UT Institute of Computer Science Graduation Theses Registry

Name

Tiina Turban

Abstract

This thesis introduces types into the ProveIt language, making it possible to perform type inference and type checking. The ProveIt language is a is a probabilistic program language used in ProveIt, a tool that helps cryptographers prove cryptographic protocols in a game-based way in the computational model. The work begins by explaining the necessary background knowledge: the computational model, game-based proving, the ProveIt prover tool and the ProveIt language. How they work and why they are relevant is also described. Introducing types into ProveIt allows further guarantee the correctness and providing better help to the user. Knowing that the user is tying to find the square root of a banana and where, might save a lot of his or her time. Although it would be easier to demand the user to state all the types for all the variables and only perform type checking, we decide not to do so and instead infer the types. This is done because our goal is to make the proving process as convenient for the user as possible. To do type inference, the work starts with defining the formal type system for the ProveIt language. Type rules for all the arithmetic operations available in ProveIt are provided and also type rules for the uniform choice statement and the assignment statement. Adding rules for typing functions and logical expressions is not in the scope of this thesis and is considered future work. In addition to the type system description, type checking and type inference were implemented. To do that, the thesis first deals with the scopes of the variables in ProveIt, as it has both local and global variables. Secondly, the relations between types are covered, including the need and means to find lowest common ancestors in directed acyclic graphs. This is necessary to be able to find the minimal common supertype if an arithmetic operation was performed between variables of different types. Next, the concepts of a minimum and a maximum type are introduced to make type inference easier and also be able to output better error messages. Finally six algorithms are given to complete the type inference and type checking.

Graduation Thesis language

English

Graduation Thesis type

Bachelor - Computer Science

Supervisor(s)

Liina Kamm, Sven Laur

Defence year

2012