diff --git a/crates/ra_hir/src/code_model_api.rs b/crates/ra_hir/src/code_model_api.rs
index 191104890a..e4008058cc 100644
--- a/crates/ra_hir/src/code_model_api.rs
+++ b/crates/ra_hir/src/code_model_api.rs
@@ -424,6 +424,10 @@ impl Function {
         self.id.module(db)
     }
 
+    pub fn name(&self, db: &impl HirDatabase) -> Name {
+        self.signature(db).name.clone()
+    }
+
     pub fn body_syntax_mapping(&self, db: &impl HirDatabase) -> Arc<BodySyntaxMapping> {
         db.body_syntax_mapping(*self)
     }
diff --git a/crates/ra_hir/src/ty.rs b/crates/ra_hir/src/ty.rs
index 31ea457062..37715a903a 100644
--- a/crates/ra_hir/src/ty.rs
+++ b/crates/ra_hir/src/ty.rs
@@ -20,6 +20,7 @@ mod tests;
 pub(crate) mod method_resolution;
 
 use std::borrow::Cow;
+use std::iter::repeat;
 use std::ops::Index;
 use std::sync::Arc;
 use std::{fmt, mem};
@@ -185,7 +186,7 @@ pub enum Ty {
 
     /// Structures, enumerations and unions.
     Adt {
-        /// The DefId of the struct/enum.
+        /// The definition of the struct/enum.
         def_id: AdtDef,
         /// The name, for displaying.
         name: Name,
@@ -209,6 +210,27 @@ pub enum Ty {
     /// `&'a mut T` or `&'a T`.
     Ref(Arc<Ty>, Mutability),
 
+    /// The anonymous type of a function declaration/definition. Each
+    /// function has a unique type, which is output (for a function
+    /// named `foo` returning an `i32`) as `fn() -> i32 {foo}`.
+    ///
+    /// For example the type of `bar` here:
+    ///
+    /// ```rust
+    /// fn foo() -> i32 { 1 }
+    /// let bar = foo; // bar: fn() -> i32 {foo}
+    /// ```
+    FnDef {
+        // Function definition
+        def: Function,
+        /// For display
+        name: Name,
+        /// Parameters and return type
+        sig: Arc<FnSig>,
+        /// Substitutions for the generic parameters of the type
+        substs: Substs,
+    },
+
     /// A pointer to a function.  Written as `fn() -> i32`.
     ///
     /// For example the type of `bar` here:
@@ -448,12 +470,12 @@ impl Ty {
         }
         // add placeholders for args that were not provided
         // TODO: handle defaults
-        for _ in segment
+        let supplied_params = segment
             .args_and_bindings
             .as_ref()
             .map(|ga| ga.args.len())
-            .unwrap_or(0)..def_generics.params.len()
-        {
+            .unwrap_or(0);
+        for _ in supplied_params..def_generics.params.len() {
             substs.push(Ty::Unknown);
         }
         assert_eq!(substs.len(), def_generics.params.len());
@@ -485,6 +507,19 @@ impl Ty {
                 }
                 sig_mut.output.walk_mut(f);
             }
+            Ty::FnDef { substs, sig, .. } => {
+                let sig_mut = Arc::make_mut(sig);
+                for input in &mut sig_mut.input {
+                    input.walk_mut(f);
+                }
+                sig_mut.output.walk_mut(f);
+                // Without an Arc::make_mut_slice, we can't avoid the clone here:
+                let mut v: Vec<_> = substs.0.iter().cloned().collect();
+                for t in &mut v {
+                    t.walk_mut(f);
+                }
+                substs.0 = v.into();
+            }
             Ty::Adt { substs, .. } => {
                 // Without an Arc::make_mut_slice, we can't avoid the clone here:
                 let mut v: Vec<_> = substs.0.iter().cloned().collect();
@@ -524,6 +559,12 @@ impl Ty {
                 name,
                 substs,
             },
+            Ty::FnDef { def, name, sig, .. } => Ty::FnDef {
+                def,
+                name,
+                sig,
+                substs,
+            },
             _ => self,
         }
     }
@@ -551,7 +592,7 @@ impl Ty {
     /// or function); so if `self` is `Option<u32>`, this returns the `u32`.
     fn substs(&self) -> Option<Substs> {
         match self {
-            Ty::Adt { substs, .. } => Some(substs.clone()),
+            Ty::Adt { substs, .. } | Ty::FnDef { substs, .. } => Some(substs.clone()),
             _ => None,
         }
     }
@@ -586,6 +627,22 @@ impl fmt::Display for Ty {
                     .to_fmt(f)?;
                 write!(f, " -> {}", sig.output)
             }
+            Ty::FnDef {
+                name, substs, sig, ..
+            } => {
+                write!(f, "fn {}", name)?;
+                if substs.0.len() > 0 {
+                    join(substs.0.iter())
+                        .surround_with("<", ">")
+                        .separator(", ")
+                        .to_fmt(f)?;
+                }
+                join(sig.input.iter())
+                    .surround_with("(", ")")
+                    .separator(", ")
+                    .to_fmt(f)?;
+                write!(f, " -> {}", sig.output)
+            }
             Ty::Adt { name, substs, .. } => {
                 write!(f, "{}", name)?;
                 if substs.0.len() > 0 {
@@ -607,11 +664,11 @@ impl fmt::Display for Ty {
 
