How to change a dataframe column from String type to Double type in PySpark?

There is no need for an UDF here. Column already provides cast method with DataType instance :

from pyspark.sql.types import DoubleType

changedTypedf = joindf.withColumn("label", joindf["show"].cast(DoubleType()))

or short string:

changedTypedf = joindf.withColumn("label", joindf["show"].cast("double"))

where canonical string names (other variations can be supported as well) correspond to simpleString value. So for atomic types:

from pyspark.sql import types 

for t in ['BinaryType', 'BooleanType', 'ByteType', 'DateType', 
          'DecimalType', 'DoubleType', 'FloatType', 'IntegerType', 
           'LongType', 'ShortType', 'StringType', 'TimestampType']:
    print(f"{t}: {getattr(types, t)().simpleString()}")

BinaryType: binary
BooleanType: boolean
ByteType: tinyint
DateType: date
DecimalType: decimal(10,0)
DoubleType: double
FloatType: float
IntegerType: int
LongType: bigint
ShortType: smallint
StringType: string
TimestampType: timestamp

and for example complex types

types.ArrayType(types.IntegerType()).simpleString()   

'array<int>'

types.MapType(types.StringType(), types.IntegerType()).simpleString()

'map<string,int>'

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Preserve the name of the column and avoid extra column addition by using the same name as input column:

from pyspark.sql.types import DoubleType
changedTypedf = joindf.withColumn("show", joindf["show"].cast(DoubleType()))

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Given answers are enough to deal with the problem but I want to share another way which may be introduced the new version of Spark (I am not sure about it) so given answer didn't catch it.

We can reach the column in spark statement with col("colum_name") keyword:

from pyspark.sql.functions import col
changedTypedf = joindf.withColumn("show", col("show").cast("double"))

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PySpark version:

df = <source data>
df.printSchema()

from pyspark.sql.types import *

# Change column type
df_new = df.withColumn("myColumn", df["myColumn"].cast(IntegerType()))
df_new.printSchema()
df_new.select("myColumn").show()

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the solution was simple -

toDoublefunc = UserDefinedFunction(lambda x: float(x),DoubleType())
changedTypedf = joindf.withColumn("label",toDoublefunc(joindf['show']))

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