In this article, we introduce several important extensions of PCF. All are obtained by adding new types. The first extension is a very simple one, a type unit with only one element. The second ext...

In this article, we will discuss how to represent iterations in PCF using recursions. Then we are going to compare the natural-number functions definable in PCF with the classes of total and partia...

In the last article, we have seen all of the structure of PCF, now we will take a step back and discuss the meaning, or semantics, in a general way. We want our discussion can be applied to a varie...

In some esports tournaments (like CS2, Dota, etc.), game officials often open up channels for fans to participate in guessing which professional team will win. People want to benefit by betting on ...

There are two normal forms in propositional logic: disjunctive normal form (DNF) and conjunctive normal form (CNF). In the last article, we know that DNF satisfying problem is easy to solve; howeve...

In this article, we will present a language for Programming Computable Functions called PCF. This is a typed functional language based on lambda calculus, and is originally formulated by Dana Scott...

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. This article introduces the applica...

A Bloom filter is a space-efficient probabilistic data structure, conceived by Burton Howard Bloom in 1970, that is used to test whether an element is a member of a set. This article will describe ...

The balls into bins problem is a classic problem in probability theory that has many applications in computer science. It aims to answer how to balanced allocate resources in a random way. In this ...

In this article, we recover some notation and mathematical conventions that will be frequently used in subsequent articles. We assume readers have basic knowledge of grammar and logic. Grammars G...