Verifying correctness of programs with dependent types in Idris programming language

Blaž Repas (2014) Verifying correctness of programs with dependent types in Idris programming language. Prešeren awards for students.

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Abstract

Formal verification of program correctness in mission critical applications is still done manually. Programming languages with dependent types used as logical frameworks present an alternative to manual verification of correctness. In this thesis we deal with type systems and programming languages with dependent types. We introduce the Idris programming language which supports arbitrarily complex dependent types. We show how to translate propositions into function types and how to prove them by implementing the functions. Correctness is then automatically verified by the compiler. With use of dependent types we provide automatically verified implementations of data structures like list, stack and queue. To demonstrate usefulness of dependent types we provide automatically verified implementation of insertion sort algorithm. We prove sortedness with linear order of natural numbers and also that the output list is a permutation of the input list.

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