23FS MAT605 Logic and Foundations with Haskell
23FS MAT605 Logic and Foundations with Haskell
-
Von Marius Furter
14 Wiedergaben 0We look at three modules that include Rational and Complex numbers as well as Polynomials. We use these to implement Newton's method. All code can be found in the… -
Von Marius Furter
33 Wiedergaben 0We build the foundations of set theory using the Zermelo-Fraenkel axioms with choice. The material follows the first chapter of Thomas Jech's "Set Theory". -
Von Marius Furter
28 Wiedergaben 0We cover the basic definitions of set theory in preparation for understanding the ZFC axioms. -
Von Marius Furter
8 Wiedergaben 0We implements datatypes for integers based in the natural numbers. All code can be found in the course git repository https://github.com/MariusFurter/MAT605-haskell-FS23 -
Von Marius Furter
12 Wiedergaben 0We implement the typeclasses Ord, Enum, Num, Real and Integral for the natural numbers. This allows us to use all standard functions for these typeclasses on our natural… -
Von Marius Furter
18 Wiedergaben 0I show how the Maybe datatype and lists can be used to deal with functions that return either no value or multiple values. -
Von Marius Furter
23 Wiedergaben 0We discuss how the foldr and foldl patterns can be used for very compact implementations. -
Von Marius Furter
24 Wiedergaben 0We prove completeness of the natural deduction proof calculus for propositional logic. -
Von Marius Furter
19 Wiedergaben 0We implement natural numbers, arithmetic and comparison using an inductive datatype. All code can be found in the course git repository… -
Von Marius Furter
35 Wiedergaben 0We show that the natural deduction proof calculus is sound for propositional logic, meaning that it only proves true formulas given true assumptions. -
Von Marius Furter
28 Wiedergaben 0We cover the semantic definitions for propositional logic which assign formulas truth values in a sigma-structure. -
Von Marius Furter
23 Wiedergaben 0We implement functions as sets of pairs in Haskell. All code can be found in the course git repository https://github.com/MariusFurter/MAT605-haskell-FS23 -
Von Marius Furter
35 Wiedergaben 0We formally define the syntax of propositional logic and prove a unique parsing theorem for its formulas. -
Von Marius Furter
14 Wiedergaben 0We cover the basic definitions for relations and implement them in code. All code can be found in the course git repository… -
Von Marius Furter
18 Wiedergaben 0In this video we implement sets and associated functions. -
Von Marius Furter
55 Wiedergaben 0This video covers the formal proof system called natural deduction (without quantifiers), along with the corresponding sequent rules. -
Von Marius Furter
33 Wiedergaben 0In this video we implement our own version of the type Bool, along with the functions in the standard library that act on Bool. -
Von Marius Furter
45 Wiedergaben 0This videos covers the rules for proving first order logic statements. A summary of the rules can be found at… -
Von Marius Furter
23 Wiedergaben 0I discuss how to define functions using pattern matching and guards. Then I introduce where, let and case expressions. -
Von Marius Furter
24 Wiedergaben 0We cover types, type variables, and typeclasses in Haskell. This video follows chapter 3 of "Learn you a Haskell for great good"…
