diff --git a/TODO b/TODO
index 340218d7a..72f439161 100644
--- a/TODO
+++ b/TODO
@@ -2,3 +2,4 @@
   - proper naming scheme
   - symbols table
   - name conflicts on globals?
+  - separate header for typedef (e.g., type::tile_shapes_t) to reduce compilation time
diff --git a/examples/matrix.cpp b/examples/matrix.cpp
index d54f19e38..86ec4f249 100644
--- a/examples/matrix.cpp
+++ b/examples/matrix.cpp
@@ -6,6 +6,7 @@
 #include "ir/context.h"
 #include "ir/module.h"
 #include "ir/print.h"
+#include "ir/context_impl.h"
 #include "codegen/selection.h"
 #include "codegen/tune.h"
 #include "codegen/shared_copy.h"
@@ -182,6 +183,9 @@ int main() {
   llvm::LLVMContext llvm_context;
   llvm::Module llvm_module("test", llvm_context);
 
+//  context.p_impl->mp_constants_[0]->set_value(16);
+//  context.p_impl->mp_constants_[1]->set_value(16);
+//  context.p_impl->mp_constants_[2]->set_value(8);
 
   // create passes
   tdl::codegen::buffer_info_pass buffer_info;
diff --git a/include/ast/ast.h b/include/ast/ast.h
index 529c4b01b..a24d0480f 100644
--- a/include/ast/ast.h
+++ b/include/ast/ast.h
@@ -5,7 +5,7 @@
 #include <cassert>
 #include <vector>
 #include <string>
-
+#include <iostream>
 
 
 namespace tdl{
@@ -56,6 +56,12 @@ enum TYPE_T{
   FLOAT32_T, FLOAT64_T
 };
 
+enum STORAGE_SPEC_T{
+  TUNABLE_T,
+  KERNEL_T,
+  READONLY_T, WRITEONLY_T,
+};
+
 class pointer;
 class identifier;
 class constant;
@@ -75,7 +81,7 @@ public:
 template<class T>
 class list: public node {
 public:
-  list(const T& x): values_{x} {}
+  list(const T& x): values_(1, x) {}
 
   node* append(const T& x){
     values_.push_back(x);
@@ -389,16 +395,30 @@ public:
 class no_op: public statement { };
 
 // Types
-
 class declaration_specifier: public node{
 public:
-  declaration_specifier(TYPE_T spec)
-    : spec_(spec) { }
+  using node::node;
+  virtual ir::type* type(ir::module *mod) const = 0;
+};
 
+class typed_declaration_specifier: public declaration_specifier {
+public:
+  typed_declaration_specifier(TYPE_T ty): ty_(ty){ }
   ir::type* type(ir::module *mod) const;
 
 private:
-  const TYPE_T spec_;
+  const TYPE_T ty_;
+};
+
+class storage_declaration_specifier: public declaration_specifier {
+public:
+  storage_declaration_specifier(STORAGE_SPEC_T storage_spec, node *decl_spec)
+    : storage_spec_(storage_spec), decl_spec_((declaration_specifier*)decl_spec) {}
+  ir::type* type(ir::module *mod) const;
+
+private:
+  const STORAGE_SPEC_T storage_spec_;
+  const declaration_specifier* decl_spec_;
 };
 
 class declarator;
@@ -495,7 +515,7 @@ public:
   : declarator((node*)((declarator*)decl)->id()),
     decl_((declarator*)decl), expr_((expression*)init){ }
 
-  void specifier(const declaration_specifier *spec);
+  void set_specifier(const declaration_specifier *spec);
   ir::value* codegen(ir::module *) const;
 
 public:
@@ -535,17 +555,17 @@ public:
 class translation_unit: public node{
 public:
   translation_unit(node *item)
-    : decls_((list<node*>*)item) { }
+    : decls_(item) { }
 
   translation_unit *add(node *item) {
-    decls_->append(item);
+    decls_.append(item);
     return this;
   }
 
   ir::value* codegen(ir::module * mod) const;
 
 private:
-  list<node*>* decls_;
+  list<node*> decls_;
 };
 
 }
diff --git a/include/ast/parser.y b/include/ast/parser.y
index 43c530e12..826204f8a 100644
--- a/include/ast/parser.y
+++ b/include/ast/parser.y
@@ -20,12 +20,14 @@ struct token: public node{
   token(BIN_OP_T value): bin_op(value){ }
   token(UNARY_OP_T value): unary_op(value){ }
   token(TYPE_T value): type(value){ }
+  token(STORAGE_SPEC_T value): storage_spec(value){ }
 
   union {
     ASSIGN_OP_T assign_op;
     BIN_OP_T bin_op;
     UNARY_OP_T unary_op;
     TYPE_T type;
+    STORAGE_SPEC_T storage_spec;
   };
 };
 
@@ -39,10 +41,12 @@ node* append_ptr_list(node *result, node *in){
 ASSIGN_OP_T get_assign_op(node *op) { return ((token*)op)->assign_op; }
 UNARY_OP_T get_unary_op(node *op) { return ((token*)op)->unary_op; }
 TYPE_T get_type_spec(node *op) { return ((token*)op)->type; }
+STORAGE_SPEC_T get_storage_spec(node *op) { return ((token*)op)->storage_spec;}
 
 %}
  
 %token IDENTIFIER CONSTANT STRING_LITERAL
+%token TUNABLE KERNEL READONLY WRITEONLY
 %token PTR_OP INC_OP DEC_OP LEFT_OP RIGHT_OP LE_OP GE_OP EQ_OP NE_OP
 %token AND_OP OR_OP MUL_ASSIGN DIV_ASSIGN MOD_ASSIGN ADD_ASSIGN
 %token SUB_ASSIGN LEFT_ASSIGN RIGHT_ASSIGN AND_ASSIGN
@@ -87,17 +91,12 @@ abstract_declarator
 	;
 
 direct_abstract_declarator
-    : '[' constant_list ']' { $$ = new tile(nullptr, $1); }
+    : '[' primary_expression_list ']' { $$ = new tile(nullptr, $1); }
 
 constant : 
     CONSTANT { $$ = new constant(atoi(yytext)); }
 	;
 	
