Strengthen TypeSignature and Coercion rule. about arrow-datafusion HOT 1 OPEN

The current ideal state in my mind

Signature does 3 things

1. Length check
2. Type check
3. Coercion

For length,
the common length check are

1. Exact number
2. Variadic (Any number)
3. VariadicNonZero (Any number but at least one)
4. VariadicEven (Less common, i.e. Map)

For types,
We have two style, Exact and Coercion. Exact rejects if the type mismatch, Coercion rejects if teh type is not coercible to the target type.

The combination of these are

• Uniform(Vec<DataType>) // Exact Number with Exact type
• UniformCoercion(Vec<DataType>) // Exact Number with coercion
• Variadic(DataType)
• VariadicCoercion(DataType)
  ...

For non-uniform length and more then on data type signature, we could use UserDefined.

The more tricky part is the DataType. We have many functions expect Numeric type that includes integer, float, ....
For function that expects string, there are Utf8, LargeUtf8, Utf8View.

For type checking, it would be nice to have more general Enum that includes more than one DataType to check against with.

enum ArgumentType {
 Numeric
 Integer
 Float
 List
 ...
}

Now, we have

• Uniform(Vec<FunctionType>) // Exact Number with Exact type
• UniformCoercion(Vec<FunctionType>) // Exact Number with coercion
• Variadic(FunctionType)
• VariadicCoercion(FunctionType)

TypeSignature::Numeric is one of the idea that comes out from it.
For other kinds of complex type check or length check, we fall back to UserDefined

from arrow-datafusion.