diff --git a/users/glittershark/achilles/Cargo.lock b/users/glittershark/achilles/Cargo.lock
index 0c5779135..a5fa644ec 100644
--- a/users/glittershark/achilles/Cargo.lock
+++ b/users/glittershark/achilles/Cargo.lock
@@ -19,6 +19,7 @@ dependencies = [
  "proptest",
  "test-strategy",
  "thiserror",
+ "void",
 ]
 
 [[package]]
@@ -761,6 +762,12 @@ version = "0.9.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b5a972e5669d67ba988ce3dc826706fb0a8b01471c088cb0b6110b805cc36aed"
 
+[[package]]
+name = "void"
+version = "1.0.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "6a02e4885ed3bc0f2de90ea6dd45ebcbb66dacffe03547fadbb0eeae2770887d"
+
 [[package]]
 name = "wait-timeout"
 version = "0.2.0"
diff --git a/users/glittershark/achilles/Cargo.toml b/users/glittershark/achilles/Cargo.toml
index c0ba4d137..ad18aaac3 100644
--- a/users/glittershark/achilles/Cargo.toml
+++ b/users/glittershark/achilles/Cargo.toml
@@ -19,6 +19,7 @@ pratt = "0.3.0"
 proptest = "1.0.0"
 test-strategy = "0.1.1"
 thiserror = "1.0.24"
+void = "1.0.2"
 
 [dev-dependencies]
 crate-root = "0.1.3"
diff --git a/users/glittershark/achilles/src/ast/hir.rs b/users/glittershark/achilles/src/ast/hir.rs
index 691b9607e..8726af509 100644
--- a/users/glittershark/achilles/src/ast/hir.rs
+++ b/users/glittershark/achilles/src/ast/hir.rs
@@ -1,3 +1,5 @@
+use std::collections::HashMap;
+
 use itertools::Itertools;
 
 use super::{BinaryOperator, Ident, Literal, UnaryOperator};
@@ -55,6 +57,7 @@ pub enum Expr<'a, T> {
     },
 
     Fun {
+        type_args: Vec<Ident<'a>>,
         args: Vec<(Ident<'a>, T)>,
         body: Box<Expr<'a, T>>,
         type_: T,
@@ -62,6 +65,7 @@ pub enum Expr<'a, T> {
 
     Call {
         fun: Box<Expr<'a, T>>,
+        type_args: HashMap<Ident<'a>, T>,
         args: Vec<Expr<'a, T>>,
         type_: T,
     },
@@ -133,16 +137,31 @@ impl<'a, T> Expr<'a, T> {
                 else_: Box::new(else_.traverse_type(f.clone())?),
                 type_: f(type_)?,
             }),
-            Expr::Fun { args, body, type_ } => Ok(Expr::Fun {
+            Expr::Fun {
+                args,
+                type_args,
+                body,
+                type_,
+            } => Ok(Expr::Fun {
                 args: args
                     .into_iter()
                     .map(|(id, t)| Ok((id, f.clone()(t)?)))
                     .collect::<Result<Vec<_>, E>>()?,
+                type_args,
                 body: Box::new(body.traverse_type(f.clone())?),
                 type_: f(type_)?,
             }),
-            Expr::Call { fun, args, type_ } => Ok(Expr::Call {
+            Expr::Call {
+                fun,
+                type_args,
+                args,
+                type_,
+            } => Ok(Expr::Call {
                 fun: Box::new(fun.traverse_type(f.clone())?),
+                type_args: type_args
+                    .into_iter()
+                    .map(|(id, ty)| Ok((id, f.clone()(ty)?)))
+                    .collect::<Result<HashMap<_, _>, E>>()?,
                 args: args
                     .into_iter()
                     .map(|e| e.traverse_type(f.clone()))
@@ -180,7 +199,7 @@ impl<'a, T> Expr<'a, T> {
                 body,
                 type_,
             } => Expr::Let {
-                bindings: bindings.into_iter().map(|b| b.to_owned()).collect(),
+                bindings: bindings.iter().map(|b| b.to_owned()).collect(),
                 body: Box::new((**body).to_owned()),
                 type_: type_.clone(),
             },
@@ -195,26 +214,43 @@ impl<'a, T> Expr<'a, T> {
                 else_: Box::new((**else_).to_owned()),
                 type_: type_.clone(),
             },
-            Expr::Fun { args, body, type_ } => Expr::Fun {
+            Expr::Fun {
+                args,
+                type_args,
+                body,
+                type_,
+            } => Expr::Fun {
                 args: args
-                    .into_iter()
+                    .iter()
                     .map(|(id, t)| (id.to_owned(), t.clone()))
                     .collect(),
+                type_args: type_args.iter().map(|arg| arg.to_owned()).collect(),
                 body: Box::new((**body).to_owned()),
                 type_: type_.clone(),
             },
-            Expr::Call { fun, args, type_ } => Expr::Call {
+            Expr::Call {
+                fun,
+                type_args,
+                args,
+                type_,
+            } => Expr::Call {
                 fun: Box::new((**fun).to_owned()),
-                args: args.into_iter().map(|e| e.to_owned()).collect(),
+                type_args: type_args
+                    .iter()
+                    .map(|(id, t)| (id.to_owned(), t.clone()))
+                    .collect(),
+                args: args.iter().map(|e| e.to_owned()).collect(),
                 type_: type_.clone(),
             },
         }
     }
 }
 
