diff --git a/src/grammar.lalrpop b/src/grammar.lalrpop
index 2c5574cb..5f9ef619 100644
--- a/src/grammar.lalrpop
+++ b/src/grammar.lalrpop
@@ -269,8 +269,8 @@ UOp: UnaryOp<RichTerm> = {
     "tag" <s: Str> => UnaryOp::Tag(s),
     "wrap" => UnaryOp::Wrap(),
     "embed" <Ident> => UnaryOp::Embed(<>),
-    "map" <Atom> => UnaryOp::ListMap(<>),
-    "recordMap" <Atom> => UnaryOp::RecordMap(<>),
+    "map"  => UnaryOp::ListMap(),
+    "recordMap" => UnaryOp::RecordMap(),
     "seq" => UnaryOp::Seq(),
     "deepSeq" => UnaryOp::DeepSeq(),
     "head" => UnaryOp::ListHead(),
diff --git a/src/operation.rs b/src/operation.rs
index 18305520..cf10eda4 100644
--- a/src/operation.rs
+++ b/src/operation.rs
@@ -434,7 +434,11 @@ fn process_unary_operation(
                 ))
             }
         }
-        UnaryOp::ListMap(f) => {
+        UnaryOp::ListMap() => {
+            let (f, _) = stack
+                .pop_arg()
+                .ok_or_else(|| EvalError::NotEnoughArgs(2, String::from("map"), pos_op))?;
+
             if let Term::List(ts) = *t {
                 let mut shared_env = Environment::new();
                 let f_as_var = f.body.closurize(&mut env, f.env);
@@ -464,7 +468,11 @@ fn process_unary_operation(
                 ))
             }
         }
-        UnaryOp::RecordMap(f) => {
+        UnaryOp::RecordMap() => {
+            let (f, _) = stack
+                .pop_arg()
+                .ok_or_else(|| EvalError::NotEnoughArgs(2, String::from("recordMap"), pos_op))?;
+
             if let Term::Record(rec) = *t {
                 let mut shared_env = Environment::new();
                 let f_as_var = f.body.closurize(&mut env, f.env);
diff --git a/src/program.rs b/src/program.rs
index 836c0c09..decdad42 100644
--- a/src/program.rs
+++ b/src/program.rs
@@ -811,15 +811,15 @@ Assume(#alwaysTrue, false)
 
         assert_eq!(
             eval_string(
-                "(%recordMap% (fun y => fun x => x + 1) { foo = 1; bar = \"it's lazy\"; }).foo"
+                "(%recordMap% { foo = 1; bar = \"it's lazy\"; } (fun y => fun x => x + 1)).foo"
             ),
             Ok(Term::Num(2.)),
         );
         assert_eq!(
             eval_string(
                 "let r = %recordMap%
-                    (fun y x => if %isNum% x then x + 1 else 0)
                     { foo = 1; bar = \"it's lazy\"; }
+                    (fun y x => if %isNum% x then x + 1 else 0)
                 in
                 (r.foo) + (r.bar)"
             ),
@@ -878,7 +878,7 @@ Assume(#alwaysTrue, false)
     fn lists() {
         assert_eq!(eval_string("%elemAt% [1,2,3] 1"), Ok(Term::Num(2.0)));
         assert_eq!(
-            eval_string("%elemAt% (%map% (fun x => x + 1) [1,2,3]) 1"),
+            eval_string("%elemAt% (%map% [1,2,3] (fun x => x + 1)) 1"),
             Ok(Term::Num(3.0))
         );
 
@@ -929,7 +929,7 @@ Assume(#alwaysTrue, false)
                             if y then true else false
                         else false
                 in
-                let all = fun pred => fun l => foldr and true (%map% pred l) in
+                let all = fun pred => fun l => foldr and true (%map% l pred) in
                 let isZ = fun x => x == 0 in
                 all isZ [0, 0, 0, 1]"
             ),
diff --git a/src/term.rs b/src/term.rs
index 7d7dc3da..6303d1a8 100644
--- a/src/term.rs
+++ b/src/term.rs
@@ -498,13 +498,13 @@ pub enum UnaryOp<CapturedTerm> {
     StaticAccess(Ident),
 
     /// Map a function on each element of a list.
-    ListMap(CapturedTerm),
+    ListMap(),
     /// Map a function on a record.
     ///
     /// The mapped function must take two arguments, the name of the field as a string, and the
     /// content of the field. `RecordMap` then replaces the content of each field by the result of the
     /// function: i.e., `recordMap f {a=2;}` evaluates to `{a=(f "a" 2);}`.
-    RecordMap(CapturedTerm),
+    RecordMap(),
 
     /// Inverse the polarity of a label.
     ChangePolarity(),
@@ -574,8 +574,8 @@ impl<Ty> UnaryOp<Ty> {
 
         match self {
             Switch(has_default) => Switch(has_default),
-            ListMap(t) => ListMap(f(t)),
-            RecordMap(t) => RecordMap(f(t)),
+            ListMap() => ListMap(),
+            RecordMap() => RecordMap(),
 
