadOnlyList;
 
 import java.util.Objects;
 
 public record IRBackendExecutableFunction(
         FileId fileId,
+        ModuleId moduleId,
         String moduleKey,
         String callableName,
         CallableId callableId,
@@ -22,8 +24,41 @@ public record IRBackendExecutableFunction(
         ReadOnlyList<Instruction> instructions,
         Span span) {
 
+    public IRBackendExecutableFunction(
+            final FileId fileId,
+            final String moduleKey,
+            final String callableName,
+            final CallableId callableId,
+            final int sourceStart,
+            final int sourceEnd,
+            final int paramSlots,
+            final int localSlots,
+            final int returnSlots,
+            final int maxStackSlots,
+            final ReadOnlyList<Instruction> instructions,
+            final Span span) {
+        this(
+                fileId,
+                ModuleId.none(),
+                moduleKey,
+                callableName,
+                callableId,
+                sourceStart,
+                sourceEnd,
+                paramSlots,
+                localSlots,
+                returnSlots,
+                maxStackSlots,
+                instructions,
+                span);
+    }
+
     public IRBackendExecutableFunction {
         fileId = Objects.requireNonNull(fileId, "fileId");
+        moduleId = moduleId == null ? ModuleId.none() : moduleId;
+        if (!moduleId.isNone()) {
+            moduleId.getIndex();
+        }
         moduleKey = moduleKey == null ? "" : moduleKey;
         callableName = Objects.requireNonNull(callableName, "callableName");
         if (callableName.isBlank()) {
@@ -52,6 +87,7 @@ public record IRBackendExecutableFunction(
 
     public record Instruction(
             InstructionKind kind,
+            ModuleId calleeModuleId,
             String calleeModuleKey,
             String calleeCallableName,
             CallableId calleeCallableId,
@@ -64,13 +100,78 @@ public record IRBackendExecutableFunction(
             Span span) {
         public Instruction(
                 final InstructionKind kind,
+                final ModuleId calleeModuleId,
                 final String calleeModuleKey,
                 final String calleeCallableName,
                 final CallableId calleeCallableId,
                 final HostCallMetadata hostCall,
                 final IntrinsicCallMetadata intrinsicCall,
                 final Span span) {
-            this(kind, calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, null, null, null, null, span);
+            this(kind, calleeModuleId, calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, null, null, null, null, span);
+        }
+
+        public Instruction(
+                final InstructionKind kind,
+                final ModuleId calleeModuleId,
+                final String calleeModuleKey,
+                final String calleeCallableName,
+                final CallableId calleeCallableId,
+                final HostCallMetadata hostCall,
+                final IntrinsicCallMetadata intrinsicCall,
+                final Integer expectedArgSlots,
+                final Integer expectedRetSlots,
+                final Span span) {
+            this(kind, calleeModuleId, calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, null, null, expectedArgSlots, expectedRetSlots, span);
+        }
+
+        public Instruction(
+                final InstructionKind kind,
+                final ModuleId calleeModuleId,
+                final String calleeModuleKey,
+                final String calleeCallableName,
+                final HostCallMetadata hostCall,
+                final IntrinsicCallMetadata intrinsicCall,
+                final Span span) {
+            this(kind, calleeModuleId, calleeModuleKey, calleeCallableName, null, hostCall, intrinsicCall, null, null, null, null, span);
+        }
+
+        public Instruction(
+                final InstructionKind kind,
+                final ModuleId calleeModuleId,
+                final String calleeModuleKey,
+                final String calleeCallableName,
+                final HostCallMetadata hostCall,
+                final IntrinsicCallMetadata intrinsicCall,
+                final Integer expectedArgSlots,
+                final Integer expectedRetSlots,
+                final Span span) {
+            this(kind, calleeModuleId, calleeModuleKey, calleeCallableName, null, hostCall, intrinsicCall, null, null, expectedArgSlots, expectedRetSlots, span);
+        }
+
+        public Instruction(
+                final InstructionKind kind,
+                final String calleeModuleKey,
+                final String calleeCallableName,
+                final CallableId calleeCallableId,
+                final HostCallMetadata hostCall,
+                final IntrinsicCallMetadata intrinsicCall,
+                final String label,
+                final String targetLabel,
+                final Integer expectedArgSlots,
+                final Integer expectedRetSlots,
+                final Span span) {
+            this(kind, ModuleId.none(), calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, label, targetLabel, expectedArgSlots, expectedRetSlots, span);
+        }
+
+        public Instruction(
+                final InstructionKind kind,
+                final String calleeModuleKey,
+                final String calleeCallableName,
+                final CallableId calleeCallableId,
+                final HostCallMetadata hostCall,
+                final IntrinsicCallMetadata intrinsicCall,
+                final Span span) {
+            this(kind, ModuleId.none(), calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, null, null, null, null, span);
         }
 
