diff --git a/crates/concrete_ast/src/expressions.rs b/crates/concrete_ast/src/expressions.rs
index 818c666..92818e9 100644
--- a/crates/concrete_ast/src/expressions.rs
+++ b/crates/concrete_ast/src/expressions.rs
@@ -99,16 +99,16 @@ pub enum BitwiseOp {
 
 #[derive(Clone, Debug, Eq, PartialEq)]
 pub struct MatchExpr {
-    pub value: Box<Expression>,
+    pub expr: Box<Expression>,
     pub variants: Vec<MatchVariant>,
     pub span: Span,
 }
 
 #[derive(Clone, Debug, Eq, PartialEq)]
 pub struct IfExpr {
-    pub value: Box<Expression>,
-    pub contents: Vec<Statement>,
-    pub r#else: Option<Vec<Statement>>,
+    pub cond: Box<Expression>,
+    pub block_stmts: Vec<Statement>,
+    pub else_stmts: Option<Vec<Statement>>,
     pub span: Span,
 }
 
diff --git a/crates/concrete_ast/src/statements.rs b/crates/concrete_ast/src/statements.rs
index f836281..0d2f348 100644
--- a/crates/concrete_ast/src/statements.rs
+++ b/crates/concrete_ast/src/statements.rs
@@ -18,7 +18,7 @@ pub enum Statement {
 
 #[derive(Clone, Debug, Eq, PartialEq)]
 pub enum LetStmtTarget {
-    Simple { name: Ident, r#type: TypeSpec },
+    Simple { id: Ident, r#type: TypeSpec },
     Destructure(Vec<Binding>),
 }
 
@@ -38,15 +38,15 @@ pub struct ReturnStmt {
 
 #[derive(Clone, Debug, Eq, PartialEq)]
 pub struct AssignStmt {
-    pub target: PathOp,
+    pub lvalue: PathOp,
     pub derefs: usize,
-    pub value: Expression,
+    pub rvalue: Expression,
     pub span: Span,
 }
 
 #[derive(Clone, Debug, Eq, Hash, PartialEq)]
 pub struct Binding {
-    pub name: Ident,
+    pub id: Ident,
     pub rename: Option<Ident>,
     pub r#type: TypeSpec,
 }
@@ -56,12 +56,12 @@ pub struct ForStmt {
     pub init: Option<LetStmt>,
     pub condition: Option<Expression>,
     pub post: Option<AssignStmt>,
-    pub contents: Vec<Statement>,
+    pub block_stmts: Vec<Statement>,
     pub span: Span,
 }
 
 #[derive(Clone, Debug, Eq, PartialEq)]
 pub struct WhileStmt {
-    pub value: Expression,
-    pub contents: Vec<Statement>,
+    pub condition: Expression,
+    pub block_stmts: Vec<Statement>,
 }
diff --git a/crates/concrete_check/src/linearity_check.rs b/crates/concrete_check/src/linearity_check.rs
index 11bf651..fbe228a 100644
--- a/crates/concrete_check/src/linearity_check.rs
+++ b/crates/concrete_check/src/linearity_check.rs
@@ -296,10 +296,10 @@ impl LinearityChecker {
             }
             Statement::If(if_stmt) => {
                 // Process all components of an if expression
-                let cond_apps = self.count_in_expression(name, &if_stmt.value);
-                let then_apps = self.count_in_statements(name, &if_stmt.contents);
+                let cond_apps = self.count_in_expression(name, &if_stmt.cond);
+                let then_apps = self.count_in_statements(name, &if_stmt.block_stmts);
                 let else_apps;
-                let else_statements = &if_stmt.r#else;
+                let else_statements = &if_stmt.else_stmts;
                 if let Some(else_statements) = else_statements {
                     else_apps = self.count_in_statements(name, else_statements);
                 } else {
@@ -308,8 +308,8 @@ impl LinearityChecker {
                 cond_apps.merge(&then_apps).merge(&else_apps)
             }
             Statement::While(while_expr) => {
-                let cond = &while_expr.value;
-                let block = &while_expr.contents;
+                let cond = &while_expr.condition;
+                let block = &while_expr.block_stmts;
                 // Handle while loops
                 self.count_in_expression(name, cond)
                     .merge(&self.count_in_statements(name, block))
@@ -320,7 +320,7 @@ impl LinearityChecker {
                 let init = &for_expr.init;
                 let cond = &for_expr.condition;
                 let post = &for_expr.post;
-                let block = &for_expr.contents;
+                let block = &for_expr.block_stmts;
                 let mut apps = Appearances::zero();
                 if let Some(init) = init {
                     if let Some(cond) = cond {
@@ -364,9 +364,9 @@ impl LinearityChecker {
 
