Pointer assignment to different types

Question

We can assign a string in C as follows:

char *string;
string = \"Hello\";
printf(\"%s\\n\", string); // string
printf(\"%p\\n\", string); // memory-address
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Answer 1

why can't we assign a pointer to a number in C just like we do with strings?

int *num;
num = 4404;

Code can do that if 4404 is a valid address for an int.

An integer may be converted to any pointer type. Except as previously specified, the result is implementation-defined, might not be correctly aligned, might not point to an entity of the referenced type, and might be a trap representation.
C11dr §6.3.2.3 5

If the address is not properly aligned --> undefined behavior (UB).
If the address is a trap --> undefined behavior (UB).

Attempting to de-reference the pointer is a problem unless it points to a valid int.

printf("%d\n", *num);

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With below, "Hello" is a string literal. It exist someplace. The assignment take the address of the string literal and assigns that to string.

char *string;
string = "Hello";

The point is that that address assigned is known to be valid for a char *.

In the num = 4404; is not known to be valid (it likely is not).

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What makes a string fundamentally different than other primitive types?

In C, a string is a C library specification, not a C language one. It is definition convenient to explaining various function therein.

A string is a contiguous sequence of characters terminated by and including the first null character §7.1.1 1

Primitive types are part of the C language.

The languages also has string literals like "Hello" in char *string; string = "Hello";. These have some similarity to strings, yet differ.

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I recommend searching for "ISO/IEC9899:2017" to find a draft copy of the current C spec. It will answer many of your 10 question of the last week.