-constant_list
-	: constant  { $$ = new list<constant*>((constant*)$1); }
-  | constant_list ',' constant { $$ = append_ptr_list<constant>($1, $3); }
-	;
-
 type_name
   : declaration_specifiers { $$ = new type_name($1, nullptr); }
   | declaration_specifiers abstract_declarator { $$ = new type_name($1, $2); }
@@ -112,7 +111,7 @@ identifier
 	;
 
 builtin
-  : GET_GLOBAL_RANGE '[' constant ']' '(' constant ')' { $$ = new get_global_range($3, $6); }
+  : GET_GLOBAL_RANGE '[' primary_expression ']' '(' constant ')' { $$ = new get_global_range($3, $6); }
   |  DOT '(' expression ',' expression ',' expression ')' { $$ = new matmul_expression($3, $5, $7); }
 
 primary_expression
@@ -124,6 +123,11 @@ primary_expression
   | '(' expression ')' { $$ = $2; }
 	;
 
+primary_expression_list
+  : primary_expression { $$ = new list<expression*>((expression*)$1); }
+  | primary_expression_list ',' primary_expression { $$ = append_ptr_list<expression>($1, $3); }
+  ;
+
 slice
   : ':' { $$ = new slice(tdl::ast::ALL); }
   | NEWAXIS { $$ = new slice(tdl::ast::NEWAXIS); }
@@ -312,7 +316,7 @@ jump_statement
 
 direct_declarator
   : identifier { $$ = $1; }
-  | identifier '[' constant_list ']' { $$ = new tile($1, $3); }
+  | identifier '[' primary_expression_list ']' { $$ = new tile($1, $3); }
   | identifier '(' parameter_list ')' { $$ = new function($1, $3); }
   | identifier '(' ')' { $$ = new function($1, nullptr); }
   ;
@@ -330,7 +334,8 @@ parameter_declaration
 
 
 declaration_specifiers
-  : type_specifier { $$ = new declaration_specifier(get_type_spec($1)); }
+  : type_specifier { $$ = new typed_declaration_specifier(get_type_spec($1)); }
+  | storage_class_specifier declaration_specifiers { $$ = new storage_declaration_specifier(get_storage_spec($1), $2); }
 	;
 
 init_declarator_list
@@ -354,6 +359,13 @@ init_declarator
   | declarator '=' initialization_expression { $$ = new initializer($1, $3); }
 	;
 
+storage_class_specifier
+  : TUNABLE   { $$ = new token(TUNABLE_T); }
+  | KERNEL    { $$ = new token(KERNEL_T); }
+  | READONLY  { $$ = new token(READONLY_T); }
+  | WRITEONLY { $$ = new token(WRITEONLY_T); }
+;
+
 /* -------------------------- */
 /*      Translation Unit 	  */
 /* -------------------------- */
diff --git a/include/ast/scanner.l b/include/ast/scanner.l
index 80da95dad..885404ca3 100644
--- a/include/ast/scanner.l
+++ b/include/ast/scanner.l
@@ -16,6 +16,10 @@ int comment();
 %}
 
 %%
+"tunable"     { count(); return(TUNABLE); }
+"kernel"      { count(); return(KERNEL); }
+"readonly"    { count(); return(READONLY); }
+"writeonly"   { count(); return(WRITEONLY); }
 "@"         { count(); return(AT); }
 "newaxis"		{ count(); return(NEWAXIS); }
 "if"			  { count(); return(IF); }
diff --git a/include/codegen/barriers.h b/include/codegen/barriers.h
index 9b476ae75..5199f94ad 100644
--- a/include/codegen/barriers.h
+++ b/include/codegen/barriers.h
@@ -32,7 +32,7 @@ private:
   void add_reference(ir::value *v, interval_vec_t &res);
   void get_read_intervals(ir::instruction *i, interval_vec_t &res);
   void get_written_intervals(ir::instruction *i, interval_vec_t &res);
-  void add(ir::basic_block *block, interval_vec_t &not_synced, std::set<ir::instruction *> &insert_pts);
+  void add(ir::basic_block *block, interval_vec_t &not_synced, ir::builder &builder);
 
 public:
   barriers(allocation *alloc, buffer_info_pass *buffer_info): alloc_(alloc), buffer_info_(buffer_info) {}
diff --git a/include/codegen/selection.h b/include/codegen/selection.h
index 2531dc74c..ec733ed57 100644
--- a/include/codegen/selection.h
+++ b/include/codegen/selection.h
@@ -100,6 +100,7 @@ class selection{
 private:
   // utils
   llvm::Type *make_vector_ty(llvm::Type *ty, size_t vector_size);
+  std::vector<unsigned> extract_shapes(ir::value *v);
 
   // LLVM conversions
   llvm::Type*        llvm_type(ir::type *ty, llvm::LLVMContext &ctx);
diff --git a/include/ir/builder.h b/include/ir/builder.h
index d7e49cf14..a6c0013fd 100644
--- a/include/ir/builder.h
+++ b/include/ir/builder.h
@@ -6,6 +6,7 @@
 #include <string>
 #include "instructions.h"
 #include "basic_block.h"
+#include "type.h"
 
 namespace tdl{
 namespace ir{
@@ -110,11 +111,11 @@ public:
   value *create_load(value *arg, const std::string &name = "");
   value *create_store(value *ptr, value *val, const std::string &name = "");
   // Tile instruction
-  value *create_splat(value *arg, const std::vector<unsigned> &shapes, const std::string &name = "");
-  value *create_reshape(value *arg, const std::vector<unsigned> &shapes, const std::string &name = "");
-  value *create_broadcast(value *arg, const std::vector<unsigned> &shapes, const std::string &name = "");
+  value *create_splat(value *arg, const type::tile_shapes_t &shapes, const std::string &name = "");
+  value *create_reshape(value *arg, const type::tile_shapes_t &shapes, const std::string &name = "");
+  value *create_broadcast(value *arg, const type::tile_shapes_t &shapes, const std::string &name = "");
   // Built-in instruction
-  value *create_get_global_range(unsigned axis, unsigned size, const std::string &name = "");
+  value *create_get_global_range(unsigned axis, type::tile_shapes_t::value_type size, const std::string &name = "");
   value *create_matmul(value *A, value *B, value *C, const std::string &name = "");
   // Intrinsics
   value *create_copy_to_shared(value *arg, const std::string &name = "");
diff --git a/include/ir/constant.h b/include/ir/constant.h
index 78814283c..132902d3a 100644
--- a/include/ir/constant.h
+++ b/include/ir/constant.h
@@ -2,6 +2,7 @@
 #define TDL_INCLUDE_IR_CONSTANT_H
 
 #include "value.h"
+#include <cassert>
 
 namespace tdl{
 namespace ir{
@@ -28,28 +29,43 @@ public:
   static undef_value* get(type* ty);
 };
 
