diff --git a/language.grammar b/language.grammar
index a3163db..09c2b62 100644
--- a/language.grammar
+++ b/language.grammar
@@ -4,12 +4,22 @@ token lower_identifier = /[a-z_][a-z_A-Z0-9]*/;
 token kw_data = /data/;
 token kw_type = /type/;
 token kw_defn = /defn/;
+token kw_let = /let/;
+token kw_letrec = /letrec/;
+token kw_in = /in/;
+token kw_case = /case/;
+token kw_of = /of/;
 token tkn_ocurly = /{/;
 token tkn_ccurly = /}/;
 token tkn_oparen = /\(/;
 token tkn_cparen = /\)/;
 token tkn_eq = /=/;
 token tkn_comma = /,/;
+token tkn_arrow = /->/;
+token op_add = /\+/;
+token op_sub = /-/;
+token op_mul = /\*/;
+token op_div = /\//;
 
 rule S = program;
 
@@ -55,7 +65,67 @@ rule defn_body
     ;
 
 rule expr
+    = expr_add
+    | expr_let
+    | expr_letrec
+    | expr_case
+    ;
+
+rule expr_add
+    = expr_add op_add expr_mul
+    | expr_add op_sub expr_mul
+    | expr_mul
+    ;
+
+rule expr_mul
+    = expr_mul op_mul expr_app
+    | expr_mul op_div expr_app
+    | expr_app
+    ;
+
+rule expr_app
+    = expr_app? expr_app_bottom
+    ;
+
+rule expr_app_bottom
     = lower_identifier
+    | upper_identifier
+    | tkn_oparen expr tkn_cparen
+    ;
+
+rule expr_curly
+    = tkn_ocurly expr tkn_ccurly
+    ;
+
+rule expr_let
+    = kw_let lower_identifier tkn_eq expr_curly kw_in expr_curly
+    ;
+
+rule expr_letrec
+    = kw_letrec lower_identifier tkn_eq expr_curly kw_in expr_curly
+    ;
+
+rule expr_case
+    = kw_case expr kw_of tkn_ocurly expr_case_branches tkn_ccurly
+    ;
+
+rule expr_case_branches
+    = expr_case_branches? expr_case_branch
+    ;
+
+rule expr_case_branch
+    = pattern tkn_arrow expr_curly
+    ;
+
+rule pattern
+    = lower_identifier
+    | upper_identifier
+    | upper_identifier tkn_oparen patterns tkn_cparen
+    ;
+
+rule patterns
+    = pattern
+    | patterns tkn_comma pattern
     ;
 
 rule type