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High-assurance User-defined Functions

Many data integration tasks require user defined functions (UDFs): for example, to convert inches to centimeters. When UDFs are defined or used incorrectly, data can be silently corrupted. In CQL, user-defined functions are first-class schema elements, and CQL's automated theorem proving technology seamlessly provides high-assurance compile-time aid to schemas with user-defined functions.

This example (built in to the IDE with name Unit Conv) defines a source schema about American airplanes, which have wing spans in inches, and a target schema about European airplanes, which have wing spans in centimeters. The type side specifies how to convert inches to centimeters, and a query which does not convert inches to centimeters is rejected. Although this example uses a relatively simply type conversion, CQL supports user-defined types defined by arbitrary equations.

We start by defining a type side that contains two user defined types, inches and centimeters, as well as a conversion between them: 

typeside Ty = literal { 
	java_types
		in = "java.lang.Double"
		cm = "java.lang.Double"		
	java_constants
		in = "return java.lang.Double.parseDouble(input[0])"
		cm = "return java.lang.Double.parseDouble(input[0])"
	java_functions
		inToCm : in -> cm = "return (2.54 * input[0])"		
}


The source and target schemas contain wingspans in inches (for American planes) and centimeters (for European planes): 

schema AmericanAirplane = literal : Ty {
	entities 
		Wing
	attributes
		wingLength : Wing -> in
}

schema EuropeanAirplane = literal : Ty {
	entities 
		Wing
	attributes
		wingLength : Wing -> cm
}


An American airplane instance is, for example: 

instance Boeing747 = literal : AmericanAirplane {
	generators
		left right : Wing
	equations
		left.wingLength = right.wingLength
		left.wingLength = 500	
}

unitconv1

To convert an American airplane to a European airplane requires converting inches to centimeters: 

query AmericanToEuropean = literal : AmericanAirplane -> EuropeanAirplane {
	entities 
		Wing -> {from w:Wing
			    return wingLength -> inToCm(w.wingLength)}
}

instance Boeing747Metric = eval AmericanToEuropean Boeing747

unitconv2

A similar query that omits the unit conversion is rejected: 

query AmericanToEuropean_disastrous_conversion = literal : AmericanAirplane -> EuropeanAirplane {
	entities 
		Wing ->	{from w:Wing
				 return wingLength -> w.wingLength}
}

Error in query AmericanToEuropean_disastrous_conversion: 
 in attribute wingLength, expected sort of wingLength(w) is cm 
 but wingLength(w) actually has sort in.


A screen shot of the entire development is shown below:

unitconv3