+
 /* Constant int */
 class constant_int: public constant{
+protected:
   constant_int(type *ty, uint64_t value);
 
 public:
   uint64_t get_value() const { return value_; }
-  static constant *get(type *ty, uint64_t value);
+  static constant_int *get(type *ty, uint64_t value);
+
+protected:
+  uint64_t value_;
+};
+
+/* Metaparameter int */
+class metaparameter: public constant_int{
+  metaparameter(type *ty, unsigned lo, unsigned hi);
+
+public:
+  static metaparameter *create(context &ctx, type *ty, unsigned lo, unsigned hi);
+  void set_value(uint64_t value) { value_ = value; }
 
 private:
-  uint64_t value_;
+  unsigned lo_;
+  unsigned hi_;
 };
 
 /* constant range */
 class constant_range: public constant{
-  constant_range(type *ty, uint64_t first, uint64_t last);
+  constant_range(type *ty, constant_int* first, constant_int* last);
 
 public:
-  static constant *get(constant *first, constant *last);
+  static constant *get(constant_int *first, constant_int *last);
 
 private:
-  uint64_t first_;
-  uint64_t last_;
+  constant_int* first_;
+  constant_int* last_;
 };
 
 /* constant fp */
diff --git a/include/ir/context_impl.h b/include/ir/context_impl.h
index cb3acc186..b9017b39c 100644
--- a/include/ir/context_impl.h
+++ b/include/ir/context_impl.h
@@ -12,6 +12,7 @@ class context;
 class constant_int;
 class constant_fp;
 class undef_value;
+class metaparameter;
 
 /* Context impl */
 class context_impl {
@@ -26,13 +27,15 @@ public:
   integer_type int1_ty, int8_ty, int16_ty, int32_ty, int64_ty, int128_ty;
   // Pointer types
   std::map<std::pair<type*, unsigned>, pointer_type*> ptr_tys;
-  std::map<std::pair<type*,std::vector<unsigned>>, tile_type*> tile_tys;
+  std::map<std::pair<type*, type::tile_shapes_t>, tile_type*> tile_tys;
   // Int constants
-  std::map<uint64_t, constant_int*> int_constants_;
+  std::map<std::pair<type*, uint64_t>, constant_int*> int_constants_;
   // Float constants
   std::map<double, constant_fp*> fp_constants_;
   // undef values
   std::map<type*, undef_value*> uv_constants_;
+  // Metaparameters
+  std::vector<metaparameter*> mp_constants_;
 };
 
 }
diff --git a/include/ir/instructions.h b/include/ir/instructions.h
index 047126cf2..ae752f78e 100644
--- a/include/ir/instructions.h
+++ b/include/ir/instructions.h
@@ -3,6 +3,7 @@
 
 #include <vector>
 #include "value.h"
+#include "ir/type.h"
 #include "llvm/IR/Instructions.h"
 
 namespace tdl{
@@ -358,7 +359,7 @@ public:
 
 class retile_inst: public unary_inst {
 protected:
-  retile_inst(value *arg, const std::vector<unsigned> &shape_suffix, const std::string &name, instruction *next);
+  retile_inst(value *arg, const type::tile_shapes_t &shapes, const std::string &name, instruction *next);
   static std::string shape_suffix(ir::type* ty);
 };
 
@@ -370,7 +371,7 @@ private:
   std::string repr_impl() const { return "reshape" + shape_suffix(get_type()); }
 
 public:
-  static instruction* create(value *arg, const std::vector<unsigned> &shape_suffix,
+  static instruction* create(value *arg, const type::tile_shapes_t &shape_suffix,
                       const std::string &name = "", instruction *next = nullptr);
 };
 
@@ -382,7 +383,7 @@ private:
   std::string repr_impl() const { return "splat" + shape_suffix(get_type()); }
 
 public:
-  static instruction* create(value *arg, const std::vector<unsigned> &shape_suffix,
+  static instruction* create(value *arg, const type::tile_shapes_t &shape_suffix,
                       const std::string &name = "", instruction *next = nullptr);
 };
 
@@ -394,7 +395,7 @@ private:
   std::string repr_impl() const { return "broadcast" + shape_suffix(get_type()); }
 
 public:
-  static instruction* create(value *arg, const std::vector<unsigned> &shape_suffix,
+  static instruction* create(value *arg, const type::tile_shapes_t &shape_suffix,
                       const std::string &name = "", instruction *next = nullptr);
 };
 
@@ -414,7 +415,7 @@ private:
   std::string repr_impl() const { return "get_global_range(" + std::to_string(axis_) + ")"; }
 
 public:
-  static instruction* create(context &ctx, unsigned axis, unsigned size,
+  static instruction* create(context &ctx, unsigned axis, type::tile_shapes_t::value_type size,
                              const std::string &name = "",
                              instruction *next = nullptr);
   unsigned get_axis() const { return axis_; }
diff --git a/include/ir/module.h b/include/ir/module.h
index 347178fda..26b6c6769 100644
--- a/include/ir/module.h
+++ b/include/ir/module.h
@@ -3,6 +3,7 @@
 
 #include <map>
 #include <set>
+#include <stack>
 #include <string>
 #include <functional>
 #include "builder.h"
@@ -12,6 +13,7 @@ namespace tdl{
 namespace ast{
 
 class iteration_statement;
+class compound_statement;
 
 }
 
@@ -69,6 +71,10 @@ public:
   const functions_list_t &get_function_list() const { return functions_; }
   functions_list_t &get_function_list()             { return functions_; }
   function *get_or_insert_function(const std::string &name, function_type *ty);
+  // Scope
+  void push_scope(const ast::compound_statement* scope)   { scopes_.push(scope); }
+  void pop_scope()                                        { scopes_.pop(); }
+  const ast::compound_statement* get_scope()              { return scopes_.top(); }
 
 
 private:
@@ -83,6 +89,7 @@ private:
   symbols_map_t symbols_;
   std::function<ir::value*()> continue_fn_;
   std::map<value*, value**> current_phi_;
+  std::stack<const ast::compound_statement*> scopes_;
 };
 
 }
diff --git a/include/ir/type.h b/include/ir/type.h
index 9f29b465b..6e2049ddd 100644
--- a/include/ir/type.h
+++ b/include/ir/type.h
@@ -3,6 +3,7 @@
 
 #include <vector>
 #include <iostream>
+#include <set>
 
 namespace tdl{
 namespace ir{
@@ -10,9 +11,13 @@ namespace ir{
 class context;
 class value;
 class integer_type;
+class constant_int;
 