 /// Compute the declared type of a function. This should not need to look at the
 /// function body.
-fn type_for_fn(db: &impl HirDatabase, f: Function) -> Ty {
-    let signature = f.signature(db);
-    let module = f.module(db);
-    let impl_block = f.impl_block(db);
-    let generics = f.generic_params(db);
+fn type_for_fn(db: &impl HirDatabase, def: Function) -> Ty {
+    let signature = def.signature(db);
+    let module = def.module(db);
+    let impl_block = def.impl_block(db);
+    let generics = def.generic_params(db);
     let input = signature
         .params()
         .iter()
@@ -624,8 +681,15 @@ fn type_for_fn(db: &impl HirDatabase, f: Function) -> Ty {
         &generics,
         signature.ret_type(),
     );
-    let sig = FnSig { input, output };
-    Ty::FnPtr(Arc::new(sig))
+    let sig = Arc::new(FnSig { input, output });
+    let substs = make_substs(&generics);
+    let name = def.name(db);
+    Ty::FnDef {
+        def,
+        sig,
+        name,
+        substs,
+    }
 }
 
 fn make_substs(generics: &GenericParams) -> Substs {
@@ -1102,7 +1166,18 @@ impl<'a, D: HirDatabase> InferenceContext<'a, D> {
             .into();
         let typable = typable?;
         let ty = self.db.type_for_def(typable);
+        let generics = GenericParams::default();
+        let substs = Ty::substs_from_path(
+            self.db,
+            &self.module,
+            self.impl_block.as_ref(),
+            &generics,
+            path,
+            typable,
+        );
+        let ty = ty.apply_substs(substs);
         let ty = self.insert_type_vars(ty);
+
         Some(ty)
     }
 
@@ -1142,7 +1217,7 @@ impl<'a, D: HirDatabase> InferenceContext<'a, D> {
                 let ty = self.insert_type_vars(ty.apply_substs(substs));
                 (ty, Some(var.into()))
             }
-            TypableDef::Enum(_) | TypableDef::Function(_) => (Ty::Unknown, None),
+            TypableDef::Function(_) | TypableDef::Enum(_) => (Ty::Unknown, None),
         }
     }
 