     fn count_in_assign_statement(&self, name: &str, assign_stmt: &AssignStmt) -> Appearances {
         let AssignStmt {
-            target,
+            lvalue: target,
             derefs,
-            value,
+            rvalue: value,
             span,
         } = assign_stmt;
         // Handle assignments
@@ -434,10 +434,10 @@ impl LinearityChecker {
             Expression::If(if_expr) => {
                 // Process all components of an if expression
                 // TODO review this code. If expressions should be processed counting both branches and comparing them
-                let cond_apps = self.count_in_expression(name, &if_expr.value);
-                let then_apps = self.count_in_statements(name, &if_expr.contents);
+                let cond_apps = self.count_in_expression(name, &if_expr.cond);
+                let then_apps = self.count_in_statements(name, &if_expr.block_stmts);
                 cond_apps.merge(&then_apps);
-                if let Some(else_block) = &if_expr.r#else {
+                if let Some(else_block) = &if_expr.else_stmts {
                     let else_apps = self.count_in_statements(name, else_block);
                     cond_apps.merge(&then_apps).merge(&else_apps);
                 }
@@ -497,7 +497,7 @@ impl LinearityChecker {
             span,
         } = binding;
         match target {
-            LetStmtTarget::Simple { name, r#type } => {
+            LetStmtTarget::Simple { id: name, r#type } => {
                 match r#type {
                     TypeSpec::Simple {
                         name: variable_type,
@@ -670,9 +670,10 @@ impl LinearityChecker {
             //Statement::If(cond, then_block, else_block) => {
             Statement::If(if_stmt) => {
                 // Handle conditional statements
-                state_tbl = self.check_expr(state_tbl, depth, &if_stmt.value, context)?;
-                state_tbl = self.check_stmts(state_tbl, depth + 1, &if_stmt.contents, context)?;
-                if let Some(else_block) = &if_stmt.r#else {
+                state_tbl = self.check_expr(state_tbl, depth, &if_stmt.cond, context)?;
+                state_tbl =
+                    self.check_stmts(state_tbl, depth + 1, &if_stmt.block_stmts, context)?;
+                if let Some(else_block) = &if_stmt.else_stmts {
                     state_tbl = self.check_stmts(state_tbl, depth + 1, else_block, context)?;
                 }
                 Ok(state_tbl)
@@ -680,9 +681,9 @@ impl LinearityChecker {
             //Statement::While(cond, block) => {
             Statement::While(while_stmt) => {
                 // Handle while loops
-                state_tbl = self.check_expr(state_tbl, depth, &while_stmt.value, context)?;
+                state_tbl = self.check_expr(state_tbl, depth, &while_stmt.condition, context)?;
                 state_tbl =
-                    self.check_stmts(state_tbl, depth + 1, &while_stmt.contents, context)?;
+                    self.check_stmts(state_tbl, depth + 1, &while_stmt.block_stmts, context)?;
                 Ok(state_tbl)
             }
             //Statement::For(init, cond, post, block) => {
@@ -698,15 +699,16 @@ impl LinearityChecker {
                     //TODO check assign statement
                     //self.check_stmt_assign(depth, post)?;
                 }
-                state_tbl = self.check_stmts(state_tbl, depth + 1, &for_stmt.contents, context)?;
+                state_tbl =
+                    self.check_stmts(state_tbl, depth + 1, &for_stmt.block_stmts, context)?;
                 Ok(state_tbl)
             }
             Statement::Assign(assign_stmt) => {
                 // Handle assignments
                 let AssignStmt {
-                    target,
+                    lvalue: target,
                     derefs,
-                    value,
+                    rvalue: value,
                     span,
                 } = assign_stmt;
                 tracing::debug!("Checking assignment: {:?}", assign_stmt);
diff --git a/crates/concrete_ir/src/lowering.rs b/crates/concrete_ir/src/lowering.rs
index 6dabc96..db16ba0 100644
--- a/crates/concrete_ir/src/lowering.rs
+++ b/crates/concrete_ir/src/lowering.rs
@@ -373,7 +373,7 @@ fn lower_func(
     for stmt in &func.body {
         if let statements::Statement::Let(info) = stmt {
             match &info.target {
-                LetStmtTarget::Simple { name, r#type } => {
+                LetStmtTarget::Simple { id: name, r#type } => {
                     let ty = lower_type(&builder.ctx, r#type, builder.local_module)?;
                     builder
                         .name_to_local
@@ -391,7 +391,7 @@ fn lower_func(
         } else if let statements::Statement::For(info) = stmt {
             if let Some(info) = &info.init {
                 match &info.target {
-                    LetStmtTarget::Simple { name, r#type } => {
+                    LetStmtTarget::Simple { id: name, r#type } => {
                         let ty = lower_type(&builder.ctx, r#type, builder.local_module)?;
                         builder
                             .name_to_local
@@ -520,7 +520,7 @@ fn lower_while(builder: &mut FnBodyBuilder, info: &WhileStmt) -> Result<(), Lowe
     });
 
