diff --git a/__tests__/expr.test.ts b/__tests__/expr.test.ts
index 1e5fad28..4d38192a 100644
--- a/__tests__/expr.test.ts
+++ b/__tests__/expr.test.ts
@@ -525,20 +525,22 @@ describe("expr", () => {
       a: [1, 2, 3, 3, 3],
       b: ["a", "a", "b", "a", "a"],
     });
-    let actual = df.select(pl.len());
-    let expected = pl.DataFrame({ len: [5] });
+    const actual = df.select(pl.len());
+    const expected = pl.DataFrame({ len: [5] });
     expect(actual).toFrameEqual(expected);
 
-    actual = df.withColumn(pl.len());
-    expected = df.withColumn(pl.lit(5).alias("len"));
-    expect(actual).toFrameEqual(expected);
+    const actual2 = df.withColumn(pl.len());
+    const expected2 = df.withColumn(pl.lit(5).alias("len"));
+    expect(actual2).toFrameEqual(expected2);
 
-    actual = df.withColumn(pl.intRange(pl.len()).alias("index"));
-    expected = df.withColumn(pl.Series("index", [0, 1, 2, 3, 4], pl.Int64));
-    expect(actual).toFrameEqual(expected);
+    const actual3 = df.withColumn(pl.intRange(pl.len()).alias("index"));
+    const expected3 = df.withColumn(
+      pl.Series("index", [0, 1, 2, 3, 4], pl.Int64),
+    );
+    expect(actual3).toFrameEqual(expected3);
 
-    actual = df.groupBy("b").agg(pl.len());
-    expect(actual.shape).toEqual({ height: 2, width: 2 });
+    const actual4 = df.groupBy("b").agg(pl.len());
+    expect(actual4.shape).toEqual({ height: 2, width: 2 });
   });
   test("list", () => {
     const df = pl.DataFrame({
diff --git a/polars/dataframe.ts b/polars/dataframe.ts
index a798854c..f4de27a0 100644
--- a/polars/dataframe.ts
+++ b/polars/dataframe.ts
@@ -466,7 +466,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
 
    * @param other DataFrame to vertically add.
    */
-  extend(other: DataFrame): DataFrame;
+  extend(other: DataFrame<T>): DataFrame<T>;
   /**
    * Fill null/missing values by a filling strategy
    *
@@ -480,7 +480,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    *   - "one"
    * @returns DataFrame with None replaced with the filling strategy.
    */
-  fillNull(strategy: FillNullStrategy): DataFrame;
+  fillNull(strategy: FillNullStrategy): DataFrame<T>;
   /**
    * Filter the rows in the DataFrame based on a predicate expression.
    * ___
@@ -519,7 +519,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * └─────┴─────┴─────┘
    * ```
    */
-  filter(predicate: any): DataFrame;
+  filter(predicate: any): DataFrame<T>;
   /**
    * Find the index of a column by name.
    * ___
@@ -764,7 +764,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
   /**
    * Interpolate intermediate values. The interpolation method is linear.
    */
-  interpolate(): DataFrame;
+  interpolate(): DataFrame<T>;
   /**
    * Get a mask of all duplicated rows in this DataFrame.
    */
@@ -937,8 +937,11 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * Get first N rows as DataFrame.
    * @see {@link head}
    */
-  limit(length?: number): DataFrame;
-  map(func: (...args: any[]) => any): any[];
+  limit(length?: number): DataFrame<T>;
+  map<ReturnT>(
+    // TODO: strong types for the mapping function
+    func: (row: any[], i: number, arr: any[][]) => ReturnT,
+  ): ReturnT[];
 