@@ -1196,9 +1271,7 @@ impl<'a, D: HirDatabase> InferenceContext<'a, D> {
                     Ty::Tuple(ref tuple_args) => &**tuple_args,
                     _ => &[],
                 };
-                let expectations_iter = expectations
-                    .into_iter()
-                    .chain(std::iter::repeat(&Ty::Unknown));
+                let expectations_iter = expectations.into_iter().chain(repeat(&Ty::Unknown));
 
                 let inner_tys = args
                     .iter()
@@ -1332,18 +1405,25 @@ impl<'a, D: HirDatabase> InferenceContext<'a, D> {
             Expr::Call { callee, args } => {
                 let callee_ty = self.infer_expr(*callee, &Expectation::none());
                 let (param_tys, ret_ty) = match &callee_ty {
-                    Ty::FnPtr(sig) => (&sig.input[..], sig.output.clone()),
+                    Ty::FnPtr(sig) => (sig.input.clone(), sig.output.clone()),
+                    Ty::FnDef { substs, sig, .. } => {
+                        let ret_ty = sig.output.clone().subst(&substs);
+                        let param_tys = sig
+                            .input
+                            .iter()
+                            .map(|ty| ty.clone().subst(&substs))
+                            .collect();
+                        (param_tys, ret_ty)
+                    }
                     _ => {
                         // not callable
                         // TODO report an error?
-                        (&[][..], Ty::Unknown)
+                        (Vec::new(), Ty::Unknown)
                     }
                 };
-                for (i, arg) in args.iter().enumerate() {
-                    self.infer_expr(
-                        *arg,
-                        &Expectation::has_type(param_tys.get(i).cloned().unwrap_or(Ty::Unknown)),
-                    );
+                let param_iter = param_tys.into_iter().chain(repeat(Ty::Unknown));
+                for (arg, param) in args.iter().zip(param_iter) {
+                    self.infer_expr(*arg, &Expectation::has_type(param));
                 }
                 ret_ty
             }
@@ -1365,21 +1445,34 @@ impl<'a, D: HirDatabase> InferenceContext<'a, D> {
                 let (expected_receiver_ty, param_tys, ret_ty) = match &method_ty {
                     Ty::FnPtr(sig) => {
                         if sig.input.len() > 0 {
-                            (&sig.input[0], &sig.input[1..], sig.output.clone())
+                            (
+                                sig.input[0].clone(),
+                                sig.input[1..].iter().cloned().collect(),
+                                sig.output.clone(),
+                            )
                         } else {
-                            (&Ty::Unknown, &[][..], sig.output.clone())
+                            (Ty::Unknown, Vec::new(), sig.output.clone())
                         }
                     }
-                    _ => (&Ty::Unknown, &[][..], Ty::Unknown),
+                    Ty::FnDef { substs, sig, .. } => {
+                        let ret_ty = sig.output.clone().subst(&substs);
+
+                        if sig.input.len() > 0 {
+                            let mut arg_iter = sig.input.iter().map(|ty| ty.clone().subst(&substs));
+                            let receiver_ty = arg_iter.next().unwrap();
+                            (receiver_ty, arg_iter.collect(), ret_ty)
+                        } else {
+                            (Ty::Unknown, Vec::new(), ret_ty)
+                        }
+                    }
+                    _ => (Ty::Unknown, Vec::new(), Ty::Unknown),
                 };
                 // TODO we would have to apply the autoderef/autoref steps here
                 // to get the correct receiver type to unify...
-                self.unify(expected_receiver_ty, &receiver_ty);
-                for (i, arg) in args.iter().enumerate() {
-                    self.infer_expr(
-                        *arg,
-                        &Expectation::has_type(param_tys.get(i).cloned().unwrap_or(Ty::Unknown)),
-                    );
+                self.unify(&expected_receiver_ty, &receiver_ty);
+                let param_iter = param_tys.into_iter().chain(repeat(Ty::Unknown));
+                for (arg, param) in args.iter().zip(param_iter) {
+                    self.infer_expr(*arg, &Expectation::has_type(param));
                 }
                 ret_ty
             }
@@ -1609,10 +1702,7 @@ impl<'a, D: HirDatabase> InferenceContext<'a, D> {
 