+#[derive(Debug, Clone)]
 pub enum Decl<'a, T> {
     Fun {
         name: Ident<'a>,
+        type_args: Vec<Ident<'a>>,
         args: Vec<(Ident<'a>, T)>,
         body: Box<Expr<'a, T>>,
         type_: T,
@@ -235,6 +271,13 @@ impl<'a, T> Decl<'a, T> {
         }
     }
 
+    pub fn set_name(&mut self, new_name: Ident<'a>) {
+        match self {
+            Decl::Fun { name, .. } => *name = new_name,
+            Decl::Extern { name, .. } => *name = new_name,
+        }
+    }
+
     pub fn type_(&self) -> Option<&T> {
         match self {
             Decl::Fun { type_, .. } => Some(type_),
@@ -249,11 +292,13 @@ impl<'a, T> Decl<'a, T> {
         match self {
             Decl::Fun {
                 name,
+                type_args,
                 args,
                 body,
                 type_,
             } => Ok(Decl::Fun {
                 name,
+                type_args,
                 args: args
                     .into_iter()
                     .map(|(id, t)| Ok((id, f(t)?)))
diff --git a/users/glittershark/achilles/src/ast/mod.rs b/users/glittershark/achilles/src/ast/mod.rs
index 22d16c936..53f222a6a 100644
--- a/users/glittershark/achilles/src/ast/mod.rs
+++ b/users/glittershark/achilles/src/ast/mod.rs
@@ -356,6 +356,26 @@ impl<'a> Type<'a> {
         let mut substs = HashMap::new();
         do_alpha_equiv(&mut substs, self, other)
     }
+
+    pub fn traverse_type_vars<'b, F>(self, mut f: F) -> Type<'b>
+    where
+        F: FnMut(Ident<'a>) -> Type<'b> + Clone,
+    {
+        match self {
+            Type::Var(tv) => f(tv),
+            Type::Function(FunctionType { args, ret }) => Type::Function(FunctionType {
+                args: args
+                    .into_iter()
+                    .map(|t| t.traverse_type_vars(f.clone()))
+                    .collect(),
+                ret: Box::new(ret.traverse_type_vars(f)),
+            }),
+            Type::Int => Type::Int,
+            Type::Float => Type::Float,
+            Type::Bool => Type::Bool,
+            Type::CString => Type::CString,
+        }
+    }
 }
 
 impl<'a> Display for Type<'a> {
diff --git a/users/glittershark/achilles/src/compiler.rs b/users/glittershark/achilles/src/compiler.rs
index f925b267d..7001e5a9a 100644
--- a/users/glittershark/achilles/src/compiler.rs
+++ b/users/glittershark/achilles/src/compiler.rs
@@ -8,6 +8,7 @@ use test_strategy::Arbitrary;
 