   /**
    * Aggregate the columns of this DataFrame to their maximum value.
@@ -962,8 +965,8 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴──────╯
    * ```
    */
-  max(): DataFrame;
-  max(axis: 0): DataFrame;
+  max(): DataFrame<T>;
+  max(axis: 0): DataFrame<T>;
   max(axis: 1): Series;
   /**
    * Aggregate the columns of this DataFrame to their mean value.
@@ -972,8 +975,8 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * @param axis - either 0 or 1
    * @param nullStrategy - this argument is only used if axis == 1
    */
-  mean(): DataFrame;
-  mean(axis: 0): DataFrame;
+  mean(): DataFrame<T>;
+  mean(axis: 0): DataFrame<T>;
   mean(axis: 1): Series;
   mean(axis: 1, nullStrategy?: "ignore" | "propagate"): Series;
   /**
@@ -997,7 +1000,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴──────╯
    * ```
    */
-  median(): DataFrame;
+  median(): DataFrame<T>;
   /**
    * Unpivot a DataFrame from wide to long format.
    * @deprecated *since 0.13.0* use {@link unpivot}
@@ -1059,8 +1062,8 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴──────╯
    * ```
    */
-  min(): DataFrame;
-  min(axis: 0): DataFrame;
+  min(): DataFrame<T>;
+  min(axis: 0): DataFrame<T>;
   min(axis: 1): Series;
   /**
    * Get number of chunks used by the ChunkedArrays of this DataFrame.
@@ -1087,12 +1090,14 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * └─────┴─────┴─────┘
    * ```
    */
-  nullCount(): DataFrame;
+  nullCount(): DataFrame<{
+    [K in keyof T]: Series<JsToDtype<number>, K & string>;
+  }>;
   partitionBy(
     cols: string | string[],
     stable?: boolean,
     includeKey?: boolean,
-  ): DataFrame[];
+  ): DataFrame<T>[];
   partitionBy<T>(
     cols: string | string[],
     stable: boolean,
@@ -1210,13 +1215,13 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴──────╯
    * ```
    */
-  quantile(quantile: number): DataFrame;
+  quantile(quantile: number): DataFrame<T>;
   /**
    * __Rechunk the data in this DataFrame to a contiguous allocation.__
    *
    * This will make sure all subsequent operations have optimal and predictable performance.
    */
-  rechunk(): DataFrame;
+  rechunk(): DataFrame<T>;
   /**
    * __Rename column names.__
    * ___
@@ -1443,12 +1448,15 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * └─────┴─────┴─────┘
    * ```
    */
-  shiftAndFill(n: number, fillValue: number): DataFrame;
-  shiftAndFill({ n, fillValue }: { n: number; fillValue: number }): DataFrame;
+  shiftAndFill(n: number, fillValue: number): DataFrame<T>;
+  shiftAndFill({
+    n,
+    fillValue,
+  }: { n: number; fillValue: number }): DataFrame<T>;
   /**
    * Shrink memory usage of this DataFrame to fit the exact capacity needed to hold the data.
    */
-  shrinkToFit(): DataFrame;
+  shrinkToFit(): DataFrame<T>;
   shrinkToFit(inPlace: true): void;
   shrinkToFit({ inPlace }: { inPlace: true }): void;
   /**
@@ -1477,8 +1485,8 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * └─────┴─────┴─────┘
    * ```
    */
-  slice({ offset, length }: { offset: number; length: number }): DataFrame;
-  slice(offset: number, length: number): DataFrame;
+  slice({ offset, length }: { offset: number; length: number }): DataFrame<T>;
+  slice(offset: number, length: number): DataFrame<T>;
   /**
    * Sort the DataFrame by column.
    * ___
@@ -1493,7 +1501,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
     descending?: boolean,
     nullsLast?: boolean,
     maintainOrder?: boolean,
-  ): DataFrame;
+  ): DataFrame<T>;
   sort({
     by,
     reverse, // deprecated
@@ -1504,7 +1512,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
     reverse?: boolean; // deprecated
     nullsLast?: boolean;
     maintainOrder?: boolean;
-  }): DataFrame;
+  }): DataFrame<T>;
   sort({
     by,
     descending,
@@ -1514,7 +1522,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
     descending?: boolean;
     nullsLast?: boolean;
     maintainOrder?: boolean;
-  }): DataFrame;
+  }): DataFrame<T>;
   /**
    * Aggregate the columns of this DataFrame to their standard deviation value.
    * ___
@@ -1536,7 +1544,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴──────╯
    * ```
    */
-  std(): DataFrame;
+  std(): DataFrame<T>;
   /**
    * Aggregate the columns of this DataFrame to their mean value.
    * ___
@@ -1544,8 +1552,8 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * @param axis - either 0 or 1
    * @param nullStrategy - this argument is only used if axis == 1
    */
-  sum(): DataFrame;
-  sum(axis: 0): DataFrame;
+  sum(): DataFrame<T>;
+  sum(axis: 0): DataFrame<T>;
   sum(axis: 1): Series;
   sum(axis: 1, nullStrategy?: "ignore" | "propagate"): Series;
   /**
@@ -1595,7 +1603,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────────┴─────╯
    * ```
    */
-  tail(length?: number): DataFrame;
+  tail(length?: number): DataFrame<T>;
   /**
    * @deprecated *since 0.4.0* use {@link writeCSV}
    * @category Deprecated
@@ -1614,7 +1622,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ```
    * @category IO
    */
-  toRecords(): Record<string, any>[];
+  toRecords(): { [K in keyof T]: DTypeToJs<T[K]["dtype"]> | null }[];
 