     let (discriminator, discriminator_type, _disc_span) =
-        lower_expression(builder, &info.value, None)?;
+        lower_expression(builder, &info.condition, None)?;
 
     let local = builder.add_temp_local(TyKind::Bool);
     let place = Place {
@@ -548,7 +548,7 @@ fn lower_while(builder: &mut FnBodyBuilder, info: &WhileStmt) -> Result<(), Lowe
     // keep idx for switch targets
     let first_then_block_idx = builder.body.basic_blocks.len();
 
-    for stmt in &info.contents {
+    for stmt in &info.block_stmts {
         lower_statement(
             builder,
             stmt,
@@ -645,7 +645,7 @@ fn lower_for(builder: &mut FnBodyBuilder, info: &ForStmt) -> Result<(), Lowering
     // keep idx for switch targets
     let first_then_block_idx = builder.body.basic_blocks.len();
 
-    for stmt in &info.contents {
+    for stmt in &info.block_stmts {
         lower_statement(
             builder,
             stmt,
@@ -687,7 +687,7 @@ fn lower_for(builder: &mut FnBodyBuilder, info: &ForStmt) -> Result<(), Lowering
 
 fn lower_if_statement(builder: &mut FnBodyBuilder, info: &IfExpr) -> Result<(), LoweringError> {
     let (discriminator, discriminator_type, _disc_span) =
-        lower_expression(builder, &info.value, None)?;
+        lower_expression(builder, &info.cond, None)?;
 
     let local = builder.add_temp_local(TyKind::Bool);
     let place = Place {
@@ -715,7 +715,7 @@ fn lower_if_statement(builder: &mut FnBodyBuilder, info: &IfExpr) -> Result<(),
     // keep idx for switch targets
     let first_then_block_idx = builder.body.basic_blocks.len();
 
-    for stmt in &info.contents {
+    for stmt in &info.block_stmts {
         lower_statement(
             builder,
             stmt,
@@ -739,7 +739,7 @@ fn lower_if_statement(builder: &mut FnBodyBuilder, info: &IfExpr) -> Result<(),
 
     let first_else_block_idx = builder.body.basic_blocks.len();
 
-    if let Some(contents) = &info.r#else {
+    if let Some(contents) = &info.else_stmts {
         for stmt in contents {
             lower_statement(
                 builder,
@@ -783,7 +783,7 @@ fn lower_if_statement(builder: &mut FnBodyBuilder, info: &IfExpr) -> Result<(),
 