             self.infer_pat(*pat, &ty);
         }
-        self.return_ty = {
-            let ty = self.make_ty(signature.ret_type());
-            ty
-        };
+        self.return_ty = self.make_ty(signature.ret_type());
     }
 
     fn infer_body(&mut self) {
diff --git a/crates/ra_hir/src/ty/snapshots/tests__infer_backwards.snap b/crates/ra_hir/src/ty/snapshots/tests__infer_backwards.snap
index 5c74bd8c78..f5840a9347 100644
--- a/crates/ra_hir/src/ty/snapshots/tests__infer_backwards.snap
+++ b/crates/ra_hir/src/ty/snapshots/tests__infer_backwards.snap
@@ -1,8 +1,8 @@
 ---
-created: "2019-01-22T14:44:59.880187500+00:00"
-creator: insta@0.4.0
+created: "2019-01-26T17:46:03.842478456+00:00"
+creator: insta@0.5.2
 expression: "&result"
-source: "crates\\ra_hir\\src\\ty\\tests.rs"
+source: crates/ra_hir/src/ty/tests.rs
 ---
 [14; 15) 'x': u32
 [22; 24) '{}': ()
@@ -10,7 +10,7 @@ source: "crates\\ra_hir\\src\\ty\\tests.rs"
 [88; 89) 'a': u32
 [92; 108) 'unknow...nction': [unknown]
 [92; 110) 'unknow...tion()': u32
-[116; 125) 'takes_u32': fn(u32) -> ()
+[116; 125) 'takes_u32': fn takes_u32(u32) -> ()
 [116; 128) 'takes_u32(a)': ()
 [126; 127) 'a': u32
 [138; 139) 'b': i32
diff --git a/crates/ra_hir/src/ty/snapshots/tests__infer_binary_op.snap b/crates/ra_hir/src/ty/snapshots/tests__infer_binary_op.snap
index c506bcadd5..b9dda2bc07 100644
--- a/crates/ra_hir/src/ty/snapshots/tests__infer_binary_op.snap
+++ b/crates/ra_hir/src/ty/snapshots/tests__infer_binary_op.snap
@@ -1,8 +1,8 @@
 ---
-created: "2019-01-22T14:44:59.880187500+00:00"
-creator: insta@0.4.0
+created: "2019-01-26T17:46:03.853259898+00:00"
+creator: insta@0.5.2
 expression: "&result"
-source: "crates\\ra_hir\\src\\ty\\tests.rs"
+source: crates/ra_hir/src/ty/tests.rs
 ---
 [6; 7) 'x': bool
 [22; 34) '{     0i32 }': i32
@@ -28,7 +28,7 @@ source: "crates\\ra_hir\\src\\ty\\tests.rs"
 [174; 196) 'minus_...ONST_2': bool
 [189; 196) 'CONST_2': isize
 [206; 207) 'c': i32
-[210; 211) 'f': fn(bool) -> i32
+[210; 211) 'f': fn f(bool) -> i32
 [210; 219) 'f(z || y)': i32
 [210; 223) 'f(z || y) + 5': i32
 [212; 213) 'z': bool
diff --git a/crates/ra_hir/src/ty/snapshots/tests__infer_function_generics.snap b/crates/ra_hir/src/ty/snapshots/tests__infer_function_generics.snap
index 7203ad1e2a..8ff6e55a6b 100644
--- a/crates/ra_hir/src/ty/snapshots/tests__infer_function_generics.snap
+++ b/crates/ra_hir/src/ty/snapshots/tests__infer_function_generics.snap
@@ -1,21 +1,21 @@
 ---
-created: "2019-01-22T14:44:59.954958500+00:00"
-creator: insta@0.4.0
+created: "2019-01-26T18:16:16.530712344+00:00"
+creator: insta@0.5.2
 expression: "&result"
-source: "crates\\ra_hir\\src\\ty\\tests.rs"
+source: crates/ra_hir/src/ty/tests.rs
 ---
 [10; 11) 't': [unknown]
 [21; 26) '{ t }': [unknown]
 [23; 24) 't': [unknown]
 [38; 98) '{     ...(1); }': ()
-[44; 46) 'id': fn(T) -> T
-[44; 52) 'id(1u32)': T
+[44; 46) 'id': fn id<u32>(T) -> T
+[44; 52) 'id(1u32)': u32
 [47; 51) '1u32': u32
-[58; 68) 'id::<i128>': fn(T) -> T
-[58; 71) 'id::<i128>(1)': T
-[69; 70) '1': T
-[81; 82) 'x': T
-[90; 92) 'id': fn(T) -> T
-[90; 95) 'id(1)': T
-[93; 94) '1': T
+[58; 68) 'id::<i128>': fn id<i128>(T) -> T
+[58; 71) 'id::<i128>(1)': i128
+[69; 70) '1': i128
+[81; 82) 'x': u64
+[90; 92) 'id': fn id<u64>(T) -> T
+[90; 95) 'id(1)': u64
+[93; 94) '1': u64
 