   /**
    * compat with `JSON.stringify`
@@ -1644,7 +1652,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ```
    * @category IO
    */
-  toObject(): { [K in keyof T]: DTypeToJs<T[K]["dtype"]>[] };
+  toObject(): { [K in keyof T]: DTypeToJs<T[K]["dtype"] | null>[] };
 
   /**
    * @deprecated *since 0.4.0* use {@link writeIPC}
@@ -1656,7 +1664,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * @category IO Deprecated
    */
   toParquet(destination?, options?);
-  toSeries(index?: number): Series;
+  toSeries(index?: number): T[keyof T];
   toString(): string;
   /**
    *  Convert a ``DataFrame`` to a ``Series`` of type ``Struct``
@@ -1768,12 +1776,12 @@ export interface DataFrame<T extends Record<string, Series> = any>
     maintainOrder?: boolean,
     subset?: ColumnSelection,
     keep?: "first" | "last",
-  ): DataFrame;
+  ): DataFrame<T>;
   unique(opts: {
     maintainOrder?: boolean;
     subset?: ColumnSelection;
     keep?: "first" | "last";
-  }): DataFrame;
+  }): DataFrame<T>;
   /**
       Decompose a struct into its fields. The fields will be inserted in to the `DataFrame` on the
       location of the `struct` type.
@@ -1833,7 +1841,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴──────╯
    * ```
    */
-  var(): DataFrame;
+  var(): DataFrame<T>;
   /**
    * Grow this DataFrame vertically by stacking a DataFrame to it.
    * @param df - DataFrame to stack.
@@ -1866,12 +1874,16 @@ export interface DataFrame<T extends Record<string, Series> = any>
    * ╰─────┴─────┴─────╯
    * ```
    */
-  vstack(df: DataFrame): DataFrame;
+  vstack(df: DataFrame<T>): DataFrame<T>;
   /**
    * Return a new DataFrame with the column added or replaced.
    * @param column - Series, where the name of the Series refers to the column in the DataFrame.
    */
-  withColumn(column: Series | Expr): DataFrame;
+  withColumn<SeriesTypeT extends DataType, SeriesNameT extends string>(
+    column: Series<SeriesTypeT, SeriesNameT>,
+  ): DataFrame<
+    Simplify<T & { [K in SeriesNameT]: Series<SeriesTypeT, SeriesNameT> }>
+  >;
   withColumn(column: Series | Expr): DataFrame;
   withColumns(...columns: (Expr | Series)[]): DataFrame;
   /**
@@ -1896,7 +1908,7 @@ export interface DataFrame<T extends Record<string, Series> = any>
    */
   withRowCount(name?: string): DataFrame;
   /** @see {@link filter} */
-  where(predicate: any): DataFrame;
+  where(predicate: any): DataFrame<T>;
   /**
     Upsample a DataFrame at a regular frequency.
 
@@ -1972,13 +1984,13 @@ shape: (7, 3)
     every: string,
     by?: string | string[],
     maintainOrder?: boolean,
-  ): DataFrame;
+  ): DataFrame<T>;
   upsample(opts: {
     timeColumn: string;
     every: string;
     by?: string | string[];
     maintainOrder?: boolean;
-  }): DataFrame;
+  }): DataFrame<T>;
 }
 