 /* Type */
 class type {
+public:
+  typedef std::vector<constant_int*>	         tile_shapes_t;
+
 protected:
   typedef std::vector<type*>                  contained_tys_vec_t;
   typedef contained_tys_vec_t::iterator       ty_iterator;
@@ -54,7 +59,7 @@ public:
   unsigned get_tile_bitwidth() const;
   unsigned get_primitive_size_in_bits() const;
   type *get_scalar_ty() const;
-  const std::vector<unsigned> &get_tile_shapes() const;
+  const tile_shapes_t& get_tile_shapes() const;
   unsigned get_tile_num_elements() const;
   type *get_tile_element_ty() const;
   unsigned get_pointer_address_space() const;
@@ -94,9 +99,25 @@ public:
   static integer_type *get_int64_ty(context &ctx);
   static integer_type *get_int128_ty(context &ctx);
 
+  // Attributes
+  type* set_tunable()   { is_tunable_ = true;     return this; }
+  type* set_readonly()  { is_readonly_ = true;    return this; }
+  type* set_writeonly() { is_writeonly_ = true;   return this; }
+  type* set_kernel()    { is_kernel_ = true;      return this; }
+
+  bool get_tunable()    { return is_tunable_; }
+  bool get_readonly()   { return is_readonly_; }
+  bool get_writeonly()  { return is_writeonly_; }
+  bool get_kernel()     { return is_kernel_; }
+
 private:
   context &ctx_;
   id_t id_;
+  // attributes
+  bool is_tunable_;
+  bool is_readonly_;
+  bool is_writeonly_;
+  bool is_kernel_;
 
 protected:
   contained_tys_vec_t contained_tys_;
@@ -132,21 +153,24 @@ public:
 
 class tile_type: public composite_type {
 private:
-  tile_type(type *ty, const std::vector<unsigned> &shapes);
+  tile_type(type *ty, const tile_shapes_t &shapes);
   static bool is_valid_elt_ty(type *ty);
 
 public:
   // accessors
-  const std::vector<unsigned>& get_shapes() const { return shapes_; }
+  const tile_shapes_t& get_shapes() const { return shapes_; }
   unsigned get_num_elements() const;
   unsigned get_bitwidth() const;
 
   // factory methods
-  static tile_type* get(type *ty, const std::vector<unsigned> &shapes);
+  static tile_type* get(type *ty, const tile_shapes_t &shapes);
   static tile_type* get_same_shapes(type *ty, type *ref);
 
+  // shortcut to get a 1 element in the shape
+  static tile_shapes_t::value_type make_one(context &ctx);
+
 private:
-  std::vector<unsigned> shapes_;
+  tile_shapes_t shapes_;
 };
 
 class pointer_type: public type {
diff --git a/lib/ast/lowering.cpp b/lib/ast/lowering.cpp
index dee27d139..993856b2d 100644
--- a/lib/ast/lowering.cpp
+++ b/lib/ast/lowering.cpp
@@ -100,6 +100,7 @@ void node::implicit_broadcast(ir::module *mod, ir::value *&lhs, ir::value *&rhs)
   ir::builder &builder = mod->get_builder();
   ir::type *lhs_ty = lhs->get_type();
   ir::type *rhs_ty = rhs->get_type();
+  ir::type::tile_shapes_t::value_type one = ir::tile_type::make_one(mod->get_context());
   // Both are scalar
   if(!lhs_ty->is_tile_ty() && !rhs_ty->is_tile_ty())
     return;
@@ -111,30 +112,30 @@ void node::implicit_broadcast(ir::module *mod, ir::value *&lhs, ir::value *&rhs)
     return;
   }
   // Both are arrays
-  std::vector<unsigned> lhs_shapes = lhs->get_type()->get_tile_shapes();
-  std::vector<unsigned> rhs_shapes = rhs->get_type()->get_tile_shapes();
+  auto lhs_shapes = lhs->get_type()->get_tile_shapes();
+  auto rhs_shapes = rhs->get_type()->get_tile_shapes();
   if(lhs_shapes == rhs_shapes)
     return;
   int lhs_dim = lhs_shapes.size();
   int rhs_dim = rhs_shapes.size();
-  std::vector<unsigned> &shortest = (lhs_dim < rhs_dim)?lhs_shapes:rhs_shapes;
-  std::vector<unsigned> &longest  = (lhs_dim < rhs_dim)?rhs_shapes:lhs_shapes;
+  auto &shortest = (lhs_dim < rhs_dim)?lhs_shapes:rhs_shapes;
+  auto &longest  = (lhs_dim < rhs_dim)?rhs_shapes:lhs_shapes;
   size_t ndim = longest.size();
   int off = longest.size() - shortest.size();
   for(int i = longest.size() - 1; i>= 0; i--){
-    if(shortest[off + i] != longest[i] && shortest[off + i] != 1 && longest[i] != 1)
+    if(shortest[off + i] != longest[i] && shortest[off + i] != one && longest[i] != one)
       throw std::runtime_error("cannot broadcast");
   }
   // Pad
   for(size_t i = 0; i < off; i++)
-    shortest.insert(shortest.begin(), 1);
+    shortest.insert(shortest.begin(), one);
   ir::value *&target = (lhs_dim < rhs_dim)?lhs:rhs;
   if(off > 0)
     target = builder.create_reshape(target, shortest);
   // Broadcast
-  std::vector<unsigned> shapes(ndim);
+  ir::type::tile_shapes_t shapes(ndim);
   for(size_t i = 0; i < ndim; i++)
-    shapes[i] = std::max(shortest[i], longest[i]);
+    shapes[i] = shortest[i]==one?longest[i]:shortest[i];
   if(shapes != lhs_shapes)
     lhs = builder.create_broadcast(lhs, shapes);
   if(shapes != rhs_shapes)
@@ -148,14 +149,15 @@ inline bool is_terminator(ir::value* x) {
 
 /* Translation unit */
 ir::value* translation_unit::codegen(ir::module *mod) const{
-  decls_->codegen(mod);
+  mod->push_scope(nullptr);
+  decls_.codegen(mod);
   return nullptr;
 }
 
