diff --git a/axc/src/main.rs b/axc/src/main.rs
index 0d3a75b..28b1e97 100644
--- a/axc/src/main.rs
+++ b/axc/src/main.rs
@@ -5,7 +5,7 @@ use std::{error::Error, fmt::Display, fs::File, io::Write, process::exit, str::F
 use axc::{
     ast2ir::ast2ir,
     backends,
-    parser::{parser, ParserError},
+    parser::{parser, ParserError, ParserMeta},
     typeck::typeck,
 };
 use clap::Parser;
@@ -254,7 +254,8 @@ fn main() {
         let args = Args::parse();
 
         let source = std::fs::read_to_string(&args.source_file)?;
-        let ast = chumsky::Parser::parse(&parser(), source).map_err(ParserError)?;
+        let meta = ParserMeta::default();
+        let ast = chumsky::Parser::parse(&parser(&meta), source).map_err(ParserError)?;
         typeck(&ast)?;
 
         let ir = ast2ir(ast);
diff --git a/axc/src/parser.rs b/axc/src/parser.rs
index b430a8d..cbbf331 100644
--- a/axc/src/parser.rs
+++ b/axc/src/parser.rs
@@ -3,7 +3,7 @@
 use std::{error::Error, fmt::Display};
 
 use chumsky::{
-    prelude::{choice, empty, end, just, todo, Simple},
+    prelude::{choice, end, just, todo, Simple},
     text::{ident, keyword},
     Parser,
 };
@@ -25,44 +25,228 @@ impl Display for ParserError {
 
