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This PR adds a builtin integer type to the surface language that is
compiled to the backend integer type.
## Inductive definition
The `Int` type is defined in the standard library as:
```
builtin int
type Int :=
| --- ofNat n represents the integer n
ofNat : Nat -> Int
| --- negSuc n represents the integer -(n + 1)
negSuc : Nat -> Int;
```
## New builtin functions defined in the standard library
```
intToString : Int -> String;
+ : Int -> Int -> Int;
neg : Int -> Int;
* : Int -> Int -> Int;
- : Int -> Int -> Int;
div : Int -> Int -> Int;
mod : Int -> Int -> Int;
== : Int -> Int -> Bool;
<= : Int -> Int -> Bool;
< : Int -> Int -> Bool;
```
Additional builtins required in the definition of the other builtins:
```
negNat : Nat -> Int;
intSubNat : Nat -> Nat -> Int;
nonNeg : Int -> Bool;
```
## REPL types of literals
In the REPL, non-negative integer literals have the inferred type `Nat`,
negative integer literals have the inferred type `Int`.
```
Stdlib.Prelude> :t 1
Nat
Stdlib.Prelude> :t -1
Int
:t let x : Int := 1 in x
Int
```
## The standard library Prelude
The definitions of `*`, `+`, `div` and `mod` are not exported from the
standard library prelude as these would conflict with the definitions
from `Stdlib.Data.Nat`.
Stdlib.Prelude
```
open import Stdlib.Data.Int hiding {+;*;div;mod} public;
```
* Closes https://github.com/anoma/juvix/issues/1679
* Closes https://github.com/anoma/juvix/issues/1984
---------
Co-authored-by: Lukasz Czajka <lukasz@heliax.dev>
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| .. | ||
| 265 | ||
| 272 | ||
| BuiltinsMultiImport | ||
| BuiltinsMultiOpenImport | ||
| Dependencies | ||
| Imports | ||
| ImportShadow | ||
| Internal | ||
| issue1333 | ||
| issue1466 | ||
| issue1693 | ||
| issue1731 | ||
| issue1879 | ||
| QualifiedConstructor | ||
| QualifiedSymbol | ||
| QualifiedSymbol2 | ||
| Reachability | ||
| StdlibImport | ||
| StdlibList | ||
| Termination | ||
| Ape.juvix | ||
| Axiom.juvix | ||
| Builtins.juvix | ||
| BuiltinsBool.juvix | ||
| Format.juvix | ||
| Inductive.juvix | ||
| InductivePipes.juvix | ||
| Judoc.juvix | ||
| juvix.yaml | ||
| LetShadow.juvix | ||
| Literals.juvix | ||
| MultiParams.juvix | ||
| MutualLet.juvix | ||
| Operators.juvix | ||
| Parsing.juvix | ||
| Polymorphism.juvix | ||
| PolymorphismHoles.juvix | ||
| ShadowPublicOpen.juvix | ||
| SignatureWithBody.juvix | ||
| Symbols.juvix | ||
| TypeAlias.juvix | ||