 /* Declaration specifier */
-ir::type* declaration_specifier::type(ir::module *mod) const {
+ir::type* typed_declaration_specifier::type(ir::module *mod) const {
   ir::context &ctx = mod->get_context();
-  switch (spec_) {
+  switch (ty_) {
   case VOID_T:      return ir::type::get_void_ty(ctx);
   case INT1_T:      return ir::type::get_int1_ty(ctx);
   case INT8_T:      return ir::type::get_int8_ty(ctx);
@@ -164,7 +166,18 @@ ir::type* declaration_specifier::type(ir::module *mod) const {
   case INT64_T:     return ir::type::get_int64_ty(ctx);
   case FLOAT32_T:   return ir::type::get_float_ty(ctx);
   case FLOAT64_T:   return ir::type::get_double_ty(ctx);
-  default: throw std::runtime_error("unreachable");
+  default:          throw std::runtime_error("unreachable");
+  }
+}
+
+ir::type* storage_declaration_specifier::type(ir::module *mod) const {
+  ir::type* result = decl_spec_->type(mod);
+  switch(storage_spec_){
+  case TUNABLE_T:   return result->set_tunable();
+  case KERNEL_T:    return result->set_kernel();
+  case READONLY_T:  return result->set_readonly();
+  case WRITEONLY_T: return result->set_writeonly();
+  default:          throw std::runtime_error("unreachable");
   }
 }
 
@@ -194,10 +207,10 @@ const std::string &identifier::name() const{
 }
 
 // Tile
-ir::type* tile::type_impl(ir::module*, ir::type *type) const{
-  std::vector<unsigned> shapes;
+ir::type* tile::type_impl(ir::module *mod, ir::type *type) const{
+  ir::type::tile_shapes_t shapes;
   for(constant *cst: shapes_->values())
-    shapes.push_back(cst->value());
+    shapes.push_back((ir::constant_int*)cst->codegen(mod));
   return ir::tile_type::get(type, shapes);
 }
 
@@ -245,6 +258,7 @@ ir::value* function_definition::codegen(ir::module *mod) const{
 
 /* Statements */
 ir::value* compound_statement::codegen(ir::module* mod) const{
+  mod->push_scope(this);
   if(decls_)
     decls_->codegen(mod);
   if(statements_){
@@ -254,6 +268,7 @@ ir::value* compound_statement::codegen(ir::module* mod) const{
         return current;
     }
   }
+  mod->pop_scope();
   return nullptr;
 }
 
@@ -337,7 +352,7 @@ ir::value* continue_statement::codegen(ir::module *mod) const{
 /* Declaration */
 ir::value* declaration::codegen(ir::module* mod) const{
   for(initializer *init: init_->values())
-    init->specifier(spec_);
+    init->set_specifier(spec_);
   init_->codegen(mod);
   return nullptr;
 }
@@ -347,7 +362,7 @@ ir::type* initializer::type_impl(ir::module *mod, ir::type *type) const{
   return decl_->type(mod, type);
 }
 
-void initializer::specifier(const declaration_specifier *spec) {
+void initializer::set_specifier(const declaration_specifier *spec) {
   spec_ = spec;
 }
 
@@ -355,6 +370,11 @@ ir::value* initializer::codegen(ir::module * mod) const{
   ir::type *ty = decl_->type(mod, spec_->type(mod));
   std::string name = decl_->id()->name();
   ir::value *value = ir::undef_value::get(ty);
+  if(ty->get_tunable()){
+    assert(expr_ == nullptr);
+    //TODO
+    value = ir::metaparameter::create(mod->get_context(), ty, 4, 8);
+  }
   if(expr_){
     value = expr_->codegen(mod);
     value = explicit_cast(mod->get_builder(), value, ty);
@@ -464,7 +484,7 @@ ir::value* binary_operator::codegen(ir::module *mod) const{
 // get_global_range
 ir::value* get_global_range::codegen(ir::module *mod) const {
   ir::builder &builder = mod->get_builder();
-  return builder.create_get_global_range(axis_->value(), size_->value());
+  return builder.create_get_global_range(axis_->value(), (ir::constant_int*)size_->codegen(mod));
 }
 
 
@@ -487,11 +507,13 @@ ir::value* matmul_expression::codegen(ir::module *mod) const {
 ir::value* indexing_expression::codegen(ir::module *mod) const{
   ir::value *in = mod->get_value(id_->name());
   const std::vector<slice*> &slices = slices_->values();
-  std::vector<unsigned> in_shapes = in->get_type()->get_tile_shapes();
-  std::vector<unsigned> out_shapes(slices.size());
+  auto in_shapes = in->get_type()->get_tile_shapes();
+  ir::type::tile_shapes_t::value_type one = ir::tile_type::make_one(mod->get_context());
+  ir::type::tile_shapes_t out_shapes(slices.size());
+  // create shapes
   size_t current = 0;
   for(size_t i = 0; i < out_shapes.size(); i++)
-    out_shapes[i] = (slices[i]->type()==NEWAXIS)?1:in_shapes[current++];
+    out_shapes[i] = (slices[i]->type()==NEWAXIS)?one:in_shapes[current++];
   return mod->get_builder().create_reshape(in, out_shapes);
 }
 
@@ -586,8 +608,8 @@ int constant::value() const{
 
 /* Constant range */
 ir::value* constant_range::codegen(ir::module *mod) const{
-  return ir::constant_range::get((ir::constant*)first_->codegen(mod),
-                                 (ir::constant*)last_->codegen(mod));
+  return ir::constant_range::get((ir::constant_int*)first_->codegen(mod),
+                                 (ir::constant_int*)last_->codegen(mod));
 }
 
 /* Named */
diff --git a/lib/codegen/barriers.cpp b/lib/codegen/barriers.cpp
index 0466d5ef3..df017931b 100644
--- a/lib/codegen/barriers.cpp
+++ b/lib/codegen/barriers.cpp
@@ -45,10 +45,15 @@ void barriers::get_written_intervals(ir::instruction *i, interval_vec_t &res){
 
 void barriers::insert_barrier(ir::instruction *instr, ir::builder &builder) {
   if(auto *phi = dynamic_cast<ir::phi_node*>(instr)) {
+    std::set<ir::value*> incoming;
     for(unsigned n = 0; n < phi->get_num_incoming(); n++){
-      ir::basic_block *block = phi->get_incoming_block(n);
-      builder.set_insert_point(block->get_inst_list().back());
-      builder.create_barrier();
+      ir::instruction *inc_val = dynamic_cast<ir::instruction*>(phi->get_incoming_value(n));
+      assert(inc_val);
+      if(incoming.insert(inc_val).second){
+        ir::basic_block *block = inc_val->get_parent();
+        builder.set_insert_point(block->get_inst_list().back());
+        builder.create_barrier();
+      }
     }
   }
   else {
@@ -57,15 +62,15 @@ void barriers::insert_barrier(ir::instruction *instr, ir::builder &builder) {
   }
 }
 
