diff --git a/analysis/src/inference.rs b/analysis/src/inference.rs
new file mode 100644
index 000000000..89f26d7cb
--- /dev/null
+++ b/analysis/src/inference.rs
@@ -0,0 +1,176 @@
+use ast::asm_analysis::{AnalysisASMFile, Expression, FunctionStatement, Machine};
+use number::FieldElement;
+
+pub fn infer<T: FieldElement>(file: AnalysisASMFile<T>) -> Result<AnalysisASMFile<T>, Vec<String>> {
+    let mut errors = vec![];
+    let mut res = AnalysisASMFile::default();
+
+    for (name, m) in file.machines {
+        match infer_machine(m) {
+            Ok(m) => {
+                res.machines.insert(name, m);
+            }
+            Err(e) => {
+                errors.extend(e);
+            }
+        }
+    }
+
+    if !errors.is_empty() {
+        Err(errors)
+    } else {
+        Ok(res)
+    }
+}
+
+fn infer_machine<T: FieldElement>(mut machine: Machine<T>) -> Result<Machine<T>, Vec<String>> {
+    let mut errors = vec![];
+
+    for f in machine.functions.iter_mut() {
+        for s in f.body.statements.iter_mut() {
+            if let FunctionStatement::Assignment(a) = s {
+                let expr_reg = match &*a.rhs {
+                    Expression::FunctionCall(c) => {
+                        let instr = machine
+                            .instructions
+                            .iter()
+                            .find(|i| i.name == c.id)
+                            .unwrap();
+                        let output = {
+                            let outputs = instr.params.outputs.as_ref().unwrap();
+                            assert!(outputs.params.len() == 1);
+                            &outputs.params[0]
+                        };
+                        assert!(output.ty.is_none());
+                        Some(output.name.clone())
+                    }
+                    _ => None,
+                };
+
+                match (&mut a.using_reg, expr_reg) {
+                    (Some(using_reg), Some(expr_reg)) if *using_reg != expr_reg => {
+                        errors.push(format!("Assignment register `{}` is incompatible with `{}`. Try replacing `<={}=` by `<==`.", using_reg, a.rhs, using_reg));
+                    }
+                    (Some(_), _) => {}
+                    (None, Some(expr_reg)) => {
+                        // infer the assignment register to that of the rhs
+                        a.using_reg = Some(expr_reg);
+                    }
+                    (None, None) => {
+                        errors.push(format!("Impossible to infer the assignment register for `{a}`. Try being more explicit."));
+                    }
+                }
+            }
+        }
+    }
+
+    if !errors.is_empty() {
+        Err(errors)
+    } else {
+        Ok(machine)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use ast::asm_analysis::AssignmentStatement;
+    use number::Bn254Field;
+
+    use crate::test_util::infer_str;
+
+    use super::*;
+
+    #[test]
+    fn inferred() {
+        let file = r#"
+            machine Incompatible {
+                reg pc[@pc];
+                reg X[<=];
+                reg Y[<=];
+                reg A;
+
+                instr foo -> X {}
+
+                function main {
+                    A <== foo();
+                }
+            }
+        "#;
+
+        let file = infer_str::<Bn254Field>(file).unwrap();
+
+        if let FunctionStatement::Assignment(AssignmentStatement { using_reg, .. }) =
+            &file.machines["Incompatible"].functions[0].body.statements[0]
+        {
+            assert_eq!(*using_reg, Some("X".to_string()));
+        } else {
+            panic!()
+        }
+    }
+
+    #[test]
+    fn compatible() {
+        let file = r#"
+            machine Incompatible {
+                reg pc[@pc];
+                reg X[<=];
+                reg Y[<=];
+                reg A;
+
+                instr foo -> X {}
+
+                function main {
+                    A <=X= foo();
+                }
+            }
+        "#;
+
+        let file = infer_str::<Bn254Field>(file).unwrap();
+
+        if let FunctionStatement::Assignment(AssignmentStatement { using_reg, .. }) =
+            &file.machines["Incompatible"].functions[0].body.statements[0]
+        {
+            assert_eq!(*using_reg, Some("X".to_string()));
