Pitfalls

The bytes remains the same despite copying, so you can get too funky:

int v = -12345;
unsigned int uv = v;

printf("v = %d, uv = %d\n", v, uv);

This prints “v = -12345, uv=4294954951”. As in: when you copy rvalues, the bit pattern gets copied and not the numerical number itself; so, it will overflow.

You can use U to force an signed quantity to be unsigned:

unsigned int uv = -12345U;

sign promotion

If you have the nerve of putting a comparing things of different types (don’t), then, the signed quantities gets promoted to be unsigned.

categorical grammar is a grammar in the language of categories.

constituents

• \(A\), a set of “expressions”
• \(C\), a set of categories of “syntax”
• \(\varphi: A \to Pow( C)\), assigning each \(a \in A\) to a set of categories \(c \subset C\)
• \(G\): a family of sets of n-place operations where \(n=1, 2, \ldots\) (what does a “3-place” op mean? idk)
• \(R\): a set of rules encoded as tuples: \((f; \{c_1, \dots c_{k}\}; c_{k+1})\), where \(f\) is a \(k\) place operation, and \(c_{j} \in C\)

requirements

The operations of this grammar behaves like so:

• categorical grammar

A category is an abstract collection of objects

constituents

• collection of objects, where if \(X\) is an object of \(C\) we write \(X \in C\)
• for a pair of objects \(X, Y \in C\), a set of morphisms acting upon the objects which we call the homset

additional information

requirements

• there exists the identity morphism; that is, \(\forall X \in C, \exists I_{X}: X\to X\)
• morphisms are always composable: given \(f: X\to Y\), and \(g: Y\to Z\), exists \(gf: X \to Z\)
• the identity morphism can compose in either direction: given \(f: X \to Y\), then \(f I_{x} = f = I_{y} f\)
• morphism composition is associative: \((hg)f=h(gf)\)

An abstract study of mathematics based on categories, functors, and natural transformations.