 fn lower_let(builder: &mut FnBodyBuilder, info: &LetStmt) -> Result<(), LoweringError> {
     match &info.target {
-        LetStmtTarget::Simple { name, r#type } => {
+        LetStmtTarget::Simple { id: name, r#type } => {
             let ty = lower_type(&builder.ctx, r#type, builder.local_module)?;
             let (rvalue, rvalue_ty, rvalue_span) =
                 lower_expression(builder, &info.value, Some(ty.clone()))?;
@@ -819,7 +819,7 @@ fn lower_let(builder: &mut FnBodyBuilder, info: &LetStmt) -> Result<(), Lowering
 }
 
 fn lower_assign(builder: &mut FnBodyBuilder, info: &AssignStmt) -> Result<(), LoweringError> {
-    let (mut place, mut ty, _path_span) = lower_path(builder, &info.target)?;
+    let (mut place, mut ty, _path_span) = lower_path(builder, &info.lvalue)?;
 
     if !builder.body.locals[place.local].is_mutable() {
         return Err(LoweringError::NotMutable {
@@ -834,8 +834,8 @@ fn lower_assign(builder: &mut FnBodyBuilder, info: &AssignStmt) -> Result<(), Lo
             TyKind::Ref(inner, is_mut) | TyKind::Ptr(inner, is_mut) => {
                 if matches!(is_mut, Mutability::Not) {
                     Err(LoweringError::BorrowNotMutable {
-                        span: info.target.first.span,
-                        name: info.target.first.name.clone(),
+                        span: info.lvalue.first.span,
+                        name: info.lvalue.first.name.clone(),
                         type_span: ty.span,
                         program_id: builder.local_module.program_id,
                     })?;
@@ -848,7 +848,7 @@ fn lower_assign(builder: &mut FnBodyBuilder, info: &AssignStmt) -> Result<(), Lo
     }
 
     let (rvalue, rvalue_ty, rvalue_span) =
-        lower_expression(builder, &info.value, Some(ty.clone()))?;
+        lower_expression(builder, &info.rvalue, Some(ty.clone()))?;
 
     if ty.kind != rvalue_ty.kind {
         return Err(LoweringError::UnexpectedType {
@@ -860,7 +860,7 @@ fn lower_assign(builder: &mut FnBodyBuilder, info: &AssignStmt) -> Result<(), Lo
     }
 
     builder.statements.push(Statement {
-        span: Some(info.target.first.span),
+        span: Some(info.lvalue.first.span),
         kind: StatementKind::Assign(place, rvalue),
     });
 
diff --git a/crates/concrete_parser/src/grammar.lalrpop b/crates/concrete_parser/src/grammar.lalrpop
index 821d76d..e7a3ed6 100644
--- a/crates/concrete_parser/src/grammar.lalrpop
+++ b/crates/concrete_parser/src/grammar.lalrpop
@@ -503,21 +503,21 @@ pub(crate) ValueExpr: ast::expressions::ValueExpr = {
 }
 
 pub(crate) IfExpr: ast::expressions::IfExpr = {
-  <lo:@L> "if" <value:Expression> "{" <contents:StatementList> "}"
+  <lo:@L> "if" <cond:Expression> "{" <block_stmts:StatementList> "}"
     <else_stmts:("else" "{" <StatementList> "}")?> <hi:@R> => {
     ast::expressions::IfExpr {
-      value: Box::new(value),
-      contents,
-      r#else: else_stmts,
+      cond: Box::new(cond),
+      block_stmts,
+      else_stmts,
       span: Span::new(lo, hi)
     }
   }
 }
 
 pub(crate) MatchExpr: ast::expressions::MatchExpr = {
-  <lo:@L> "match" <value:Expression> "{" <variants:Comma<MatchVariant>> "}" <hi:@R> => {
+  <lo:@L> "match" <expr:Expression> "{" <variants:Comma<MatchVariant>> "}" <hi:@R> => {
     ast::expressions::MatchExpr {
-      value: Box::new(value),
+      expr: Box::new(expr),
       variants,
       span: Span::new(lo, hi)
     }
@@ -594,19 +594,19 @@ pub(crate) Statement: ast::statements::Statement = {
 }
 