 use crate::codegen::{self, Codegen};
 use crate::common::Result;
+use crate::passes::hir::monomorphize;
 use crate::{parser, tc};
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Hash, Arbitrary)]
@@ -55,7 +56,8 @@ pub struct CompilerOptions {
 pub fn compile_file(input: &Path, output: &Path, options: &CompilerOptions) -> Result<()> {
     let src = fs::read_to_string(input)?;
     let (_, decls) = parser::toplevel(&src)?; // TODO: statements
-    let decls = tc::typecheck_toplevel(decls)?;
+    let mut decls = tc::typecheck_toplevel(decls)?;
+    monomorphize::run_toplevel(&mut decls);
 
     let context = codegen::Context::create();
     let mut codegen = Codegen::new(
diff --git a/users/glittershark/achilles/src/interpreter/mod.rs b/users/glittershark/achilles/src/interpreter/mod.rs
index 3bfeeb52e..bcd474b3a 100644
--- a/users/glittershark/achilles/src/interpreter/mod.rs
+++ b/users/glittershark/achilles/src/interpreter/mod.rs
@@ -96,7 +96,12 @@ impl<'a> Interpreter<'a> {
                 }
                 Ok(Value::from(*interpreter.eval(body)?.as_type::<i64>()?))
             }
-            Expr::Fun { args, body, type_ } => {
+            Expr::Fun {
+                type_args: _,
+                args,
+                body,
+                type_,
+            } => {
                 let type_ = match type_ {
                     Type::Function(ft) => ft.clone(),
                     _ => unreachable!("Function expression without function type"),
diff --git a/users/glittershark/achilles/src/main.rs b/users/glittershark/achilles/src/main.rs
index d5b00d6b6..5ae1b59b3 100644
--- a/users/glittershark/achilles/src/main.rs
+++ b/users/glittershark/achilles/src/main.rs
@@ -6,6 +6,7 @@ pub(crate) mod commands;
 pub(crate) mod common;
 pub mod compiler;
 pub mod interpreter;
+pub(crate) mod passes;
 #[macro_use]
 pub mod parser;
 pub mod tc;
diff --git a/users/glittershark/achilles/src/passes/hir/mod.rs b/users/glittershark/achilles/src/passes/hir/mod.rs
new file mode 100644
index 000000000..fb2f64e08
--- /dev/null
+++ b/users/glittershark/achilles/src/passes/hir/mod.rs
@@ -0,0 +1,179 @@
+use std::collections::HashMap;
+
+use crate::ast::hir::{Binding, Decl, Expr};
+use crate::ast::{BinaryOperator, Ident, Literal, UnaryOperator};
+
+pub(crate) mod monomorphize;
+
+pub(crate) trait Visitor<'a, 'ast, T: 'ast>: Sized + 'a {
+    type Error;
+
+    fn visit_type(&mut self, _type: &mut T) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_ident(&mut self, _ident: &mut Ident<'ast>) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_literal(&mut self, _literal: &mut Literal<'ast>) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_unary_operator(&mut self, _op: &mut UnaryOperator) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_binary_operator(&mut self, _op: &mut BinaryOperator) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_binding(&mut self, binding: &mut Binding<'ast, T>) -> Result<(), Self::Error> {
+        self.visit_ident(&mut binding.ident)?;
+        self.visit_type(&mut binding.type_)?;
+        self.visit_expr(&mut binding.body)?;
+        Ok(())
+    }
+
+    fn post_visit_call(
+        &mut self,
+        _fun: &mut Expr<'ast, T>,
+        _type_args: &mut HashMap<Ident<'ast>, T>,
+        _args: &mut Vec<Expr<'ast, T>>,
+    ) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn pre_visit_call(
+        &mut self,
+        _fun: &mut Expr<'ast, T>,
+        _type_args: &mut HashMap<Ident<'ast>, T>,
+        _args: &mut Vec<Expr<'ast, T>>,
+    ) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_expr(&mut self, expr: &mut Expr<'ast, T>) -> Result<(), Self::Error> {
+        match expr {
+            Expr::Ident(id, t) => {
+                self.visit_ident(id)?;
+                self.visit_type(t)?;
+            }
+            Expr::Literal(lit, t) => {
+                self.visit_literal(lit)?;
+                self.visit_type(t)?;
+            }
+            Expr::UnaryOp { op, rhs, type_ } => {
+                self.visit_unary_operator(op)?;
+                self.visit_expr(rhs)?;
+                self.visit_type(type_)?;
+            }
+            Expr::BinaryOp {
+                lhs,
+                op,
+                rhs,
+                type_,
+            } => {
+                self.visit_expr(lhs)?;
+                self.visit_binary_operator(op)?;
+                self.visit_expr(rhs)?;
+                self.visit_type(type_)?;
+            }
+            Expr::Let {
+                bindings,
+                body,
+                type_,
+            } => {
+                for binding in bindings.iter_mut() {
+                    self.visit_binding(binding)?;