+        } else {
+            panic!()
+        }
+    }
+
+    #[test]
+    fn incompatible() {
+        let file = r#"
+            machine Incompatible {
+                reg pc[@pc];
+                reg X[<=];
+                reg Y[<=];
+                reg A;
+
+                instr foo -> X {}
+
+                function main {
+                    A <=Y= foo();
+                }
+            }
+        "#;
+
+        assert_eq!(infer_str::<Bn254Field>(file).unwrap_err(), vec!["Assignment register `Y` is incompatible with `foo()`. Try replacing `<=Y=` by `<==`."]);
+    }
+
+    #[test]
+    fn unclear() {
+        let file = r#"
+            machine Incompatible {
+                reg pc[@pc];
+                reg X[<=];
+                reg Y[<=];
+                reg A;
+
+                function main {
+                    A <== 1;
+                }
+            }
+        "#;
+
+        assert_eq!(infer_str::<Bn254Field>(file).unwrap_err(), vec!["Impossible to infer the assignment register for `A <== 1;`. Try being more explicit.".to_string()]);
+    }
+}
diff --git a/analysis/src/lib.rs b/analysis/src/lib.rs
index c366f4d65..0878d7864 100644
--- a/analysis/src/lib.rs
+++ b/analysis/src/lib.rs
@@ -1,4 +1,5 @@
 mod batcher;
+mod inference;
 mod macro_expansion;
 mod romgen;
 mod type_check;
@@ -12,7 +13,33 @@ use number::FieldElement;
 pub fn analyze<T: FieldElement>(file: ASMFile<T>) -> Result<AnalysisASMFile<T>, Vec<String>> {
     let expanded = macro_expansion::expand(file);
     let checked = type_check::check(expanded)?;
-    let rommed = romgen::generate_rom(checked);
+    let inferred = inference::infer(checked)?;
+    let rommed = romgen::generate_rom(inferred);
     let batched = batcher::batch(rommed);
     Ok(batched)
 }
+
+#[cfg(test)]
+mod test_util {
+    use ast::{asm_analysis::AnalysisASMFile, parsed::asm::ASMFile};
+    use number::FieldElement;
+    use parser::parse_asm;
+
+    use crate::{inference, macro_expansion, type_check};
+
+    /// A test utility to process a source file until after macro expansion
+    pub fn expand_str<T: FieldElement>(source: &str) -> ASMFile<T> {
+        let file = parse_asm(None, source).unwrap();
+        macro_expansion::expand(file)
+    }
+
+    /// A test utility to process a source file until after type checking
+    pub fn check_str<T: FieldElement>(source: &str) -> Result<AnalysisASMFile<T>, Vec<String>> {
+        type_check::check(expand_str(source))
+    }
+
+    /// A test utility to process a source file until after inference
+    pub fn infer_str<T: FieldElement>(source: &str) -> Result<AnalysisASMFile<T>, Vec<String>> {
+        inference::infer(check_str(source).unwrap())
+    }
+}
diff --git a/ast/src/asm_analysis/mod.rs b/ast/src/asm_analysis/mod.rs
index 446a799fa..52e2e6f0c 100644
--- a/ast/src/asm_analysis/mod.rs
+++ b/ast/src/asm_analysis/mod.rs
@@ -6,17 +6,19 @@ use num_bigint::BigUint;
 
 use crate::parsed::{
     asm::{InstructionBody, Params, RegisterFlag},
-    Expression, PilStatement,
+    PilStatement,
 };
 
-#[derive(Clone)]
+pub use crate::parsed::Expression;
+
+#[derive(Clone, Debug)]
 pub struct RegisterDeclarationStatement {
     pub start: usize,
     pub name: String,
     pub flag: Option<RegisterFlag>,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct InstructionDefinitionStatement<T> {
     pub start: usize,
     pub name: String,
@@ -24,12 +26,12 @@ pub struct InstructionDefinitionStatement<T> {
     pub body: InstructionBody<T>,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct FunctionBody<T> {
     pub statements: Vec<FunctionStatement<T>>,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct FunctionDefinitionStatement<T> {
     pub start: usize,
     pub name: String,
@@ -37,12 +39,12 @@ pub struct FunctionDefinitionStatement<T> {
     pub body: FunctionBody<T>,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct DegreeStatement {
     pub degree: BigUint,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub enum FunctionStatement<T> {
     Assignment(AssignmentStatement<T>),
     Instruction(InstructionStatement<T>),
@@ -74,7 +76,7 @@ impl<T> From<DebugDirective> for FunctionStatement<T> {
     }
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct AssignmentStatement<T> {
     pub start: usize,
