Implement bidirectional typechecker

This commit replaces the previous typechecker with a bidirectional one,
following the "algorithmic context" design in Complete & Easy
Bidirectional Typechecking by Dunfield & Krishnaswami.

examples/fail/application_with_non_function.uplp

@@ -1,9 +1,8 @@
 -- category = "error"
 --
 -- [metadata]
--- error = "Type.mismatch"
+-- error = "Type.invalid_application"
 --
 -- [metadata.expectation]
--- expected = "?0 -> ?1"
--- got = "Num"
+-- applied_type = "Num"
 let a = 1 in a 5

examples/pass/variable_shadowing.uplp

@@ -0,0 +1,5 @@
+-- category = 'value'
+--
+-- [metadata]
+-- type = 'Unit'
+let f = |x: Num| |x: Unit| (x : Unit) in f 1 ()

src/error.rs

@@ -1,10 +1,10 @@
-use crate::{interner, parser::Token, typ::Type};
+use crate::{interner, parser::Token, typ};
 use lalrpop_util;
 
 #[derive(Debug, PartialEq, Eq)]
 pub enum Error {
     ParseError(ParseError),
-    TypeError(TypeError),
+    TypeError(typ::Error),
     EvaluationError(EvaluationError),
 }
 
@@ -76,20 +76,6 @@ impl From<ParseError> for Error {
     }
 }
 
-// Type Errors
-
-#[derive(Debug, PartialEq, Eq)]
-pub enum TypeError {
-    Mismatch { got: Type, expected: Type },
-    BadApplication,
-}
-
-impl From<TypeError> for Error {
-    fn from(e: TypeError) -> Self {
-        Error::TypeError(e)
-    }
-}
-
 // Evaluation Errors
 
 #[derive(Debug, PartialEq, Eq)]

src/lib.rs

@@ -28,18 +28,15 @@ pub fn parse(input: &str) -> Result<Box<RawExpr>, Error> {
 }
 
 pub fn check_types(input: &str) -> Result<Type, Error> {
-    let mut type_checker = typ::check::er();
-
     let expr = parse_and_scope_check(input)?;
-    let typ = type_checker.infer(&expr)?;
+    let typ = typ::infer(&expr)?;
     Ok(typ)
 }
 
 pub fn evaluate(input: &str) -> Result<values::Val, error::Error> {
     let expr = parse_and_scope_check(input)?;
 
-    let mut type_checker = typ::check::er();
-    let _ = type_checker.infer(&expr)?;
+    let _ = typ::infer(&expr)?;
 
     let compiler = vm::Compiler::new();
     let code = compiler.compile(&expr);

src/parser.lalrpop

@@ -96,9 +96,9 @@ Type: Type = {
 }
 
 PrimType: Type = {
-    "Bool" => Type::Bool,
-    "Num" => Type::Num,
-    "Unit" => Type::Unit,
+    "Bool" => Type::bool(),
+    "Num" => Type::num(),
+    "Unit" => Type::unit(),
     "(" <Type> ")" => <>,
 };