+                }
+                self.visit_expr(body)?;
+                self.visit_type(type_)?;
+            }
+            Expr::If {
+                condition,
+                then,
+                else_,
+                type_,
+            } => {
+                self.visit_expr(condition)?;
+                self.visit_expr(then)?;
+                self.visit_expr(else_)?;
+                self.visit_type(type_)?;
+            }
+            Expr::Fun {
+                args,
+                body,
+                type_args,
+                type_,
+            } => {
+                for (ident, t) in args {
+                    self.visit_ident(ident)?;
+                    self.visit_type(t)?;
+                }
+                for ta in type_args {
+                    self.visit_ident(ta)?;
+                }
+                self.visit_expr(body)?;
+                self.visit_type(type_)?;
+            }
+            Expr::Call {
+                fun,
+                args,
+                type_args,
+                type_,
+            } => {
+                self.pre_visit_call(fun, type_args, args)?;
+                self.visit_expr(fun)?;
+                for arg in args.iter_mut() {
+                    self.visit_expr(arg)?;
+                }
+                self.visit_type(type_)?;
+                self.post_visit_call(fun, type_args, args)?;
+            }
+        }
+
+        Ok(())
+    }
+
+    fn post_visit_decl(&mut self, decl: &'a Decl<'ast, T>) -> Result<(), Self::Error> {
+        Ok(())
+    }
+
+    fn visit_decl(&mut self, decl: &'a mut Decl<'ast, T>) -> Result<(), Self::Error> {
+        match decl {
+            Decl::Fun {
+                name,
+                type_args,
+                args,
+                body,
+                type_,
+            } => {
+                self.visit_ident(name)?;
+                for type_arg in type_args {
+                    self.visit_ident(type_arg)?;
+                }
+                for (arg, t) in args {
+                    self.visit_ident(arg)?;
+                    self.visit_type(t)?;
+                }
+                self.visit_expr(body)?;
+                self.visit_type(type_)?;
+            }
+            Decl::Extern {
+                name,
+                arg_types,
+                ret_type,
+            } => {
+                self.visit_ident(name)?;
+                for arg_t in arg_types {
+                    self.visit_type(arg_t)?;
+                }
+                self.visit_type(ret_type)?;
+            }
+        }
+
+        self.post_visit_decl(decl)?;
+        Ok(())
+    }
+}
diff --git a/users/glittershark/achilles/src/passes/hir/monomorphize.rs b/users/glittershark/achilles/src/passes/hir/monomorphize.rs
new file mode 100644
index 000000000..251a988f4
--- /dev/null
+++ b/users/glittershark/achilles/src/passes/hir/monomorphize.rs
@@ -0,0 +1,139 @@
+use std::cell::RefCell;
+use std::collections::{HashMap, HashSet};
+use std::convert::TryInto;
+use std::mem;
+
+use void::{ResultVoidExt, Void};
+
+use crate::ast::hir::{Decl, Expr};
+use crate::ast::{self, Ident};
+
+use super::Visitor;
+
+#[derive(Default)]
+pub(crate) struct Monomorphize<'a, 'ast> {
+    decls: HashMap<&'a Ident<'ast>, &'a Decl<'ast, ast::Type<'ast>>>,
+    extra_decls: Vec<Decl<'ast, ast::Type<'ast>>>,
+    remove_decls: HashSet<Ident<'ast>>,
+}
+
+impl<'a, 'ast> Monomorphize<'a, 'ast> {
+    pub(crate) fn new() -> Self {
+        Default::default()
+    }
+}
+
+impl<'a, 'ast> Visitor<'a, 'ast, ast::Type<'ast>> for Monomorphize<'a, 'ast> {
+    type Error = Void;
+
+    fn post_visit_call(
+        &mut self,
+        fun: &mut Expr<'ast, ast::Type<'ast>>,
+        type_args: &mut HashMap<Ident<'ast>, ast::Type<'ast>>,
+        args: &mut Vec<Expr<'ast, ast::Type<'ast>>>,
+    ) -> Result<(), Self::Error> {
+        let new_fun = match fun {
+            Expr::Ident(id, _) => {
+                let decl: Decl<_> = (**self.decls.get(id).unwrap()).clone();
+                let name = RefCell::new(id.to_string());
+                let type_args = mem::take(type_args);
+                let mut monomorphized = decl
+                    .traverse_type(|ty| -> Result<_, Void> {
+                        Ok(ty.clone().traverse_type_vars(|v| {
+                            let concrete = type_args.get(&v).unwrap();
+                            name.borrow_mut().push_str(&concrete.to_string());
+                            concrete.clone()
+                        }))
+                    })
+                    .void_unwrap();
+                let name: Ident = name.into_inner().try_into().unwrap();
+                if name != *id {
