diff --git a/packages/cubejs-schema-compiler/src/compiler/CubeEvaluator.ts b/packages/cubejs-schema-compiler/src/compiler/CubeEvaluator.ts
index c58823b4ac9c6..c97d922f1c514 100644
--- a/packages/cubejs-schema-compiler/src/compiler/CubeEvaluator.ts
+++ b/packages/cubejs-schema-compiler/src/compiler/CubeEvaluator.ts
@@ -1,7 +1,7 @@
 /* eslint-disable no-restricted-syntax */
 import R from 'ramda';
 
-import { CubeSymbols } from './CubeSymbols';
+import { CubeSymbols, type ToString } from './CubeSymbols';
 import { UserError } from './UserError';
 import { BaseQuery } from '../adapter';
 import type { CubeValidator } from './CubeValidator';
@@ -28,7 +28,7 @@ export type DimensionDefinition = {
 };
 
 export type TimeShiftDefinition = {
-  timeDimension: Function,
+  timeDimension: (...args: Array<unknown>) => ToString,
   interval: string,
   type: 'next' | 'prior',
 };
@@ -48,9 +48,9 @@ export type MeasureDefinition = {
   primaryKey?: true,
   drillFilters?: any,
   multiStage?: boolean,
-  groupBy?: Function,
-  reduceBy?: Function,
-  addGroupBy?: Function,
+  groupBy?: (...args: Array<unknown>) => Array<ToString>,
+  reduceBy?: (...args: Array<unknown>) => Array<ToString>,
+  addGroupBy?: (...args: Array<unknown>) => Array<ToString>,
   timeShift?: TimeShiftDefinition[],
   groupByReferences?: string[],
   reduceByReferences?: string[],
@@ -65,6 +65,40 @@ export type PreAggregationFilters = {
   scheduled?: boolean,
 };
 
+type PreAggregationDefinition = {
+  allowNonStrictDateRangeMatch?: boolean,
+  timeDimensionReference?: () => ToString,
+  granularity: string,
+  timeDimensionReferences: Array<{ dimension: () => ToString, granularity: string }>,
+  dimensionReferences: () => Array<ToString>,
+  segmentReferences: () => Array<ToString>,
+  measureReferences: () => Array<ToString>,
+  rollupReferences: () => Array<ToString>,
+};
+
+type PreAggregationTimeDimensionReference = {
+  dimension: string,
+  granularity: string,
+};
+
+type PreAggregationReferences = {
+  allowNonStrictDateRangeMatch?: boolean,
+  dimensions: Array<string>,
+  measures: Array<string>,
+  timeDimensions: Array<PreAggregationTimeDimensionReference>,
+  rollups: Array<string>,
+};
+
+type PreAggregationInfo = {
+  id: string,
+  preAggregationName: string,
+  preAggregation: unknown,
+  cube: string,
+  references: PreAggregationReferences,
+  refreshKey: unknown,
+  indexesReferences: unknown,
+};
+
 export class CubeEvaluator extends CubeSymbols {
   public evaluatedCubes: Record<string, any> = {};
 
@@ -492,7 +526,7 @@ export class CubeEvaluator extends CubeSymbols {
   /**
    * Returns pre-aggregations filtered by the specified selector.
    */
-  public preAggregations(filter: PreAggregationFilters) {
+  public preAggregations(filter: PreAggregationFilters): Array<PreAggregationInfo> {
     const { scheduled, dataSources, cubes, preAggregationIds } = filter || {};
     const idFactory = ({ cube, preAggregationName }) => `${cube}.${preAggregationName}`;
 
@@ -510,7 +544,7 @@ export class CubeEvaluator extends CubeSymbols {
           )
         )
       ))
-      .map(cube => {
+      .flatMap(cube => {
         const preAggregations = this.preAggregationsForCube(cube);
         return Object.keys(preAggregations)
           .filter(
@@ -547,11 +581,10 @@ export class CubeEvaluator extends CubeSymbols {
               }, {})
             };
           });
-      })
-      .reduce((a, b) => a.concat(b), []);
+      });
   }
 
