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Soundness & Completeness in Type Theory
Prashant Basnet
Dec 12, 2024
39 views
To explain the concepts of soundness and completeness, particularly in the context of type checking and type inference, we can use analogies to make them easier to grasp.
Soundness and completeness are two properties that describe the reliability of a system, especially in logical systems and type systems.
Analogy: A Reliable Book Review System
Relations between static typing, dynamic typing, and type inference
Relation between Soundness and Completeness:
Soundness and completeness are fundamental concepts in formal verification and type systems. They are often used to evaluate the correctness and power of system.
Soundness:
A system is sound if it only accepts correct program. In other words, if a program is accepted by the system, it is guaranteed to be free of errors. If a program is correct by type system it won't have type errors when it runs. Imagine a teacher grading exams, if the teacher is sound, it means every answer they mark correct is indeed correct.
Completness:
A system is complete if it accepts all correct program. In other words if a program is correct it should be accepted by the system.Now, if the teacher is complete, then teacher can handle any exam within that subject and grade it correctly.
For type systems:
So, when talking about a complete type system:
The relation between them: A system that is both sound and complete ensures that it produces only correct results and covers all possible cases.
is a mechanism in programming languages that automatically determines the types of expressions without needing explicit type annotations from the programmer.