本課程將講授程式語言領域之入門理論與知識，希望培養學生以型式邏輯進行清晰思考的能力，了解邏輯與程式語言、型別系統的密切關係，以及型別系統在程式語言中扮演的角色，使學生能以遞迴／迭構方式理解並解決程式設計問題，能運用軟體工具輔助邏輯推理及證明程式正確性，並具備進一步探索程式語言相關領域的知識基礎。
FLOLAC 2024 很榮幸邀請到劍橋大學 Neel Krishnaswami 教授擔任特別講師，講題待定。
This course uses Haskell as a tool to provide an overview of some of the essential knowledge related to function programming in order to bridge the gap with other courses. Starting with structural induction, we will talk about data structures and the inductive definition of functions, and discover that the definition of a function can follow the definition of a data structure. If you want to prove the properties of a function, you can use induction, and the proof will follow the definition of the function. We then turn to the notion of fold, which we find can be regarded as an abstraction of structural induction. Finally, the red-black tree will be used as an example of programming and inductive proofs, in preparation for the subsequent course on dependent types.
Mathematical proofs are built upon valid inference structures; in formal logic, we express these structures with precise and succinct symbols, and study their properties. This course module focuses on the natural deduction system of propositional intuitionistic logic, introduces the basic syntactic and semantic proof methods used in formal logic, and points out the intimate relationship between logic and computation, leading into the topic of dependently typed programming. By studying the inference structures formally, this course module also introduces the necessary proof techniques used in other modules.
Nowadays many languages such as Haskell and Agda are based on variants of λ-calculus. In this course module, we will investigate λ-calculus and its notions and properties mathematically. For example, we will define computation and computational equivalence; after introducing types, we show how ‘a well-typed program does not go wrong’. Apart from theoretical interests, we also discuss a prevalent language feature —polymorphism— which has been applied to solve the code duplication problem in practice. Continuing into the dependently typed programming module, we will use Agda to implement λ-calculus and prove its properties.