2020 Mathematical Theory of Programs

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Academic unit or major
Graduate major in Computer Science
Nishizaki Shin-Ya 
Class Format
Lecture    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(大岡山GSIC 3階 307号室, Ookayama GSIC bldg. 3F room# 307)  Thr3-4(大岡山GSIC 3階 307号室, Ookayama GSIC bldg. 3F room# 307)  
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Academic year
Offered quarter
Syllabus updated
Lecture notes updated
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Course description and aims

Mathematical Theory of Programs is an area of theoretical computer science to build mathematical models of computer programs and to give a basis for analyzing, verifying and understanding their properties. In this course, you learn basic theories such as operational semantics, denotational semantics, axiomatic semantics and formal verification techniques for program behaviors. As applications of basic theories, you also learn domain theory and attribute grammar.

Student learning outcomes

The main theme of this lecture is to build a basis to apply concept and theory of program theories such as operational semantics, denotational semantics, axiomatic semantics. Through this course, you learn the formal definitions of programming languages. You also learn techniques of proof for validations of program behavior in a level that you can apply them to another area of computer science through exercises.


Operational Semantics, Denotational Semantics, Axiomatic semantics, Principles of induction, Hoare Logic, Domain theory, Concurrent Computation Model

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Classroom learning. After learning of basic concepts and definitions of formal semantics, study techniques of proof for validations of program behavior through running examples.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Formal semantics of programming languages Understanding the importance of formal semantics of programming languages
Class 2 Basic Concept Explaining basic Concept of program theory
Class 3 Operational Semantics (Expression valuation and Command execution) Explaining operational Semantics (Expression valuation and Command execution)
Class 4 Inductive definitions and principles of induction. Explaining inductive definitions and principles of induction.
Class 5 Proof rules for operational semantics Explaining proof rules for operational semantics
Class 6 Denotational Semantics Explaining denotational semantics
Class 7 The relationship between Operational Semantics and Denotational Semantics Explaining the relationship between Operational Semantics and Denotational Semantics
Class 8 Axiomatic semantics, Hoare Logic Explaining axiomatic semantics, Hoare Logic
Class 9 Soundness and Completeness of the Hoare rules Explain soundness and completeness of the Hoare rules
Class 10 Verification and Validation Explaining verification and validation
Class 11 Domain theory (1) Definitions Explaining definitions in domain theory
Class 12 Domain theory (2) Domain Theory and Various Properties Explaining the domain theory and various properties
Class 13 Models of Concurrent Computation: Definitions Explaining the various definitions of concurrent models
Class 14 Models of Concurrent Computations: Examples Understanding of the model of concurrent computing through examples
Class 15 Advanced Topics of Formal Semantics Understanding of advanced topics

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


None. Slides are available in lecture.

Reference books, course materials, etc.

Semantics with Applications: An Appetizer, Riis Nielson, Hanne, Nielson, Flemming , Springer , 2007
Communicating and mobile systems: the pi-calculus, Robin Milner, Cambrdge University Press.

Assessment criteria and methods

Grades will be assessed through reports (40%) and exams (60%).:except in 2020.
In 2020, grades will be assessed through reports.

Related courses

  • CSC.T261 : Logic in Computer Science
  • MCS.T416 : Logic and Computation

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Mathematical Logic

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