What part of Hindley-Milner do you not understand?

Question

I swear there used to be a T-shirt for sale featuring the immortal words:

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What part of

Answer 1

if somebody could at least tell me where to start looking to comprehend what this sea of symbols means

See "Practical Foundations of Programming Languages.", chapters 2 and 3, on the style of logic through judgements and derivations. The entire book is now available on Amazon.

Chapter 2

Inductive Definitions

Inductive definitions are an indispensable tool in the study of programming languages. In this chapter we will develop the basic framework of inductive definitions, and give some examples of their use. An inductive definition consists of a set of rules for deriving judgments, or assertions, of a variety of forms. Judgments are statements about one or more syntactic objects of a specified sort. The rules specify necessary and sufficient conditions for the validity of a judgment, and hence fully determine its meaning.

2.1 Judgments

We start with the notion of a judgment, or assertion about a syntactic object. We shall make use of many forms of judgment, including examples such as these:

• n nat — n is a natural number
• n = n1 + n2 — n is the sum of n1 and n2
• τ type — τ is a type
• e : τ — expression e has type τ
• e ⇓ v — expression e has value v

A judgment states that one or more syntactic objects have a property or stand in some relation to one another. The property or relation itself is called a judgment form, and the judgment that an object or objects have that property or stand in that relation is said to be an instance of that judgment form. A judgment form is also called a predicate, and the objects constituting an instance are its subjects. We write a J for the judgment asserting that J holds of a. When it is not important to stress the subject of the judgment, (text cuts off here)