-void barriers::add(ir::basic_block *block, interval_vec_t &not_synced, std::set<ir::instruction*> &insert_pts) {
-  for(ir::instruction *i: block->get_inst_list()){
+void barriers::add(ir::basic_block *block, interval_vec_t &not_synced, ir::builder &builder) {
+  ir::basic_block::inst_list_t instructions = block->get_inst_list();
+  for(ir::instruction *i: instructions){
     interval_vec_t read, written;
     get_read_intervals(i, read);
     get_written_intervals(i, written);
-    if(intersect(not_synced, read)
-        || intersect(not_synced, written)) {
+    if(intersect(not_synced, read)) {
       not_synced.clear();
-      insert_pts.insert(i);
+      insert_barrier(i, builder);
     }
     std::copy(written.begin(), written.end(), std::back_inserter(not_synced));
   }
@@ -76,12 +81,8 @@ void barriers::run(ir::module &mod) {
   for(ir::function *fn: mod.get_function_list()){
     // find barrier location
     interval_vec_t not_synced;
-    std::set<ir::instruction*> insert_pts;
     for(ir::basic_block *block: fn->blocks())
-      add(block, not_synced, insert_pts);
-    // insert barrier
-    for(ir::instruction *i: insert_pts)
-      insert_barrier(i, builder);
+      add(block, not_synced, builder);
   }
 }
 
diff --git a/lib/codegen/selection.cpp b/lib/codegen/selection.cpp
index ed17b2fcb..8665714a2 100644
--- a/lib/codegen/selection.cpp
+++ b/lib/codegen/selection.cpp
@@ -44,6 +44,7 @@ llvm::Type *distributed_tile::make_vector_ty(llvm::Type *ty, size_t vector_size)
   return VectorType::get(ty, vector_size);
 }
 
+
 distributed_tile::distributed_tile(Type *ty, const shapes_t &shapes, const axes_t &axes, llvm::IRBuilder<> &builder, bool vectorize)
     : tile(make_vector_ty(ty, vectorize?axes[0].contiguous:1), shapes), axes_(axes), builder_(builder) {
   vector_size_ = vectorize?ty_->getVectorNumElements():1;
@@ -149,6 +150,16 @@ Value* shared_tile::get_value(indices_t idx) {
   return builder_.CreateLoad(ptr);
 }
 
+/* Utils */
+std::vector<unsigned> selection::extract_shapes(ir::value *v) {
+  const auto& shapes = v->get_type()->get_tile_shapes();
+  std::vector<unsigned> result(shapes.size());
+  for(ir::constant_int* cst: shapes)
+    result.push_back(cst->get_value());
+  return result;
+}
+
+
 /* convert ir::type to Type */
 Type *selection::llvm_type(ir::type *ty, LLVMContext &ctx) {
   // function
@@ -299,11 +310,12 @@ std::vector<Value*> delinearize(Value *trailing, std::vector<unsigned> &shapes,
 }
 
 void selection::init_axes(ir::value *v, IRBuilder<> &builder, Value *u_thread_id, Value *u_warp_id) {
-  const auto& shapes = v->get_type()->get_tile_shapes();
+  const auto& shapes = extract_shapes(v);
   size_t dim = shapes.size();
   std::vector<unsigned> contiguous(dim);
   std::vector<unsigned> warp_size(dim);
   std::vector<unsigned> n_warps(dim);
+  std::cout << v->get_name() << " " << typeid(*v).name() << std::endl;
   for(unsigned i = 0; i < shapes.size(); i++){
     std::string str_i = std::to_string(i);
     contiguous[i] = *params_->get_param(v, "p0.d" + str_i);
@@ -336,7 +348,7 @@ void selection::create_grids(std::vector<ir::value*> &grids,
   // get number of dimensions greater than 1
   auto get_tile_gt1_dim = [&](ir::value *v){
     unsigned result = 0;
-    for(unsigned shape: v->get_type()->get_tile_shapes()) {
+    for(unsigned shape: extract_shapes(v)) {
       result += (shape > 1)?shape:0;
     }
     return result;
@@ -353,7 +365,7 @@ void selection::create_grids(std::vector<ir::value*> &grids,
       for(ir::value *op: user->ops())
         bind_references(op);
     // bind
-    const auto& shapes = v->get_type()->get_tile_shapes();
+    const auto& shapes = extract_shapes(v);
     if(dynamic_cast<ir::copy_to_shared_inst*>(v) || buffer_info_->is_double(v))
       return;
     for(size_t d = 0; d < shapes.size(); d++){
@@ -385,7 +397,7 @@ void selection::create_tile(ir::value *v, IRBuilder<> &builder,
     for(ir::value *op: user->ops())
       create_tile(op, builder, references, seen, sh_mem_ptr);
   LLVMContext &ctx = builder.getContext();
-  const auto& shapes = v->get_type()->get_tile_shapes();
+  const auto& shapes = extract_shapes(v);
   Type* ty = llvm_type(v->get_type()->get_scalar_ty(), ctx);
   // create shared tile
   if(dynamic_cast<ir::copy_to_shared_inst*>(v) || (buffer_info_->is_double(v))){
@@ -429,7 +441,7 @@ void selection::create_tile(ir::value *v, IRBuilder<> &builder,
   }
   // create distributed tile
   else {
-    const auto &shapes = v->get_type()->get_tile_shapes();
+    const auto &shapes = extract_shapes(v);
     std::vector<distributed_axis> axes(shapes.size());
     for(size_t d = 0; d < shapes.size(); d++){
       if(shapes[d] > 1){
@@ -530,7 +542,7 @@ void selection::lower_tile_instruction(ir::instruction *ins, llvm::IRBuilder<> &
     distributed_tile* result = (distributed_tile*)ti;
     if(!ins->get_type()->is_tile_ty())
       return;
-    const auto& shapes = ins->get_type()->get_tile_shapes();
+    const auto& shapes = extract_shapes(ins);
     // global_range
     if(auto *x = dynamic_cast<ir::get_global_range_inst*>(ins)) {
       static std::array<Intrinsic::ID, 3> ctaid = {
@@ -568,7 +580,7 @@ void selection::lower_tile_instruction(ir::instruction *ins, llvm::IRBuilder<> &
     // broadcast
     else if(dynamic_cast<ir::broadcast_inst*>(ins)) {
       ir::value* in = ins->get_operand(0);
-      const auto& in_shapes = in->get_type()->get_tile_shapes();
+      const auto& in_shapes = extract_shapes(in);
       distributed_tile *in_tile = (distributed_tile*)tmap_.at(in);
       result->for_each([&](indices_t out_idx){
         indices_t in_idx = out_idx;
@@ -615,7 +627,7 @@ void selection::lower_tile_instruction(ir::instruction *ins, llvm::IRBuilder<> &
       Function *f_mul_add = Intrinsic::getDeclaration(module, Intrinsic::fmuladd, {llvm_type(C->get_type()->get_scalar_ty(), ctx)});
       result->for_each([&](indices_t idx){
         Value *res = tmap_.at(C)->get_value(idx);
-        unsigned NK = A->get_type()->get_tile_shapes()[1];
+        unsigned NK = extract_shapes(A)[1];
         for(unsigned K = 0; K < NK; ++K){
           indices_t a_idx = {idx[0], builder.getInt32(K)};
           indices_t b_idx = {idx[1], builder.getInt32(K)};
diff --git a/lib/codegen/tune.cpp b/lib/codegen/tune.cpp
index 5de551924..3dc5c4e87 100644
--- a/lib/codegen/tune.cpp
+++ b/lib/codegen/tune.cpp
@@ -3,6 +3,8 @@
 #include "ir/type.h"
 #include "ir/module.h"
 #include "ir/function.h"
+#include "ir/context_impl.h"
+
 #include <cstdlib>
 