diff --git a/crates/ra_hir/src/ty/snapshots/tests__infer_generic_chain.snap b/crates/ra_hir/src/ty/snapshots/tests__infer_generic_chain.snap
index 4435180a10..f21bffa754 100644
--- a/crates/ra_hir/src/ty/snapshots/tests__infer_generic_chain.snap
+++ b/crates/ra_hir/src/ty/snapshots/tests__infer_generic_chain.snap
@@ -1,8 +1,8 @@
 ---
-created: "2019-01-22T14:44:59.961936900+00:00"
-creator: insta@0.4.0
+created: "2019-01-26T17:46:03.866825843+00:00"
+creator: insta@0.5.2
 expression: "&result"
-source: "crates\\ra_hir\\src\\ty\\tests.rs"
+source: crates/ra_hir/src/ty/tests.rs
 ---
 [53; 57) 'self': A<[unknown]>
 [65; 87) '{     ...     }': [unknown]
@@ -12,25 +12,25 @@ source: "crates\\ra_hir\\src\\ty\\tests.rs"
 [110; 115) '{ t }': [unknown]
 [112; 113) 't': [unknown]
 [135; 261) '{     ....x() }': i128
-[146; 147) 'x': T
-[150; 151) '1': T
-[162; 163) 'y': T
-[166; 168) 'id': fn(T) -> T
-[166; 171) 'id(x)': T
-[169; 170) 'x': T
-[182; 183) 'a': A<T>
-[186; 200) 'A { x: id(y) }': A<T>
-[193; 195) 'id': fn(T) -> T
-[193; 198) 'id(y)': T
-[196; 197) 'y': T
-[211; 212) 'z': T
-[215; 217) 'id': fn(T) -> T
-[215; 222) 'id(a.x)': T
-[218; 219) 'a': A<T>
-[218; 221) 'a.x': T
-[233; 234) 'b': A<T>
-[237; 247) 'A { x: z }': A<T>
-[244; 245) 'z': T
-[254; 255) 'b': A<T>
+[146; 147) 'x': i32
+[150; 151) '1': i32
+[162; 163) 'y': i32
+[166; 168) 'id': fn id<i32>(T) -> T
+[166; 171) 'id(x)': i32
+[169; 170) 'x': i32
+[182; 183) 'a': A<i32>
+[186; 200) 'A { x: id(y) }': A<i32>
+[193; 195) 'id': fn id<i32>(T) -> T
+[193; 198) 'id(y)': i32
+[196; 197) 'y': i32
+[211; 212) 'z': i32
+[215; 217) 'id': fn id<i32>(T) -> T
+[215; 222) 'id(a.x)': i32
+[218; 219) 'a': A<i32>
+[218; 221) 'a.x': i32
+[233; 234) 'b': A<i32>
+[237; 247) 'A { x: z }': A<i32>
+[244; 245) 'z': i32
+[254; 255) 'b': A<i32>
 [254; 259) 'b.x()': i128
 