+                    self.remove_decls.insert(id.clone());
+                    monomorphized.set_name(name.clone());
+                    let type_ = monomorphized.type_().unwrap().clone();
+                    self.extra_decls.push(monomorphized);
+                    Some(Expr::Ident(name, type_))
+                } else {
+                    None
+                }
+            }
+            _ => todo!(),
+        };
+        if let Some(new_fun) = new_fun {
+            *fun = new_fun;
+        }
+        Ok(())
+    }
+
+    fn post_visit_decl(
+        &mut self,
+        decl: &'a Decl<'ast, ast::Type<'ast>>,
+    ) -> Result<(), Self::Error> {
+        self.decls.insert(decl.name(), decl);
+        Ok(())
+    }
+}
+
+pub(crate) fn run_toplevel<'a>(toplevel: &mut Vec<Decl<'a, ast::Type<'a>>>) {
+    let mut pass = Monomorphize::new();
+    for decl in toplevel.iter_mut() {
+        pass.visit_decl(decl).void_unwrap();
+    }
+    let remove_decls = mem::take(&mut pass.remove_decls);
+    let mut extra_decls = mem::take(&mut pass.extra_decls);
+    toplevel.retain(|decl| !remove_decls.contains(decl.name()));
+    extra_decls.append(toplevel);
+    *toplevel = extra_decls;
+}
+
+#[cfg(test)]
+mod tests {
+    use std::convert::TryFrom;
+
+    use super::*;
+    use crate::parser::toplevel;
+    use crate::tc::typecheck_toplevel;
+
+    #[test]
+    fn call_id_decl() {
+        let (_, program) = toplevel(
+            "ty id : fn a -> a
+             fn id x = x
+
+             ty main : fn -> int
+             fn main = id 0",
+        )
+        .unwrap();
+        let mut program = typecheck_toplevel(program).unwrap();
+        run_toplevel(&mut program);
+
+        let find_decl = |ident: &str| {
+            program.iter().find(|decl| {
+                matches!(decl, Decl::Fun {name, ..} if name == &Ident::try_from(ident).unwrap())
+            }).unwrap()
+        };
+
+        let main = find_decl("main");
+        let body = match main {
+            Decl::Fun { body, .. } => body,
+            _ => unreachable!(),
+        };
+
+        let expected_type = ast::Type::Function(ast::FunctionType {
+            args: vec![ast::Type::Int],
+            ret: Box::new(ast::Type::Int),
+        });
+
+        match &**body {
+            Expr::Call { fun, .. } => {
+                let fun = match &**fun {
+                    Expr::Ident(fun, _) => fun,
+                    _ => unreachable!(),
+                };
+                let called_decl = find_decl(fun.into());
+                assert_eq!(called_decl.type_().unwrap(), &expected_type);
+            }
+            _ => unreachable!(),
+        }
+    }
+}
diff --git a/users/glittershark/achilles/src/passes/mod.rs b/users/glittershark/achilles/src/passes/mod.rs
new file mode 100644
index 000000000..306869bef
--- /dev/null
+++ b/users/glittershark/achilles/src/passes/mod.rs
@@ -0,0 +1 @@
+pub(crate) mod hir;
diff --git a/users/glittershark/achilles/src/tc/mod.rs b/users/glittershark/achilles/src/tc/mod.rs
index f3cb40a8b..137561978 100644
--- a/users/glittershark/achilles/src/tc/mod.rs
+++ b/users/glittershark/achilles/src/tc/mod.rs
@@ -266,6 +266,7 @@ impl<'ast> Typechecker<'ast> {
                         args: args.iter().map(|(_, ty)| ty.clone()).collect(),
                         ret: Box::new(body.type_().clone()),
                     },
+                    type_args: vec![], // TODO fill in once we do let generalization
                     args,
                     body: Box::new(body),
                 })
@@ -289,9 +290,10 @@ impl<'ast> Typechecker<'ast> {
                         Ok(arg)
                     })
                     .try_collect()?;
-                self.commit_instantiations();
+                let type_args = self.commit_instantiations();
                 Ok(hir::Expr::Call {
                     fun: Box::new(fun),
+                    type_args,
                     args,
                     type_: ret_ty,
                 })
@@ -325,8 +327,14 @@ impl<'ast> Typechecker<'ast> {
                 self.env.set(name.clone(), type_);
                 self.env.pop();
                 match body {
-                    hir::Expr::Fun { args, body, type_ } => Ok(Some(hir::Decl::Fun {
+                    hir::Expr::Fun {
+                        type_args,
+                        args,
+                        body,
+                        type_,
+                    } => Ok(Some(hir::Decl::Fun {
                         name,
+                        type_args,
                         args,
                         body,
                         type_,
@@ -538,17 +546,21 @@ impl<'ast> Typechecker<'ast> {
             })
     }
 