     pub lhs: Vec<String>,
@@ -82,32 +84,32 @@ pub struct AssignmentStatement<T> {
     pub rhs: Box<Expression<T>>,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct InstructionStatement<T> {
     pub start: usize,
     pub instruction: String,
     pub inputs: Vec<Expression<T>>,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct LabelStatement {
     pub start: usize,
     pub name: String,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct DebugDirective {
     pub start: usize,
     pub directive: crate::parsed::asm::DebugDirective,
 }
 
-#[derive(Clone)]
+#[derive(Clone, Debug)]
 pub struct PilBlock<T> {
     pub start: usize,
     pub statements: Vec<PilStatement<T>>,
 }
 
-#[derive(Clone, Default)]
+#[derive(Clone, Default, Debug)]
 pub struct Machine<T> {
     pub degree: Option<DegreeStatement>,
     pub registers: Vec<RegisterDeclarationStatement>,
@@ -130,12 +132,13 @@ impl<T> Machine<T> {
     }
 }
 
-#[derive(Clone, Default)]
+#[derive(Clone, Default, Debug)]
 pub struct Rom<T> {
     pub statements: Vec<FunctionStatement<T>>,
     pub batches: Option<Vec<BatchMetadata>>,
 }
 
+#[derive(Default, Debug)]
 pub struct AnalysisASMFile<T> {
     pub machines: BTreeMap<String, Machine<T>>,
 }
diff --git a/book/src/asm/functions.md b/book/src/asm/functions.md
index 59814f1dd..e67e9c481 100644
--- a/book/src/asm/functions.md
+++ b/book/src/asm/functions.md
@@ -38,8 +38,6 @@ One important requirement is for the assignment register of the assignment to be
 {{#include ../../../test_data/asm/book/function.asm:square}}
 ```
 
-> Specifying the assignment register of the assignment is currently required even in cases where it could be inferred. That restriction may be lifted in the future.
-
 ### Instructions
 
 Instructions which do not return outputs can be used as statements.
diff --git a/riscv/src/compiler.rs b/riscv/src/compiler.rs
index 904917050..5546ef097 100644
--- a/riscv/src/compiler.rs
+++ b/riscv/src/compiler.rs
@@ -150,7 +150,7 @@ fn replace_dynamic_label_references(
     load_dynamic s10, LABEL
     which is then turned into
 
-    s10 <=X= load_label(LABEL)
+    s10 <== load_label(LABEL)
 
     It gets more complicated by the fact that sometimes, labels
     and debugging directives occur between the two statements
@@ -280,7 +280,7 @@ fn store_data_objects<'a>(
                             // code reference
                             // TODO should be possible without temporary
                             object_code.extend([
-                                format!("tmp1 <=X= load_label({});", escape_label(sym)),
+                                format!("tmp1 <== load_label({});", escape_label(sym)),
                                 "mstore tmp1;".to_string(),
                             ]);
                         }
@@ -876,7 +876,7 @@ fn only_if_no_write_to_zero_vec(statements: Vec<String>, reg: Register) -> Vec<S
 }
 
 static COPROCESSOR_SUBSTITUTIONS: &[(&str, &str)] =
-    &[("poseidon_coprocessor", "x10 <=X= poseidon(x10, x11);")];
+    &[("poseidon_coprocessor", "x10 <== poseidon(x10, x11);")];
 
 fn try_coprocessor_substitution(label: &str) -> Option<&'static str> {
     COPROCESSOR_SUBSTITUTIONS
@@ -909,27 +909,27 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         // Arithmetic
         "add" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= wrap({r1} + {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== wrap({r1} + {r2});"), rd)
         }
         "addi" => {
             let (rd, rs, imm) = rri(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= wrap({rs} + {imm});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== wrap({rs} + {imm});"), rd)
         }
         "sub" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= wrap_signed({r1} - {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== wrap_signed({r1} - {r2});"), rd)
         }
         "neg" => {
             let (rd, r1) = rr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= wrap_signed(0 - {r1});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== wrap_signed(0 - {r1});"), rd)
         }
         "mul" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= mul({r1}, {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== mul({r1}, {r2});"), rd)
         }