 
@@ -29,7 +31,8 @@ void tune::init_c_phi(ir::instruction *v) {
 
 void tune::init_c_graph(ir::instruction *v) {
   // Reference shape
-  std::vector<unsigned> shapes;
+  ir::type::tile_shapes_t::value_type one = ir::tile_type::make_one(v->get_parent()->get_context());
+  ir::type::tile_shapes_t shapes;
   if(auto *store = dynamic_cast<ir::store_inst*>(v))
     shapes = store->get_pointer_operand()->get_type()->get_tile_shapes();
   else
@@ -39,7 +42,7 @@ void tune::init_c_graph(ir::instruction *v) {
     ir::value *op = v->get_operand(0);
     unsigned current = 0;
     for(unsigned i = 0; i < shapes.size(); i ++){
-      if(shapes[i] == 1)
+      if(shapes[i] == one)
         static_params_.insert({{v, i}, 1});
       else
         add_constraint({v, i}, {op, current++});
@@ -99,6 +102,7 @@ void tune::connected_components(node_t x, const std::vector<unsigned *> vals, st
 std::vector<unsigned*> tune::get_params(ir::module &mod) {
   std::vector<unsigned *> result;
   std::set<unsigned*> seen;
+
   for(ir::function *fn: mod.get_function_list())
   for(ir::basic_block *block: fn->blocks())
   for(ir::instruction *i : block->get_inst_list())
@@ -143,8 +147,9 @@ void tune::create_grids(std::vector<ir::instruction*> &grids,
   // get number of dimensions greater than 1
   auto get_tile_gt1_dim = [&](ir::value *v){
     unsigned result = 0;
-    for(unsigned shape: v->get_type()->get_tile_shapes()) {
-      result += (shape > 1)?shape:0;
+    auto one = ir::tile_type::make_one(fn->get_fn_type()->get_context());
+    for(ir::constant_int *shape: v->get_type()->get_tile_shapes()) {
+      result += (shape != one);
     }
     return result;
   };
@@ -194,8 +199,8 @@ for(ir::function *fn: mod.get_function_list()){
       unsigned *s1 = params_[i]["p1.d" + strk];
       unsigned *s2 = params_[i]["p2.d" + strk];
       unsigned multiple = (*s0)*(*s1)*(*s2);
-      if(shapes[k] % multiple != 0)
-        errors[i].push_back("for dim " + strk + ": shape (" + to_string(shapes[k]) + ")"
+      if(shapes[k]->get_value() % multiple != 0)
+        errors[i].push_back("for dim " + strk + ": shape (" + to_string(shapes[k]->get_value()) + ")"
                             " is not a multiple of layout (" + to_string(multiple)  + ")");
     }
     // the number of thread per warp must be 32
diff --git a/lib/ir/builder.cpp b/lib/ir/builder.cpp
index cb5edd2b6..6622125b5 100644
--- a/lib/ir/builder.cpp
+++ b/lib/ir/builder.cpp
@@ -244,15 +244,15 @@ value *builder::create_store(value *ptr, value *val, const std::string &name){
 //                               tile instructions
 //===----------------------------------------------------------------------===//
 
-value *builder::create_reshape(value *arg, const std::vector<unsigned> &shapes, const std::string &name) {
+value *builder::create_reshape(value *arg, const type::tile_shapes_t &shapes, const std::string &name) {
   return insert(reshape_inst::create(arg, shapes, name));
 }
 
-value *builder::create_splat(value *arg, const std::vector<unsigned> &shapes, const std::string &name) {
+value *builder::create_splat(value *arg, const type::tile_shapes_t &shapes, const std::string &name) {
   return insert(splat_inst::create(arg, shapes, name));
 }
 
-value *builder::create_broadcast(value *arg, const std::vector<unsigned> &shapes, const std::string &name) {
+value *builder::create_broadcast(value *arg, const type::tile_shapes_t &shapes, const std::string &name) {
   return insert(broadcast_inst::create(arg, shapes, name));
 }
 
@@ -260,7 +260,7 @@ value *builder::create_broadcast(value *arg, const std::vector<unsigned> &shapes
 //                               built-in instructions
 //===----------------------------------------------------------------------===//
 
-value *builder::create_get_global_range(unsigned axis, unsigned size, const std::string &name) {
+value *builder::create_get_global_range(unsigned axis, type::tile_shapes_t::value_type size, const std::string &name) {
   return insert(get_global_range_inst::create(ctx_, axis, size, name));
 }
 
diff --git a/lib/ir/constant.cpp b/lib/ir/constant.cpp
index 58f3b1ab7..87f669e4d 100644
--- a/lib/ir/constant.cpp
+++ b/lib/ir/constant.cpp
@@ -48,24 +48,27 @@ constant *constant::get_all_ones_value(type *ty) {
 constant_int::constant_int(type *ty, uint64_t value)
   : constant(ty, 0), value_(value){ }
 
-constant *constant_int::get(type *ty, uint64_t value) {
-  return new constant_int(ty, value);
+constant_int *constant_int::get(type *ty, uint64_t value) {
+  context_impl *impl = ty->get_context().p_impl.get();
+  constant_int *& cst = impl->int_constants_[std::make_pair(ty, value)];
+  if(cst == nullptr)
+    cst = new constant_int(ty, value);
+  return cst;
 }
 
 // constant_range
 // FIXME use something like APInt
 
-constant_range::constant_range(type *ty, uint64_t first, uint64_t last)
+constant_range::constant_range(type *ty, constant_int *first, constant_int *last)
   : constant(ty, 0), first_(first), last_(last){ }
 