 impl Error for ParserError {}
 
+/// Information required to be able to parse AlexScript code, beyond the code itself.
+pub struct ParserMeta {
+    // This struct is just a total hacky workaround for the fact that chumsky isn't capable of
+    // parsing a context-sensitive grammar. I don't intend on ever fixing this: the stage-1 compiler
+    // will have a hardcoded list of operators, and the stage-2 compiler will have fully
+    // overloadable custom operators.
+    /// The list of registered binary operators.
+    operators: Vec<OperatorDef>,
+}
+
+/// Definition of an operator.
+struct OperatorDef {
+    /// The string of symbols that goes between two terms to invoke this operator.
+    name: String,
+
+    /// The precedence level; if X has lower precedence than Y, then a X b Y c is a X (b Y c);
+    /// otherwise, it is (a X b) Y c.
+    precedence: u32,
+
+    /// The associativity; if this is Left, then a X b X c is (a X b) X c; for Right, it is a X (b X
+    /// c); for None, it is a syntax error.
+    assoc: Option<Associativity>,
+}
+
+/// The possible associativity directions of an operator.
+enum Associativity {
+    Left,
+    Right,
+}
+
+impl Default for ParserMeta {
+    fn default() -> Self {
+        use Associativity::*;
+        Self {
+            // These are mostly stolen from Haskell.
+            operators: vec![
+                OperatorDef {
+                    // Exponentiation.
+                    name: "^".to_string(),
+                    precedence: 8,
+                    assoc: Some(Right),
+                },
+                OperatorDef {
+                    name: "*".to_string(),
+                    precedence: 7,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Division, which always returns an exact result and does not round to an
+                    // integer (unlike C etc.).
+                    name: "/".to_string(),
+                    precedence: 7,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Modulo, defined as Euclidean remainder.
+                    name: "%".to_string(),
+                    precedence: 7,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    name: "+".to_string(),
+                    precedence: 6,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    name: "-".to_string(),
+                    precedence: 6,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Append to head of list. This might get removed since it's inefficient,
+                    // depending.
+                    name: "::".to_string(),
+                    precedence: 5,
+                    assoc: Some(Right),
+                },
+                OperatorDef {
+                    // Append lists.
+                    name: "++".to_string(),
+                    precedence: 5,
+                    assoc: Some(Right),
+                },
+                OperatorDef {
+                    name: "==".to_string(),
+                    precedence: 4,
+                    assoc: None,
+                },
+                OperatorDef {
+                    name: "!=".to_string(),
+                    precedence: 4,
+                    assoc: None,
+                },
+                OperatorDef {
+                    name: "<".to_string(),
+                    precedence: 4,
+                    assoc: None,
+                },
+                OperatorDef {
+                    name: "<=".to_string(),
+                    precedence: 4,
+                    assoc: None,
+                },
+                OperatorDef {
+                    name: ">".to_string(),
+                    precedence: 4,
+                    assoc: None,
+                },
+                OperatorDef {
+                    name: ">=".to_string(),
+                    precedence: 4,
+                    assoc: None,
+                },
+                OperatorDef {
+                    // Functor map.
+                    name: "<$>".to_string(),
+                    precedence: 4,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Functor map to constant.
+                    name: "<$".to_string(),
+                    precedence: 4,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Flipped `<$`.
+                    name: "$>".to_string(),
+                    precedence: 4,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Sequential application of applicative actions.
+                    name: "<*>".to_string(),
+                    precedence: 4,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Sequence applicative actions, discarding the left value.
+                    name: "*>".to_string(),
+                    precedence: 4,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Sequence applicative actions, discarding the right value.
+                    name: "<*".to_string(),
+                    precedence: 4,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Binary and boolean `and`.
+                    name: "&".to_string(),
+                    precedence: 3,
+                    assoc: Some(Right),
+                },
+                OperatorDef {
+                    // Binary and boolean `or`.
+                    name: "|".to_string(),
+                    precedence: 2,
+                    assoc: Some(Right),
+                },
+                OperatorDef {
+                    // Monad sequence.
+                    name: ">>".to_string(),
+                    precedence: 1,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Monad bind.
+                    name: ">>=".to_string(),
+                    precedence: 1,
+                    assoc: Some(Left),
+                },
+                OperatorDef {
+                    // Function application.
+                    name: "$".to_string(),
+                    precedence: 1,
+                    assoc: Some(Left),
+                },
+            ],
+        }
+    }
+}
+
 /// Parser for AlexScript code.
-pub fn parser() -> impl Parser<char, SyntaxTree, Error = Simple<char>> {
-    parse_statement()
+pub fn parser(m: &ParserMeta) -> impl Parser<char, SyntaxTree, Error = Simple<char>> {
+    parse_statement(m)
         .repeated()
         .map(SyntaxTree)
         .then_ignore(end())
 }
 
-fn parse_statement() -> impl Parser<char, Statement, Error = Simple<char>> {
+fn parse_statement(m: &ParserMeta) -> impl Parser<char, Statement, Error = Simple<char>> {
     choice((
-        parse_type_def(),
-        parse_instance_def(),
-        parse_class_def(),
-        parse_class_decl_stmt(),
+        parse_type_def(m),
+        parse_instance_def(m),
+        parse_class_def(m),
+        parse_class_decl_stmt(m),
     ))
 }
 
-fn parse_type_def() -> impl Parser<char, Statement, Error = Simple<char>> {
+fn parse_type_def(m: &ParserMeta) -> impl Parser<char, Statement, Error = Simple<char>> {
     keyword("data")
-        .ignore_then(parse_type())
+        .ignore_then(parse_type(m))
         .then_ignore(just('='))
-        .then(parse_constructor().repeated())
+        .then(parse_constructor(m).repeated())
         .then_ignore(just(';'))
         .map(|(typ, constructors)| Statement::TypeDefinition { typ, constructors })
 }
 
-fn parse_constructor() -> impl Parser<char, TypeConstructor, Error = Simple<char>> {
+fn parse_constructor(m: &ParserMeta) -> impl Parser<char, TypeConstructor, Error = Simple<char>> {
     ident()
-        .then(parse_type().repeated())
+        .then(parse_type(m).repeated())
         .map(|(name, args)| TypeConstructor { name, args })
 }
 