         public Instruction(
@@ -83,7 +184,7 @@ public record IRBackendExecutableFunction(
                 final Integer expectedArgSlots,
                 final Integer expectedRetSlots,
                 final Span span) {
-            this(kind, calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, null, null, expectedArgSlots, expectedRetSlots, span);
+            this(kind, ModuleId.none(), calleeModuleKey, calleeCallableName, calleeCallableId, hostCall, intrinsicCall, null, null, expectedArgSlots, expectedRetSlots, span);
         }
 
         public Instruction(
@@ -93,7 +194,7 @@ public record IRBackendExecutableFunction(
                 final HostCallMetadata hostCall,
                 final IntrinsicCallMetadata intrinsicCall,
                 final Span span) {
-            this(kind, calleeModuleKey, calleeCallableName, null, hostCall, intrinsicCall, null, null, null, null, span);
+            this(kind, ModuleId.none(), calleeModuleKey, calleeCallableName, null, hostCall, intrinsicCall, null, null, null, null, span);
         }
 
         public Instruction(
@@ -105,12 +206,16 @@ public record IRBackendExecutableFunction(
                 final Integer expectedArgSlots,
                 final Integer expectedRetSlots,
                 final Span span) {
-            this(kind, calleeModuleKey, calleeCallableName, null, hostCall, intrinsicCall, null, null, expectedArgSlots, expectedRetSlots, span);
+            this(kind, ModuleId.none(), calleeModuleKey, calleeCallableName, null, hostCall, intrinsicCall, null, null, expectedArgSlots, expectedRetSlots, span);
         }
 
         public Instruction {
             Objects.requireNonNull(kind, "kind");
             span = span == null ? Span.none() : span;
+            calleeModuleId = calleeModuleId == null ? ModuleId.none() : calleeModuleId;
+            if (!calleeModuleId.isNone()) {
+                calleeModuleId.getIndex();
+            }
             calleeModuleKey = calleeModuleKey == null ? "" : calleeModuleKey;
             calleeCallableName = calleeCallableName == null ? "" : calleeCallableName;
             label = label == null ? "" : label;

prometeu-compiler/prometeu-frontend-api/src/main/java/p/studio/compiler/models/IRBackendFile.java

@@ -3,6 +3,7 @@ package p.studio.compiler.models;
 import p.studio.compiler.source.identifiers.FileId;
 import p.studio.compiler.source.tables.CallableSignatureRef;
 import p.studio.compiler.source.tables.IntrinsicReference;
+import p.studio.compiler.source.tables.ModuleReference;
 import p.studio.utilities.structures.ReadOnlyList;
 
 import java.util.Objects;
@@ -12,6 +13,7 @@ public record IRBackendFile(
         ReadOnlyList<IRFunction> functions,
         ReadOnlyList<IRBackendExecutableFunction> executableFunctions,
         IRReservedMetadata reservedMetadata,
+        ReadOnlyList<ModuleReference> modulePool,
         ReadOnlyList<CallableSignatureRef> callableSignatures,
         ReadOnlyList<IntrinsicReference> intrinsicPool) {
     public IRBackendFile {
@@ -19,6 +21,7 @@ public record IRBackendFile(
         functions = functions == null ? ReadOnlyList.empty() : functions;
         executableFunctions = executableFunctions == null ? ReadOnlyList.empty() : executableFunctions;
         reservedMetadata = reservedMetadata == null ? IRReservedMetadata.empty() : reservedMetadata;
+        modulePool = modulePool == null ? ReadOnlyList.empty() : modulePool;
         callableSignatures = callableSignatures == null ? ReadOnlyList.empty() : callableSignatures;
         intrinsicPool = intrinsicPool == null ? ReadOnlyList.empty() : intrinsicPool;
     }
@@ -26,17 +29,55 @@ public record IRBackendFile(
     public IRBackendFile(
             final FileId fileId,
             final ReadOnlyList<IRFunction> functions) {
-        this(fileId, functions, ReadOnlyList.empty(), IRReservedMetadata.empty(), ReadOnlyList.empty(), ReadOnlyList.empty());
+        this(
+                fileId,
+                functions,
+                ReadOnlyList.empty(),
+                IRReservedMetadata.empty(),
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty());
     }
 
     public static IRBackendFile empty(final FileId fileId) {
-        return new IRBackendFile(fileId, ReadOnlyList.empty(), ReadOnlyList.empty(), IRReservedMetadata.empty(), ReadOnlyList.empty(), ReadOnlyList.empty());
+        return new IRBackendFile(
+                fileId,
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty(),
+                IRReservedMetadata.empty(),
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty());
     }
 
