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2016　Mathematical Theory of Programs

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Academic unit or major
Graduate major in Computer Science
Instructor(s)
Kobayashi Takashi  Nishizaki Shin-Ya 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Mon7-8(W935)  Thr7-8(W935)  
Group
-
Course number
CSC.T422
Credits
2
Academic year
2016
Offered quarter
1Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Mathematical Theory of Programs is is an area of theoretical computer science to build mathematical models of computer programs and to give a basis of 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 apprications of basic theories, you also learn domain theory and attribute grammar.

Student learning outcomes

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. By studying this lecture, 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 other area of computer science through exercises.

Keywords

Operational Semantics, Denotational Semantics, Axiomatic semantics, Principles of induction, Hoare Logic, Domain theory, Attribute Grammar

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 Formal semantics of programming languages
Class 2 Basic Concept Basic Concept
Class 3 Operational Semantics (Expression valuation and Command execution) Operational Semantics (Expression valuation and Command execution)
Class 4 Inductive definitions and principles of induction. Inductive definitions and principles of induction.
Class 5 Proof rules for operational semantics Proof rules for operational semantics
Class 6 Denotational Semantics Denotational Semantics
Class 7 Relationship between Operational Semantics and Denotational Semantics Relationship between Operational Semantics and Denotational Semantics
Class 8 Axiomatic semantics, Hoare Logic Axiomatic semantics, Hoare Logic
Class 9 Partial correctness assertions, Examples of proof Partial correctness assertions, Examples of proof
Class 10 Soundness and Completeness of the Hoare rules Soundness and Completeness of the Hoare rules
Class 11 Verification and Validation Verification and Validation
Class 12 Domain theory (1) Definitions Domain theory (1) Definitions
Class 13 Domain theory (2) Domain Theory and Theory of computation Domain theory (2) Domain Theory and Theory of computation
Class 14 Attribute Grammar : Definitions Attribute Grammar : Definitions
Class 15 Attribute Grammar : Example Attribute Grammar : Example

Textbook(s)

None. Slides are available in lecture.

Reference books, course materials, etc.

The Formal Semantics of Programming Languages Glynn and Winskel ， MIT Press ， 1993

Assessment criteria and methods

Evaluating report with quality of mini reports (40%) and final report (60%).

Related courses

  • CSC.T425 ： Concurrent System Theory
  • CSC.T436 ： Workshop on System Verification

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

Mathematical Logic

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