         "mulhu" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= mulhu({r1}, {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== mulhu({r1}, {r2});"), rd)
         }
         "divu" => {
             let (rd, r1, r2) = rrr(args);
@@ -939,31 +939,31 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         // bitwise
         "xor" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= xor({r1}, {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== xor({r1}, {r2});"), rd)
         }
         "xori" => {
             let (rd, r1, imm) = rri(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= xor({r1}, {imm});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== xor({r1}, {imm});"), rd)
         }
         "and" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= and({r1}, {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== and({r1}, {r2});"), rd)
         }
         "andi" => {
             let (rd, r1, imm) = rri(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= and({r1}, {imm});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== and({r1}, {imm});"), rd)
         }
         "or" => {
             let (rd, r1, r2) = rrr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= or({r1}, {r2});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== or({r1}, {r2});"), rd)
         }
         "ori" => {
             let (rd, r1, imm) = rri(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= or({r1}, {imm});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== or({r1}, {imm});"), rd)
         }
         "not" => {
             let (rd, rs) = rr(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= wrap_signed(-{rs} - 1);"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== wrap_signed(-{rs} - 1);"), rd)
         }
 
         // shift
@@ -972,11 +972,11 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             assert!(amount <= 31);
             only_if_no_write_to_zero_vec(
                 if amount <= 16 {
-                    vec![format!("{rd} <=X= wrap16({rs} * {});", 1 << amount)]
+                    vec![format!("{rd} <== wrap16({rs} * {});", 1 << amount)]
                 } else {
                     vec![
-                        format!("tmp1 <=X= wrap16({rs} * {});", 1 << 16),
-                        format!("{rd} <=X= wrap16(tmp1 * {});", 1 << (amount - 16)),
+                        format!("tmp1 <== wrap16({rs} * {});", 1 << 16),
+                        format!("{rd} <== wrap16(tmp1 * {});", 1 << (amount - 16)),
                     ]
                 },
                 rd,
@@ -986,8 +986,8 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             let (rd, r1, r2) = rrr(args);
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("tmp1 <=X= and({r2}, 0x1f);"),
-                    format!("{rd} <=X= shl({r1}, tmp1);"),
+                    format!("tmp1 <== and({r2}, 0x1f);"),
+                    format!("{rd} <== shl({r1}, tmp1);"),
                 ],
                 rd,
             )
@@ -996,15 +996,15 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // logical shift right
             let (rd, rs, amount) = rri(args);
             assert!(amount <= 31);
-            only_if_no_write_to_zero(format!("{rd} <=X= shr({rs}, {amount});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== shr({rs}, {amount});"), rd)
         }
         "srl" => {
             // logical shift right
             let (rd, r1, r2) = rrr(args);
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("tmp1 <=X= and({r2}, 0x1f);"),
-                    format!("{rd} <=X= shr({r1}, tmp1);"),
+                    format!("tmp1 <== and({r2}, 0x1f);"),
+                    format!("{rd} <== shr({r1}, tmp1);"),
                 ],
                 rd,
             )
@@ -1018,14 +1018,14 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             assert!(amount <= 31);
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("tmp1 <=X= to_signed({rs});"),
-                    format!("tmp1 <=Y= is_positive(0 - tmp1);"),
+                    format!("tmp1 <== to_signed({rs});"),
+                    format!("tmp1 <== is_positive(0 - tmp1);"),
                     format!("tmp1 <=X= tmp1 * 0xffffffff;"),
                     // Here, tmp1 is the full bit mask if rs is negative
                     // and zero otherwise.