-constant *constant_range::get(constant *first, constant *last) {
+constant *constant_range::get(constant_int *first, constant_int *last) {
   assert(first->get_type()->is_integer_ty());
   assert(first->get_type() == last->get_type());
   unsigned vfirst = ((constant_int*)first)->get_value();
-  unsigned vlast = ((constant_int*)last)->get_value();
-  assert(vlast > vfirst);
-  type *ty = tile_type::get(first->get_type(), {vlast - vfirst});
-  return new constant_range(ty, vfirst, vlast);
+  assert(vfirst == 0);
+  type *ty = tile_type::get(first->get_type(), {last});
+  return new constant_range(ty, first, last);
 }
 
 
@@ -94,6 +97,17 @@ constant *constant_fp::get(context &ctx, double v){
   return result;
 }
 
+// metaparameter
+metaparameter::metaparameter(type *ty, unsigned lo, unsigned hi)
+  : constant_int(ty, 0), lo_(lo), hi_(hi){ }
+
+metaparameter* metaparameter::create(context &ctx, type *ty, unsigned lo, unsigned hi) {
+  context_impl *impl = ctx.p_impl.get();
+  metaparameter *result = new metaparameter(ty, lo, hi);
+  impl->mp_constants_.push_back(result);
+  return result;
+}
+
 // undef value
 undef_value::undef_value(type *ty)
   : constant(ty, 0) { }
diff --git a/lib/ir/instructions.cpp b/lib/ir/instructions.cpp
index acf0c0329..38adcc377 100644
--- a/lib/ir/instructions.cpp
+++ b/lib/ir/instructions.cpp
@@ -409,7 +409,7 @@ std::string retile_inst::shape_suffix(ir::type* ty){
   std::string res = "[";
   const auto& shapes = ty->get_tile_shapes();
   for(unsigned i = 0; i < shapes.size(); i++){
-    res += std::to_string(ty->get_tile_shapes()[i]);
+    res += std::to_string(ty->get_tile_shapes()[i]->get_value());
     if(i < shapes.size() - 1)
       res += ", ";
   }
@@ -417,13 +417,13 @@ std::string retile_inst::shape_suffix(ir::type* ty){
   return res;
 }
 
-retile_inst::retile_inst(value *arg, const std::vector<unsigned> &shapes,
+retile_inst::retile_inst(value *arg, const type::tile_shapes_t &shapes,
                          const std::string &name, instruction *next)
    : unary_inst(tile_type::get(arg->get_type()->get_scalar_ty(), shapes), arg, name, next) { }
 
 // reshape
 
-instruction* reshape_inst::create(value *arg, const std::vector<unsigned> &shapes,
+instruction* reshape_inst::create(value *arg, const type::tile_shapes_t &shapes,
                                   const std::string &name, instruction *next) {
   return new reshape_inst(arg, shapes, name, next);
 }
@@ -431,14 +431,14 @@ instruction* reshape_inst::create(value *arg, const std::vector<unsigned> &shape
 
 // splat
 
-instruction* splat_inst::create(value *arg, const std::vector<unsigned> &shapes,
+instruction* splat_inst::create(value *arg, const type::tile_shapes_t &shapes,
                                   const std::string &name, instruction *next) {
   return new splat_inst(arg, shapes, name, next);
 }
 
 // broadcast
 
-instruction* broadcast_inst::create(value *arg, const std::vector<unsigned> &shapes,
+instruction* broadcast_inst::create(value *arg, const type::tile_shapes_t &shapes,
                                   const std::string &name, instruction *next) {
   return new broadcast_inst(arg, shapes, name, next);
 }
@@ -470,7 +470,7 @@ get_global_range_inst::get_global_range_inst(type *ty, unsigned axis,
 
 }
 
-instruction* get_global_range_inst::create(context &ctx, unsigned axis, unsigned size,
+instruction* get_global_range_inst::create(context &ctx, unsigned axis, type::tile_shapes_t::value_type size,
                                            const std::string &name, instruction *next) {
   type *int_ty = type::get_int32_ty(ctx);
   type *tile_ty = tile_type::get(int_ty, {size});
diff --git a/lib/ir/type.cpp b/lib/ir/type.cpp
index c790120fb..5aebd94a5 100644
--- a/lib/ir/type.cpp
+++ b/lib/ir/type.cpp
@@ -3,6 +3,7 @@
 #include "ir/context.h"
 #include "ir/context_impl.h"
 #include "ir/value.h"
+#include "ir/constant.h"
 
 namespace tdl{
 namespace ir{
@@ -63,7 +64,7 @@ type * type::get_pointer_element_ty() const {
 }
 
 
-const std::vector<unsigned> &type::get_tile_shapes() const {
+const type::tile_shapes_t &type::get_tile_shapes() const {
   assert(is_tile_ty());
   return ((tile_type*)this)->get_shapes();
 }
@@ -148,7 +149,7 @@ bool composite_type::index_valid(value *idx) const{
 //                               tile_type class
 //===----------------------------------------------------------------------===//
 
-tile_type::tile_type(type *ty, const std::vector<unsigned> &shapes)
+tile_type::tile_type(type *ty, const tile_shapes_t &shapes)
     : composite_type(ty->get_context(), TileTyID), shapes_(shapes) {
   contained_tys_.push_back(ty);
 }
@@ -159,8 +160,8 @@ bool tile_type::is_valid_elt_ty(type *ty) {
 
 unsigned tile_type::get_num_elements() const {
   unsigned res = 1;
-  for(unsigned shape: shapes_)
-    res *= shape;
+  for(auto shape: shapes_)
+    res *= shape->get_value();
   return res;
 }
 
@@ -168,7 +169,7 @@ unsigned tile_type::get_bitwidth() const {
   return get_num_elements() * get_tile_element_ty()->get_primitive_size_in_bits();
 }
 
-tile_type* tile_type::get(type *elt_ty, const std::vector<unsigned> &shapes) {
+tile_type* tile_type::get(type *elt_ty, const tile_shapes_t &shapes) {
   assert(elt_ty && "Can't get a tile of <null> type!");
   assert(shapes.size() && "Can't create a tile with empty shapes!");
   assert(is_valid_elt_ty(elt_ty) && "Invalid type for pointer element!");
@@ -185,6 +186,10 @@ tile_type* tile_type::get_same_shapes(type *ty, type *ref){
   return get(ty, ref->get_tile_shapes());
 }
 
+type::tile_shapes_t::value_type tile_type::make_one(ir::context& ctx){
+  return constant_int::get(type::get_int32_ty(ctx), 1);
+}
+
 
 //===----------------------------------------------------------------------===//
 //                               function_type class