* Closes#2426
A coercion from trait `T` to `T'` can be declared with the syntax
```
coercion instance
coeName {A} {{T A}} : T' A := ...
```
Coercions can be seen as instances with special resolution rules.
Coercion resolution rules
-------------------------
* If a non-coercion instance can be applied in a single instance
resolution step, no coercions are considered. No ambiguity results if
there exists some coercion which could be applied, but a non-coercion
instance exists - the non-coercion instances have priority.
* If no non-coercion instance can be applied in a single resolution
step, all minimal coercion paths which lead to an applicable
non-coercion instance are considered. If there is more than one,
ambiguity is reported.
Examples
----------
The following type-checks because:
1. There is no non-coercion instance found for `U String`.
2. There are two minimal coercion paths `U` <- `U1` and `U` <- `U2`, but
only one of them (`U` <- `U2`) ends in an applicable non-coercion
instance (`instU2` for `U2 String`).
```
trait
type U A := mkU {pp : A -> A};
trait
type U1 A := mkU1 {pp : A -> A};
trait
type U2 A := mkU2 {pp : A -> A};
coercion instance
fromU1toU {A} {{U1 A}} : U A :=
mkU@{
pp := U1.pp
};
coercion instance
fromU2toU {A} {{U2 A}} : U A :=
mkU@{
pp := U2.pp
};
instance
instU2 : U2 String := mkU2 id;
main : IO := printStringLn (U.pp "X")
```
The following results in an ambiguity error because:
1. There is no non-coercion instance found for `T Unit`.
2. There are two minimal coercion paths `T` <- `T1` and `T` <- `T2`,
both of which end in applicable non-coercion instances.
```
trait
type T A := mkT { pp : A → A };
trait
type T1 A := mkT1 { pp : A → A };
trait
type T2 A := mkT2 { pp : A → A };
instance
unitT1 : T1 Unit := mkT1 (pp := λ{_ := unit});
instance
unitT2 : T2 Unit := mkT2 (pp := λ{_ := unit});
coercion instance
fromT1toT {A} {{T1 A}} : T A := mkT@{
pp := T1.pp
};
coercion instance
fromT2toT {A} {{T2 A}} : T A := mkT@{
pp := T2.pp
};
main : Unit := T.pp unit;
```
The following type-checks, because there exists a non-coercion instance
for `T2 String`, so the coercion `fromT1toT2` is ignored during instance
resolution.
```
trait
type T1 A := mkT1 {pp : A -> A};
trait
type T2 A := mkT2 {pp : A -> A};
instance
instT1 {A} : T1 A :=
mkT1@{
pp := id
};
coercion instance
fromT1toT2 {A} {{M : T1 A}} : T2 A :=
mkT2@{
pp := T1.pp {{M}}
};
instance
instT2 : T2 String :=
mkT2@{
pp (s : String) : String := s ++str "!"
};
main : String := T2.pp "a";
```
This PR removes the CaseBranchImplicit error from the scoper. This error
is already handled in the arity/typechecker with a good error message:
The arity checker error message for
```
case b of {
| {{true}} := false
```
is
```
Expected an explicit pattern but found an implicit instance pattern: {{true}}
```
* Closes https://github.com/anoma/juvix/issues/2356
* Closes#1646
Implements a basic trait framework. A simple instance search mechanism
is included which fails if there is more than one matching instance at
any step.
Example usage:
```
import Stdlib.Prelude open hiding {Show; mkShow; show};
trait
type Show A :=
mkShow {
show : A → String
};
instance
showStringI : Show String := mkShow (show := id);
instance
showBoolI : Show Bool := mkShow (show := λ{x := if x "true" "false"});
instance
showNatI : Show Nat := mkShow (show := natToString);
showList {A} : {{Show A}} → List A → String
| nil := "nil"
| (h :: t) := Show.show h ++str " :: " ++str showList t;
instance
showListI {A} {{Show A}} : Show (List A) := mkShow (show := showList);
showMaybe {A} {{Show A}} : Maybe A → String
| (just x) := "just (" ++str Show.show x ++str ")"
| nothing := "nothing";
instance
showMaybeI {A} {{Show A}} : Show (Maybe A) := mkShow (show := showMaybe);
main : IO :=
printStringLn (Show.show true) >>
printStringLn (Show.show false) >>
printStringLn (Show.show 3) >>
printStringLn (Show.show [true; false]) >>
printStringLn (Show.show [1; 2; 3]) >>
printStringLn (Show.show [1; 2]) >>
printStringLn (Show.show [true; false]) >>
printStringLn (Show.show [just true; nothing; just false]) >>
printStringLn (Show.show [just [1]; nothing; just [2; 3]]) >>
printStringLn (Show.show "abba") >>
printStringLn (Show.show ["a"; "b"; "c"; "d"]);
```
It is possible to manually provide an instance and to match on implicit
instances:
```
f {A} : {{Show A}} -> A -> String
| {{mkShow s}} x -> s x;
f' {A} : {{Show A}} → A → String
| {{M}} x := Show.show {{M}} x;
```
The trait parameters in instance types are checked to be structurally
decreasing to avoid looping in the instance search. So the following is
rejected:
```
type Box A := box A;
trait
type T A := mkT { pp : A → A };
instance
boxT {A} : {{T (Box A)}} → T (Box A) := mkT (λ{x := x});
```
We check whether each parameter is a strict subterm of some trait
parameter in the target. This ordering is included in the finite
multiset extension of the subterm ordering, hence terminating.
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>
Previously we were:
* discarding the types table
* discarding the name ids state
after processing an expression in the REPL.
For example evaluating:
```
let even : _; odd : _; odd zero := false; odd (suc n) := not (even n); even zero := true; even (suc n) := not (odd n) in even 10
```
would loop in the REPL.
We noticed that the `n` in `suc n` was being given type `Type` instead
of `Nat`. This was because the name id given to n was incorrect, the
REPL started using name ids from 0 again.
We fixed this issue by storing information, including the types table
and name ids state in the Artifacts data structure that is returned when
we run the pipeline for the first time. This information is then used
when we call functions to compile / type check REPL expressions.
---------
Co-authored-by: Paul Cadman <git@paulcadman.dev>