-fn parse_instance_def() -> impl Parser<char, Statement, Error = Simple<char>> {
+fn parse_instance_def(m: &ParserMeta) -> impl Parser<char, Statement, Error = Simple<char>> {
     keyword("instance")
         .ignore_then(ident())
-        .then(parse_type())
+        .then(parse_type(m))
         .then(
-            parse_class_member()
+            parse_class_member(m)
                 .repeated()
                 .delimited_by(just('{'), just('}')),
         )
@@ -73,22 +257,19 @@ fn parse_instance_def() -> impl Parser<char, Statement, Error = Simple<char>> {
         })
 }
 
-fn parse_class_decl_stmt() -> impl Parser<char, Statement, Error = Simple<char>> {
-    parse_class_member().map(Statement::ClassMember)
+fn parse_class_decl_stmt(m: &ParserMeta) -> impl Parser<char, Statement, Error = Simple<char>> {
+    parse_class_member(m).map(Statement::ClassMember)
 }
 
-fn parse_class_member() -> impl Parser<char, ClassMember, Error = Simple<char>> {
-    choice((parse_func_decl(), parse_type_alias()))
+fn parse_class_member(m: &ParserMeta) -> impl Parser<char, ClassMember, Error = Simple<char>> {
+    choice((parse_func_decl(m), parse_type_alias(m)))
 }
 
-fn parse_func_decl() -> impl Parser<char, ClassMember, Error = Simple<char>> {
+fn parse_func_decl(m: &ParserMeta) -> impl Parser<char, ClassMember, Error = Simple<char>> {
     keyword("def")
         .ignore_then(ident())
-        .then(parse_pattern().repeated())
-        .then(choice((
-            just('=').ignore_then(parse_expression()).map(Some),
-            empty().to(None),
-        )))
+        .then(parse_pattern(m).repeated())
+        .then(just('=').ignore_then(parse_expression(m)).or_not())
         .then_ignore(just(';'))
         .map(|((name, arguments), definition)| ClassMember::Function {
             name,
@@ -97,37 +278,34 @@ fn parse_func_decl() -> impl Parser<char, ClassMember, Error = Simple<char>> {
         })
 }
 
-fn parse_type_alias() -> impl Parser<char, ClassMember, Error = Simple<char>> {
+fn parse_type_alias(m: &ParserMeta) -> impl Parser<char, ClassMember, Error = Simple<char>> {
     keyword("type")
-        .ignore_then(parse_type())
-        .then(choice((
-            just('=').ignore_then(parse_type()).map(Some),
-            empty().to(None),
-        )))
+        .ignore_then(parse_type(m))
+        .then(just('=').ignore_then(parse_type(m)).or_not())
         .then_ignore(just(';'))
         .map(|(left, right)| ClassMember::TypeAlias { left, right })
 }
 
-fn parse_class_def() -> impl Parser<char, Statement, Error = Simple<char>> {
+fn parse_class_def(m: &ParserMeta) -> impl Parser<char, Statement, Error = Simple<char>> {
     keyword("class")
         .ignore_then(ident())
         .then(ident())
         .then(
-            parse_class_member()
+            parse_class_member(m)
                 .repeated()
                 .delimited_by(just('{'), just('}')),
         )
         .map(|((name, var), decls)| Statement::ClassDefinition { name, var, decls })
 }
 
-fn parse_expression() -> impl Parser<char, Expr, Error = Simple<char>> {
+fn parse_expression(m: &ParserMeta) -> impl Parser<char, Expr, Error = Simple<char>> {
     todo()
 }
 
-fn parse_type() -> impl Parser<char, Type, Error = Simple<char>> {
+fn parse_type(m: &ParserMeta) -> impl Parser<char, Type, Error = Simple<char>> {
     todo()
 }
 
-fn parse_pattern() -> impl Parser<char, Pattern, Error = Simple<char>> {
+fn parse_pattern(m: &ParserMeta) -> impl Parser<char, Pattern, Error = Simple<char>> {
     todo()
 }