             Ite() => Ite(),
 
diff --git a/src/typecheck.rs b/src/typecheck.rs
index 4e0a7627..c4b99374 100644
--- a/src/typecheck.rs
+++ b/src/typecheck.rs
@@ -1335,8 +1335,8 @@ fn instantiate_foralls(state: &mut State, mut ty: TypeWrapper, inst: ForallInst)
 /// Type of unary operations.
 pub fn get_uop_type(
     state: &mut State,
-    envs: Envs,
-    strict: bool,
+    _envs: Envs,
+    _strict: bool,
     op: &UnaryOp<RichTerm>,
 ) -> Result<TypeWrapper, TypecheckError> {
     Ok(match op {
@@ -1398,20 +1398,16 @@ pub fn get_uop_type(
 
             mk_tyw_arrow!(mk_tyw_record!((id.clone(), res.clone()); row), res)
         }
-        // List -> List
-        // Unify f with a -> b.
-        UnaryOp::ListMap(f) => {
+        // forall a b. List -> (a -> b) -> List
+        UnaryOp::ListMap() => {
             let a = TypeWrapper::Ptr(new_var(state.table));
             let b = TypeWrapper::Ptr(new_var(state.table));
 
             let f_type = mk_tyw_arrow!(a.clone(), b.clone());
-            type_check_(state, envs.clone(), strict, f, f_type)?;
-
-            mk_tyw_arrow!(AbsType::List(), AbsType::List())
+            mk_tyw_arrow!(AbsType::List(), f_type, AbsType::List())
         }
-        // { _ : a} -> { _ : b }
-        // Unify f with Str -> a -> b.
-        UnaryOp::RecordMap(f) => {
+        // forall a b. { _ : a} -> (Str -> a -> b) -> { _ : b }
+        UnaryOp::RecordMap() => {
             // Assuming f has type Str -> a -> b,
             // this has type DynRecord(a) -> DynRecord(b)
 
@@ -1419,9 +1415,11 @@ pub fn get_uop_type(
             let b = TypeWrapper::Ptr(new_var(state.table));
 
             let f_type = mk_tyw_arrow!(AbsType::Str(), a.clone(), b.clone());
-            type_check_(state, envs.clone(), strict, f, f_type)?;
-
-            mk_tyw_arrow!(mk_typewrapper::dyn_record(a), mk_typewrapper::dyn_record(b))
+            mk_tyw_arrow!(
+                mk_typewrapper::dyn_record(a),
+                f_type,
+                mk_typewrapper::dyn_record(b)
+            )
         }
         // forall a b. a -> b -> b
         UnaryOp::Seq() | UnaryOp::DeepSeq() => {
@@ -2079,7 +2077,7 @@ mod tests {
         parse_and_typecheck("fun l => %tail% l : List -> List").unwrap();
         parse_and_typecheck("fun l => %head% l : List -> Dyn").unwrap();
         parse_and_typecheck(
-            "fun f l => %map% f l : forall a. (forall b. (a -> b) -> List -> List)",
+            "fun f l => %map% l f : forall a. (forall b. (a -> b) -> List -> List)",
         )
         .unwrap();
         parse_and_typecheck("(fun l1 => fun l2 => l1 @ l2) : List -> List -> List").unwrap();
@@ -2087,7 +2085,7 @@ mod tests {
 
         parse_and_typecheck("(fun l => %head% l) : forall a. (List -> a)").unwrap_err();
         parse_and_typecheck(
-            "(fun f l => %elemAt% (%map% f l) 0) : forall a. (forall b. (a -> b) -> List -> b)",
+            "(fun f l => %elemAt% (%map% l f) 0) : forall a. (forall b. (a -> b) -> List -> b)",
         )
         .unwrap_err();
     }
diff --git a/stdlib/contracts.ncl b/stdlib/contracts.ncl
index 3606bbab..bde17055 100644
--- a/stdlib/contracts.ncl
+++ b/stdlib/contracts.ncl
@@ -38,7 +38,7 @@
 
   dyn_record = fun contr l t =>
       if %isRecord% t then
-          %recordMap% (fun _field => contr l) t
+          %recordMap% t (fun _field => contr l)
       else
           %blame% (%tag% "not a record" l);
 
diff --git a/stdlib/lists.ncl b/stdlib/lists.ncl
index 091c41ad..f2e6ca5e 100644
--- a/stdlib/lists.ncl
+++ b/stdlib/lists.ncl
@@ -6,7 +6,7 @@
 
     length : List -> Num = fun l => %length% l;
 
-    map : (Dyn -> Dyn) -> List -> List = fun f l => %map% f l;
+    map : (Dyn -> Dyn) -> List -> List = fun f l => %map% l f;
 
     elemAt : List -> Num -> Dyn = fun l n => %elemAt% l n;
 
diff --git a/stdlib/records.ncl b/stdlib/records.ncl
index 2d35c37b..1826a0fc 100644
--- a/stdlib/records.ncl
+++ b/stdlib/records.ncl
@@ -1,6 +1,6 @@
 {
   records = {
-    map : forall a b. (Str -> a -> b) -> {_: a} -> {_: b} = fun f r => %recordMap% f r;
+    map : forall a b. (Str -> a -> b) -> {_: a} -> {_: b} = fun f r => %recordMap% r f;
 
     // TODO: change Dyn to { | Dyn} once the PR introducing open contracts lands
     fieldsOf : Dyn -> List = fun r => %fieldsOf% r;