 pub(crate) LetStmt: ast::statements::LetStmt = {
-  <lo:@L> "let" <is_mutable:"mut"?> <name:Ident> ":" <target_type:TypeSpec> "=" <value:Expression> <hi:@R> => ast::statements::LetStmt {
+  <lo:@L> "let" <is_mutable:"mut"?> <id:Ident> ":" <target_type:TypeSpec> "=" <value:Expression> <hi:@R> => ast::statements::LetStmt {
     is_mutable: is_mutable.is_some(),
     target: ast::statements::LetStmtTarget::Simple {
-      name,
+      id,
       r#type: target_type
     },
     value,
     span: Span::new(lo, hi),
   },
-  <lo:@L> "let" <is_mutable:"mut"?> <name:Ident> ":" <target_type:TypeSpec> "=" <value:StructInitExpr> <hi:@R> => ast::statements::LetStmt {
+  <lo:@L> "let" <is_mutable:"mut"?> <id:Ident> ":" <target_type:TypeSpec> "=" <value:StructInitExpr> <hi:@R> => ast::statements::LetStmt {
     is_mutable: is_mutable.is_some(),
     target: ast::statements::LetStmtTarget::Simple {
-      name,
+      id,
       r#type: target_type
     },
     value: ast::expressions::Expression::StructInit(value),
@@ -615,15 +615,15 @@ pub(crate) LetStmt: ast::statements::LetStmt = {
 }
 
 pub(crate) AssignStmt: ast::statements::AssignStmt = {
-  <lo:@L> <derefs:"*"*> <target:PathOp> "=" <value:Expression> <hi:@R> => ast::statements::AssignStmt {
-    target,
-    value,
+  <lo:@L> <derefs:"*"*> <lvalue:PathOp> "=" <rvalue:Expression> <hi:@R> => ast::statements::AssignStmt {
+    lvalue,
+    rvalue,
     derefs: derefs.len(),
     span: Span::new(lo, hi),
   },
-   <lo:@L> <derefs:"*"*> <target:PathOp> "=" <value:StructInitExpr> <hi:@R> => ast::statements::AssignStmt {
-    target,
-    value: ast::expressions::Expression::StructInit(value),
+   <lo:@L> <derefs:"*"*> <lvalue:PathOp> "=" <rvalue:StructInitExpr> <hi:@R> => ast::statements::AssignStmt {
+    lvalue,
+    rvalue: ast::expressions::Expression::StructInit(rvalue),
     derefs: derefs.len(),
     span: Span::new(lo, hi),
   },
@@ -637,40 +637,40 @@ pub(crate) ReturnStmt: ast::statements::ReturnStmt = {
 }
 
 pub(crate) WhileStmt: ast::statements::WhileStmt = {
-  "while" <value:Expression> "{" <contents:StatementList> "}" => {
+  "while" <condition:Expression> "{" <block_stmts:StatementList> "}" => {
     ast::statements::WhileStmt {
-      value,
-      contents,
+      condition,
+      block_stmts,
     }
   }
 }
 
 
 pub(crate) ForStmt: ast::statements::ForStmt = {
-  <lo:@L> "for" "(" <init:LetStmt?> ";" <condition:Expression?> ";" <post:AssignStmt?> ")" "{" <contents:StatementList> "}" <hi:@R> => {
+  <lo:@L> "for" "(" <init:LetStmt?> ";" <condition:Expression?> ";" <post:AssignStmt?> ")" "{" <block_stmts:StatementList> "}" <hi:@R> => {
     ast::statements::ForStmt {
       init,
       condition,
       post,
-      contents,
+      block_stmts,
       span: Span::new(lo, hi)
     }
   },
-  <lo:@L> "for" "(" <condition:Expression> ")" "{" <contents:StatementList> "}" <hi:@R> => {
+  <lo:@L> "for" "(" <condition:Expression> ")" "{" <block_stmts:StatementList> "}" <hi:@R> => {
     ast::statements::ForStmt {
       init: None,
       condition: Some(condition),
       post: None,
-      contents,
+      block_stmts, 
       span: Span::new(lo, hi)
     }
   },
-  <lo:@L> "for" "{" <contents:StatementList> "}" <hi:@R> => {
+  <lo:@L> "for" "{" <block_stmts:StatementList> "}" <hi:@R> => {
     ast::statements::ForStmt {
       init: None,
       condition: None,
       post: None,
-      contents,
+      block_stmts,
       span: Span::new(lo, hi)
     }
   }