-    fn commit_instantiations(&mut self) {
+    fn commit_instantiations(&mut self) -> HashMap<Ident<'ast>, Type> {
+        let mut res = HashMap::new();
         let mut ctx = mem::take(&mut self.ctx);
         for (_, v) in ctx.iter_mut() {
             if let Type::Univ(tv) = v {
-                if let Some(concrete) = self.instantiations.resolve(&self.name_univ(*tv)) {
+                let tv_name = self.name_univ(*tv);
+                if let Some(concrete) = self.instantiations.resolve(&tv_name) {
+                    res.insert(tv_name, concrete.clone());
                     *v = concrete.clone();
                 }
             }
         }
         self.ctx = ctx;
         self.instantiations.pop();
+        res
     }
 
     fn types_match(&self, type_: &Type, ast_type: &ast::Type<'ast>) -> bool {
diff --git a/users/glittershark/achilles/tests/compile.rs b/users/glittershark/achilles/tests/compile.rs
index 1b4da463a..51ffb239b 100644
--- a/users/glittershark/achilles/tests/compile.rs
+++ b/users/glittershark/achilles/tests/compile.rs
@@ -14,12 +14,11 @@ const FIXTURES: &[Fixture] = &[
         exit_code: 5,
         expected_output: "",
     },
-    // TODO(grfn): needs monomorphization
-    // Fixture {
-    //     name: "functions",
-    //     exit_code: 9,
-    //     expected_output: "",
-    // },
+    Fixture {
+        name: "functions",
+        exit_code: 9,
+        expected_output: "",
+    },
     Fixture {
         name: "externs",
         exit_code: 0,