-  public scheduledPreAggregations() {
+  public scheduledPreAggregations(): Array<PreAggregationInfo> {
     return this.preAggregations({ scheduled: true });
   }
 
@@ -704,8 +737,8 @@ export class CubeEvaluator extends CubeSymbols {
     return { cubeReferencesUsed, pathReferencesUsed, evaluatedSql };
   }
 
-  protected evaluatePreAggregationReferences(cube, aggregation) {
-    const timeDimensions: any = [];
+  protected evaluatePreAggregationReferences(cube: string, aggregation: PreAggregationDefinition): PreAggregationReferences {
+    const timeDimensions: Array<PreAggregationTimeDimensionReference> = [];
 
     if (aggregation.timeDimensionReference) {
       timeDimensions.push({
diff --git a/packages/cubejs-schema-compiler/src/compiler/CubeSymbols.ts b/packages/cubejs-schema-compiler/src/compiler/CubeSymbols.ts
index 5c00edacdf94d..dffa59b9e017c 100644
--- a/packages/cubejs-schema-compiler/src/compiler/CubeSymbols.ts
+++ b/packages/cubejs-schema-compiler/src/compiler/CubeSymbols.ts
@@ -9,9 +9,11 @@ import { BaseQuery } from '../adapter';
 
 import type { ErrorReporter } from './ErrorReporter';
 
+export type ToString = { toString(): string };
+
 interface CubeDefinition {
   name: string;
-  extends?: string;
+  extends?: (...args: Array<unknown>) => { __cubeName: string };
   measures?: Record<string, any>;
   dimensions?: Record<string, any>;
   segments?: Record<string, any>;
@@ -292,7 +294,8 @@ export class CubeSymbols {
         // If the hierarchy is included all members from it should be included as well
         // Extend `includes` with members from hierarchies that should be auto-included
         const cubes = type === 'dimensions' ? cube.cubes.map((it) => {
-          const fullPath = this.evaluateReferences(null, it.joinPath, { collectJoinHints: true });
+          // TODO recheck `it.joinPath` typing
+          const fullPath = this.evaluateReferences(null, it.joinPath as () => ToString, { collectJoinHints: true });
           const split = fullPath.split('.');
           const cubeRef = split[split.length - 1];
 
@@ -332,7 +335,8 @@ export class CubeSymbols {
           const hierarchy = this.getResolvedMember(type, cubeName, hierarchyName);
 
           if (hierarchy) {
-            const levels = this.evaluateReferences(cubeName, this.getResolvedMember('hierarchies', cubeName, hierarchyName).levels, { originalSorting: true });
+            // TODO recheck `this.getResolvedMember(...).levels` typing
+            const levels = this.evaluateReferences(cubeName, this.getResolvedMember('hierarchies', cubeName, hierarchyName).levels as () => Array<ToString>, { originalSorting: true });
 
             levels.forEach((level) => autoIncludeMembers.add(level));
           }
@@ -370,7 +374,8 @@ export class CubeSymbols {
 
   protected membersFromCubes(parentCube: CubeDefinition, cubes: any[], type: string, errorReporter: ErrorReporter, splitViews: SplitViews, memberSets: any) {
     return R.unnest(cubes.map(cubeInclude => {
-      const fullPath = this.evaluateReferences(null, cubeInclude.joinPath, { collectJoinHints: true });
+      // TODO recheck `cubeInclude.joinPath` typing
+      const fullPath = this.evaluateReferences(null, cubeInclude.joinPath as () => ToString, { collectJoinHints: true });
       const split = fullPath.split('.');
       const cubeReference = split[split.length - 1];
       const cubeName = cubeInclude.alias || cubeReference;
@@ -453,7 +458,7 @@ export class CubeSymbols {
     return includes.filter(include => !excludesMap.has(include.member));
   }
 
-  protected membersFromIncludeExclude(referencesFn: any, cubeName: string, type: string) {
+  protected membersFromIncludeExclude(referencesFn: (...args: Array<unknown>) => Array<ToString>, cubeName: string, type: string) {
     const references = this.evaluateReferences(cubeName, referencesFn);
     return R.unnest(references.map((ref: string) => {
       const path = ref.split('.');
@@ -550,7 +555,12 @@ export class CubeSymbols {
     return res;
   }
 
