leo/docs/rfc/004-integer-type-casts.md

# Leo RFC 004: Integer Type Casts

## Authors

The Aleo Team.

## Status

FINAL

## Summary

This proposal provides support for casts among integer types in Leo.
The syntax is similar to Rust.
The semantics is _value-preserving_,
i.e. the casts just serve to change types
but cause errors when the mathematical values are not representable in the new types.

## Motivation

Currently the Leo integer types are "siloed":
arithmetic integer operations require operands of the same type
and return results of the same type.
There are no implicit or explicit ways to turn, for example,
a `u8` into a `u16`, even though
every non-negative integer that fits in 8 bits also fits in 16 bits.
However, the ability to convert values between different (integer) types
is a useful feature that is normally found in programming languages.

## Design

### Background

Recall that Leo supports the following _integer types_:
```
u8 u16 u32 u64 u128
i8 i16 i32 i64 i128
```

### Scope

This RFC proposes type casts between any two integer types,
but not between two non-integer types
or between an integer type and a non-integer type.

This RFC does not propose any implicit cast,
even widening casts (i.e. upcasts)
from a type to another type with the same signedness
and with the same or larger size
(e.g. from `u8` to `u16`).
All the type casts must be explicit.

### Syntax and Static Semantics

The proposed syntax is
```
<expression> as <integer-type>
```
where `<expression>` must have an integer type.

The ABNF grammar of Leo is modified as follows:
```
; add this rule:
cast-expression = unary-expression
                / cast-expression %s"as" integer-type

; modify this rule:
exponential-expression = cast-expression
                       / cast-expression "**" exponential-expression
```
There is no need to modify the `keyword` rule
because it already includes `as` as one of the keywords.
Note the use of `integer-type` in the `cast-expression` rule;
an alternative is to use `type` there
and check post-parsing that the type is in fact an integer one.

The above grammar rules imply that casts bind
tighter than binary operators and looser than unary operators.
For instance,
```
x + - y as u8
```
is like
```
x + ((- y) as u8)
```
This precedence is the same as in Rust:
see [here](https://doc.rust-lang.org/stable/reference/expressions.html#expression-precedence).

### Dynamic Semantics

When the mathematical integer value of the expression
is representable in the type that the expression is cast to,
there is no question that the cast must succeed
and merely change the type of the Leo value,
but not its mathematical integer value.
This is always the case when the cast is to a type
with the same signedness and with the same or larger size.
This is also the case when
the cast is to a type whose range does not cover the range of the source type
but the value in question is in the intersection of the two ranges.

When the mathematical integer value of the expression
is not representable in the type that the expression is cast to,
there are two possible approaches:
_value-preserving casts_,
which just serve to change types
but cause errors when values are not representable in the new types;
and _values-changing casts_,
which never cause errors but may change the mathematical values.

Based on discussion and consensus within the Leo team,
this RFC proposes value-preserving casts;
value-changing casts are discussed in the 'Alternatives' section,
for completeness.

With value-preserving casts,
when the mathematical integer value of the expression
is not representable in the type that the expression is cast to,
it is an error.
That is, we require casts to always preserve the mathematical integer values.
Recall that all inputs are known at compile time in Leo,
so these checks can be performed easily.

Thus integer casts only serve to change types, never values.
When values are to be changed, separate (built-in) functions can be used,
e.g. to mask bits and achieve the same effect as
the value-changing casts discussed below.

This approach Leo's treatment of potentially erroneous situations like integer overflows.
The principle is that developers should explicitly use
operations that may overflow if that is their intention,
rather than having those situation possibly occur unexpectedly.

A value-preserving cast to a type
whose range does not cover the original type's range
implicitly expresses a developer expectation that the value
is actually in the intersection of the two types' ranges,
in the same way that the use of integer addition
implicitly expresses the expectation that the addition does not overflow.

Consider this somewhat abstract example:
```
... // some computations on u32 values, which could not be done with u16
let r: u32 = ...; // this is the final result of the u32 operations above
let s: u16 = r as u16; // but r is expected to fit in u16, so we cast it here
```
With value-preserving casts, the expectation mentioned above
is checked by the Leo compiler during proof generation,
in the same way as with integer overflow.

In the example above,
if instead the variable `s` is meant to contain the low 16 bits of `r`,
e.g. in a cryptographic computation,
then the value-preserving cast should be preceded by
an explicit operation to obtain the low 16 bits, making the intent clear:
```
... // some computations on u32 values, which could not be done with u16
let r: u32 = ...; // this is the final result of the u32 operations above
let r_low16: u32 = r & 0xFFFF; // assuming we have bitwise ops and hex literals
let s: u16 = r_low16 as u16; // no value change here
```

### Compilation to R1CS

It may be more efficient (in terms of number of R1CS constraints)
to compile Leo casts as if they had a value-changing semantics.
If the R1CS constraints represent Leo integers as bits,
the bits of the new value can be determined from the bits of the old value,
with additional zero or sign extension bits when needed
(see the details of the value-changing semantics in the 'Alternatives' section).
There is no need to add checks to the R1CS constraints
because the compiler ensures that the cast values do not actually change given the known inputs,
and therefore the value-changing and value-preserving semantics are equivalent on the known inputs.
The idea is that the R1CS constraints can have a "don't care" behavior on inputs that cause errors in Leo.

## Drawbacks

This proposal does not appear to bring any drawbacks,
other than making the language and compiler inevitably more complex.
But the benefits to support type casts justifies the extra complexity.

## Effect on Ecosystem

This proposal does not appear to have any direct effects on the ecosystem.

## Alternatives

As mentioned above, an alternative semantics for casts is value-changing:
 1. `uN` to `uM` with `N < M`: just change type of value.
 2. `uN` to `uM` with `N > M`: take low `M` bits of value.
 3. `iN` to `iM` with `N < M`: just change type of value.
 4. `iN` to `iM` with `N > M`: take low `M` bits of value.
 5. `uN` to `iM` with `N < M`: zero-extend to `M` bits and re-interpret as signed.
 6. `uN` to `iM` with `N > M`: take low `M` bits and re-interpret as signed.
 7. `uN` to `iN`: re-interpret as signed
 8. `iN` to `uM` with `N < M`: sign-extend to `M` bits and re-interpret as unsigned.
 9. `iN` to `uM` with `N > M`: take low `M` bits and re-interpret as unsigned.
10. `iN` to `uN`: re-interpret as unsigned
Except for the 1st and 3rd cases, the value may change.

This approach is common in other programming languages.
However, it should be noted that other programming languages
typically do not check for overflow in integer operations either
(at least, not for production code).
Presumably, the behavior of type casts in those programming languages
is motivated by efficiency of execution, at least in part.
Since in Leo the input data is available at compile time,
considerations that apply to typical programming languages
do not necessarily apply to Leo.

Back to the somewhat abstract example in the section on value-preserving casts,
note that, with value-changing casts, the expectation that the final result fits in `u16`
would have to be checked with explicit code:
```
... // some computations on u32 values, which could not be done with u16
let r: u32 = ...; // this is the final result of the u32 operations above
if (r > 0xFFFF) {
    ... // error
}
let s: u16 = r as u16; // could change value in principle, but does not here
```
However, it would be easy for a developer to neglect to add the checking code,
and thus have the Leo code silently produce an unexpected result.