diff --git a/crates/ra_hir/src/ty/snapshots/tests__infer_paths.snap b/crates/ra_hir/src/ty/snapshots/tests__infer_paths.snap
index 0bceffaef6..afbe2f747a 100644
--- a/crates/ra_hir/src/ty/snapshots/tests__infer_paths.snap
+++ b/crates/ra_hir/src/ty/snapshots/tests__infer_paths.snap
@@ -1,16 +1,16 @@
 ---
-created: "2019-01-22T14:44:59.975899500+00:00"
-creator: insta@0.4.0
+created: "2019-01-26T17:46:03.928773630+00:00"
+creator: insta@0.5.2
 expression: "&result"
-source: "crates\\ra_hir\\src\\ty\\tests.rs"
+source: crates/ra_hir/src/ty/tests.rs
 ---
 [15; 20) '{ 1 }': u32
 [17; 18) '1': u32
 [48; 53) '{ 1 }': u32
 [50; 51) '1': u32
 [67; 91) '{     ...c(); }': ()
-[73; 74) 'a': fn() -> u32
+[73; 74) 'a': fn a() -> u32
 [73; 76) 'a()': u32
-[82; 86) 'b::c': fn() -> u32
+[82; 86) 'b::c': fn c() -> u32
 [82; 88) 'b::c()': u32
 
diff --git a/crates/ra_hir/src/ty/snapshots/tests__infer_type_param.snap b/crates/ra_hir/src/ty/snapshots/tests__infer_type_param.snap
new file mode 100644
index 0000000000..a993232642
--- /dev/null
+++ b/crates/ra_hir/src/ty/snapshots/tests__infer_type_param.snap
@@ -0,0 +1,26 @@
+---
+created: "2019-01-27T16:54:18.368427685+00:00"
+creator: insta@0.5.2
+expression: "&result"
+source: crates/ra_hir/src/ty/tests.rs
+---
+[10; 11) 'x': [unknown]
+[21; 30) '{     x }': [unknown]
+[27; 28) 'x': [unknown]
+[44; 45) 'x': &[unknown]
+[56; 65) '{     x }': &[unknown]
+[62; 63) 'x': &[unknown]
+[77; 157) '{     ...(1); }': ()
+[87; 88) 'y': u32
+[91; 96) '10u32': u32
+[102; 104) 'id': fn id<u32>(T) -> T
+[102; 107) 'id(y)': u32
+[105; 106) 'y': u32
+[117; 118) 'x': bool
+[127; 132) 'clone': fn clone<bool>(&T) -> T
+[127; 135) 'clone(z)': bool
+[133; 134) 'z': &bool
+[141; 151) 'id::<i128>': fn id<i128>(T) -> T
+[141; 154) 'id::<i128>(1)': i128
+[152; 153) '1': i128
+
diff --git a/crates/ra_hir/src/ty/tests.rs b/crates/ra_hir/src/ty/tests.rs
index f74d6f5ea3..ac12d974b8 100644
--- a/crates/ra_hir/src/ty/tests.rs
+++ b/crates/ra_hir/src/ty/tests.rs
@@ -594,6 +594,29 @@ fn test() {
     );
 }
 
+#[test]
+fn infer_type_param() {
+    check_inference(
+        "infer_type_param",
+        r#"
+fn id<T>(x: T) -> T {
+    x
+}
+
+fn clone<T>(x: &T) -> T {
+    x
+}
+
+fn test() {
+    let y = 10u32;
+    id(y);
+    let x: bool = clone(z);
+    id::<i128>(1);
+}
+"#,
+    );
+}
+
 fn infer(content: &str) -> String {
     let (db, _, file_id) = MockDatabase::with_single_file(content);
     let source_file = db.parse(file_id);