-  protected evaluateReferences(cube, referencesFn, options: any = {}) {
+  protected evaluateReferences<T extends ToString | Array<ToString>>(
+    cube: string | null,
+    referencesFn: (...args: Array<unknown>) => T,
+    options: { collectJoinHints?: boolean, originalSorting?: boolean } = {}
+  ):
+  T extends Array<ToString> ? Array<string> : T extends ToString ? string : string | Array<string> {
     const cubeEvaluator = this;
 
     const fullPath = (joinHints, path) => {
@@ -561,7 +571,7 @@ export class CubeSymbols {
       }
     };
 
-    const arrayOrSingle = cubeEvaluator.resolveSymbolsCall(referencesFn, (name) => {
+    const arrayOrSingle: T = cubeEvaluator.resolveSymbolsCall(referencesFn, (name) => {
       const referencedCube = cubeEvaluator.symbols[name] && name || cube;
       const resolvedSymbol =
         cubeEvaluator.resolveSymbol(
@@ -582,25 +592,35 @@ export class CubeSymbols {
       collectJoinHints: options.collectJoinHints,
     });
     if (!Array.isArray(arrayOrSingle)) {
-      return arrayOrSingle.toString();
+      // arrayOrSingle is of type `T`, and we just checked that it is not an array
+      // Which means it `T` be an object with `toString`, and result must be `string`
+      // For any branch of return type that can can contain just an object it's OK to return string
+      return arrayOrSingle.toString() as any;
     }
 
-    const references = arrayOrSingle.map(p => p.toString());
-    return options.originalSorting ? references : R.sortBy(R.identity, references);
+    const references: Array<string> = arrayOrSingle.map(p => p.toString());
+    // arrayOrSingle is of type `T`, and we just checked that it is an array
+    // Which means that both `T` and result must be arrays
+    // For any branch of return type that can contain array it's OK to return array
+    return options.originalSorting ? references : R.sortBy(R.identity, references) as any;
   }
 
   public pathFromArray(array) {
     return array.join('.');
   }
 
-  protected resolveSymbolsCall(func, nameResolver, context?: any) {
+  protected resolveSymbolsCall<T>(
+    func: (...args: Array<unknown>) => T | DynamicReference<T>,
+    nameResolver: (id: string) => unknown,
+    context?: unknown,
+  ): T {
     const oldContext = this.resolveSymbolsCallContext;
     this.resolveSymbolsCallContext = context;
     try {
       // eslint-disable-next-line prefer-spread
-      let res = func.apply(null, this.funcArguments(func).map((id) => nameResolver(id.trim())));
+      const res = func.apply(null, this.funcArguments(func).map((id) => nameResolver(id.trim())));
       if (res instanceof DynamicReference) {
-        res = res.fn.apply(null, res.memberNames.map((id) => nameResolver(id.trim())));
+        return res.fn.apply(null, res.memberNames.map((id) => nameResolver(id.trim())));
       }
       return res;
     } finally {
diff --git a/packages/cubejs-schema-compiler/src/compiler/DynamicReference.js b/packages/cubejs-schema-compiler/src/compiler/DynamicReference.js
deleted file mode 100644
index 9a3166e91629c..0000000000000
--- a/packages/cubejs-schema-compiler/src/compiler/DynamicReference.js
+++ /dev/null
@@ -1,6 +0,0 @@
-export class DynamicReference {
-  constructor(memberNames, fn) {
-    this.memberNames = memberNames;
-    this.fn = fn;
-  }
-}
diff --git a/packages/cubejs-schema-compiler/src/compiler/DynamicReference.ts b/packages/cubejs-schema-compiler/src/compiler/DynamicReference.ts
new file mode 100644
index 0000000000000..c2b4fce377cab
--- /dev/null
+++ b/packages/cubejs-schema-compiler/src/compiler/DynamicReference.ts
@@ -0,0 +1,4 @@
+export class DynamicReference<T> {
+  public constructor(public memberNames: Array<string>, public fn: (...args: Array<unknown>) => T) {
+  }
+}