 function prepareOtherArg(anyValue: any): Series {
diff --git a/polars/datatypes/datatype.ts b/polars/datatypes/datatype.ts
index d3c38cb0..0a9400c2 100644
--- a/polars/datatypes/datatype.ts
+++ b/polars/datatypes/datatype.ts
@@ -491,6 +491,20 @@ export type DTypeToJs<T> = T extends DataType.Decimal
           : T extends DataType.Utf8
             ? string
             : never;
+// some objects can be constructed with a looser JS type than they’d return when converted back to JS
+export type DTypeToJsLoose<T> = T extends DataType.Decimal
+  ? number | bigint
+  : T extends DataType.Float64
+    ? number | bigint
+    : T extends DataType.Int64
+      ? number | bigint
+      : T extends DataType.Int32
+        ? number | bigint
+        : T extends DataType.Bool
+          ? boolean
+          : T extends DataType.Utf8
+            ? string
+            : never;
 export type DtypeToJsName<T> = T extends DataType.Decimal
   ? "Decimal"
   : T extends DataType.Float64
diff --git a/polars/lazy/functions.ts b/polars/lazy/functions.ts
index 35988b8d..3b8385a3 100644
--- a/polars/lazy/functions.ts
+++ b/polars/lazy/functions.ts
@@ -204,8 +204,22 @@ export function intRange(opts: {
   end: number | Expr;
   step?: number | Expr;
   dtype?: DataType;
+  eager?: false;
+}): Expr;
+export function intRange<DT extends DataType = DataType.Int64>(opts: {
+  start: number | Expr;
+  end: number | Expr;
+  step?: number | Expr;
+  dtype?: DT;
+  eager: true;
+}): Series<DT>;
+export function intRange<DT extends DataType = DataType.Int64>(opts: {
+  start: number | Expr;
+  end: number | Expr;
+  step?: number | Expr;
+  dtype?: DT;
   eager?: boolean;
-});
+}): Expr | Series<DT>;
 /** @deprecated *since 0.15.0* use `start` and `end` instead */
 export function intRange(opts: {
   low: number | Expr;
@@ -213,27 +227,27 @@ export function intRange(opts: {
   step?: number | Expr;
   dtype?: DataType;
   eager?: boolean;
-});
+}): Expr | Series;
 export function intRange(
   start: number | Expr,
   end?: number | Expr,
   step?: number | Expr,
   dtype?: DataType,
-  eager?: true,
-): Series;
-export function intRange(
+  eager?: false,
+): Expr;
+export function intRange<DT extends DataType = DataType.Int64>(
   start: number | Expr,
   end?: number | Expr,
   step?: number | Expr,
-  dtype?: DataType,
-  eager?: false,
-): Expr;
-export function intRange(
+  dtype?: DT,
+  eager?: true,
+): Series<DT>;
+export function intRange<DT extends DataType = DataType.Int64>(
   opts: any,
-  end?,
+  end?: number | Expr,
   step = 1 as number | Expr,
-  dtype: DataType = DataType.Int64,
-  eager?,
+  dtype?: DT,
+  eager?: boolean,
 ): Series | Expr {
   // @deprecated since 0.15.0
   if (typeof opts?.low === "number") {
@@ -256,7 +270,7 @@ export function intRange(
       .select(intRange(start, end, step).alias("intRange") as any)
       .getColumn("intRange") as any;
   }
-  return _Expr(pli.intRange(start, end, step, dtype));
+  return _Expr(pli.intRange(start, end, step, dtype || DataType.Int64));
 }
 /***
  * Generate a range of integers for each row of the input columns.
@@ -554,7 +568,7 @@ export function head(column: Series | ExprOrString, n?): Series | Expr {
   └───────┴──────┴──────┴─────┘
   ```
 */
-export function len(): any {
+export function len(): Expr {
   return _Expr(pli.len());
 }
 /** Get the last value. */
diff --git a/polars/series/index.ts b/polars/series/index.ts
index 375616b9..d4cfadfe 100644
--- a/polars/series/index.ts
+++ b/polars/series/index.ts
@@ -2,6 +2,7 @@ import { DataFrame, _DataFrame } from "../dataframe";
 import { DTYPE_TO_FFINAME, DataType, type Optional } from "../datatypes";
 import type {
   DTypeToJs,
+  DTypeToJsLoose,
   DtypeToJsName,
   JsToDtype,
   JsType,
@@ -1933,7 +1934,7 @@ export interface SeriesConstructor extends Deserialize<Series> {
   ): Series<JsToDtype<T1>, Name>;
   <T2 extends DataType, Name extends string>(
     name: Name,
-    values: ArrayLike<DTypeToJs<T2 | null>>,
+    values: ArrayLike<DTypeToJsLoose<T2 | null>>,
     dtype?: T2,
   ): Series<T2, Name>;
   (name: string, values: any[], dtype?): Series;