     public IRBackendFile(
             final FileId fileId,
             final ReadOnlyList<IRFunction> functions,
             final IRReservedMetadata reservedMetadata) {
-        this(fileId, functions, ReadOnlyList.empty(), reservedMetadata, ReadOnlyList.empty(), ReadOnlyList.empty());
+        this(
+                fileId,
+                functions,
+                ReadOnlyList.empty(),
+                reservedMetadata,
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty(),
+                ReadOnlyList.empty());
+    }
+
+    public IRBackendFile(
+            final FileId fileId,
+            final ReadOnlyList<IRFunction> functions,
+            final ReadOnlyList<IRBackendExecutableFunction> executableFunctions,
+            final IRReservedMetadata reservedMetadata,
+            final ReadOnlyList<CallableSignatureRef> callableSignatures,
+            final ReadOnlyList<IntrinsicReference> intrinsicPool) {
+        this(
+                fileId,
+                functions,
+                executableFunctions,
+                reservedMetadata,
+                ReadOnlyList.empty(),
+                callableSignatures,
+                intrinsicPool);
     }
 }

prometeu-compiler/prometeu-frontend-api/src/test/java/p/studio/compiler/models/IRBackendExecutableContractTest.java

@@ -5,8 +5,10 @@ import p.studio.compiler.source.Span;
 import p.studio.compiler.source.identifiers.CallableId;
 import p.studio.compiler.source.identifiers.FileId;
 import p.studio.compiler.source.identifiers.IntrinsicId;
+import p.studio.compiler.source.identifiers.ModuleId;
 import p.studio.compiler.source.tables.CallableSignatureRef;
 import p.studio.compiler.source.tables.IntrinsicReference;
+import p.studio.compiler.source.tables.ModuleReference;
 import p.studio.utilities.structures.ReadOnlyList;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
@@ -300,4 +302,76 @@ class IRBackendExecutableContractTest {
         assertEquals(21, emittedInstructionSpan.getStart());
         assertEquals(34, emittedInstructionSpan.getEnd());
     }
+
+    @Test
+    void aggregatorMustReindexModulesIntoGlobalDensePool() {
+        final var fileA = new IRBackendFile(
+                new FileId(1),
+                ReadOnlyList.empty(),
+                ReadOnlyList.from(new IRBackendExecutableFunction(
+                        new FileId(1),
+                        new ModuleId(0),
+                        "app:mod/a",
+                        "entry",
+                        new CallableId(0),
+                        0,
+                        5,
+                        0,
+                        0,
+                        0,
+                        1,
+                        ReadOnlyList.from(new IRBackendExecutableFunction.Instruction(
+                                IRBackendExecutableFunction.InstructionKind.RET,
+                                "",
+                                "",
+                                null,
+                                null,
+                                Span.none())),
+                        Span.none())),
+                IRReservedMetadata.empty(),
+                ReadOnlyList.from(new ModuleReference("app", ReadOnlyList.from("mod", "a"))),
+                ReadOnlyList.from(new CallableSignatureRef(new ModuleId(0), "app:mod/a", "entry", 0, "() -> unit")),
+                ReadOnlyList.empty());
+        final var fileB = new IRBackendFile(
+                new FileId(2),
+                ReadOnlyList.empty(),
+                ReadOnlyList.from(new IRBackendExecutableFunction(
+                        new FileId(2),
+                        new ModuleId(0),
+                        "app:mod/b",
+                        "aux",
+                        new CallableId(0),
+                        6,
+                        10,
+                        0,
+                        0,
+                        0,
+                        1,
+                        ReadOnlyList.from(new IRBackendExecutableFunction.Instruction(
+                                IRBackendExecutableFunction.InstructionKind.RET,
+                                "",
+                                "",
+                                null,
+                                null,
+                                Span.none())),
+                        Span.none())),
+                IRReservedMetadata.empty(),
+                ReadOnlyList.from(new ModuleReference("app", ReadOnlyList.from("mod", "b"))),
+                ReadOnlyList.from(new CallableSignatureRef(new ModuleId(0), "app:mod/b", "aux", 0, "() -> unit")),
+                ReadOnlyList.empty());
+
+        final var aggregator = IRBackend.aggregator();
+        aggregator.merge(fileA);
+        aggregator.merge(fileB);
+        final var backend = aggregator.emit();
+
+        assertEquals(2, backend.getModulePool().size());
+        assertEquals("mod", backend.getModulePool().get(0).pathSegments().get(0));
+        assertEquals("a", backend.getModulePool().get(0).pathSegments().get(1));
+        assertEquals("b", backend.getModulePool().get(1).pathSegments().get(1));
+        assertEquals(0, backend.getExecutableFunctions().get(0).moduleId().getIndex());
+        assertEquals(1, backend.getExecutableFunctions().get(1).moduleId().getIndex());
+        assertEquals(0, backend.getCallableSignatures().get(0).moduleId().getIndex());
+        assertEquals(1, backend.getCallableSignatures().get(1).moduleId().getIndex());
+    }
 }