-                    format!("{rd} <=X= xor(tmp1, {rs});"),
-                    format!("{rd} <=X= shr({rd}, {amount});"),
-                    format!("{rd} <=X= xor(tmp1, {rd});"),
+                    format!("{rd} <== xor(tmp1, {rs});"),
+                    format!("{rd} <== shr({rd}, {amount});"),
+                    format!("{rd} <== xor(tmp1, {rd});"),
                 ],
                 rd,
             )
@@ -1044,7 +1044,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             let (rd, rs, imm) = rri(args);
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("tmp1 <=X= to_signed({rs});"),
+                    format!("tmp1 <== to_signed({rs});"),
                     format!("{rd} <=Y= is_positive({} - tmp1);", imm as i32),
                 ],
                 rd,
@@ -1053,8 +1053,8 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         "slt" => {
             let (rd, r1, r2) = rrr(args);
             vec![
-                format!("tmp1 <=X= to_signed({r1});"),
-                format!("tmp2 <=X= to_signed({r2});"),
+                format!("tmp1 <== to_signed({r1});"),
+                format!("tmp2 <== to_signed({r2});"),
                 format!("{rd} <=Y= is_positive(tmp2 - tmp1);"),
             ]
         }
@@ -1069,7 +1069,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         "sgtz" => {
             let (rd, rs) = rr(args);
             vec![
-                format!("tmp1 <=X= to_signed({rs});"),
+                format!("tmp1 <== to_signed({rs});"),
                 format!("{rd} <=Y= is_positive(tmp1);"),
             ]
         }
@@ -1091,7 +1091,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         "bgez" => {
             let (r1, label) = rl(args);
             vec![
-                format!("tmp1 <=X= to_signed({r1});"),
+                format!("tmp1 <== to_signed({r1});"),
                 format!("branch_if_positive tmp1 + 1, {label};"),
             ]
         }
@@ -1104,8 +1104,8 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // Branch if r1 < r2 (signed).
             // TODO does this fulfill the input requirements for branch_if_positive?
             vec![
-                format!("tmp1 <=X= to_signed({r1});"),
-                format!("tmp2 <=X= to_signed({r2});"),
+                format!("tmp1 <== to_signed({r1});"),
+                format!("tmp2 <== to_signed({r2});"),
                 format!("branch_if_positive tmp2 - tmp1, {label};"),
             ]
         }
@@ -1114,8 +1114,8 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // Branch if r1 >= r2 (signed).
             // TODO does this fulfill the input requirements for branch_if_positive?
             vec![
-                format!("tmp1 <=X= to_signed({r1});"),
-                format!("tmp2 <=X= to_signed({r2});"),
+                format!("tmp1 <== to_signed({r1});"),
+                format!("tmp2 <== to_signed({r2});"),
                 format!("branch_if_positive tmp1 - tmp2 + 1, {label};"),
             ]
         }
@@ -1129,7 +1129,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // branch less or equal zero
             let (r1, label) = rl(args);
             vec![
-                format!("tmp1 <=X= to_signed({r1});"),
+                format!("tmp1 <== to_signed({r1});"),
                 format!("branch_if_positive -tmp1 + 1, {label};"),
             ]
         }
@@ -1137,7 +1137,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // branch if 0 < r1 < 2**31
             let (r1, label) = rl(args);
             vec![
-                format!("tmp1 <=X= to_signed({r1});"),
+                format!("tmp1 <== to_signed({r1});"),
                 format!("branch_if_positive tmp1, {label};"),
             ]
         }
@@ -1226,8 +1226,8 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // TODO we need to consider misaligned loads / stores
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("addr <=X= wrap({rs} + {off});"),
-                    format!("{rd} <=X= mload();"),
+                    format!("addr <== wrap({rs} + {off});"),
+                    format!("{rd} <== mload();"),
                 ],
                 rd,
             )
@@ -1237,12 +1237,12 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             let (rd, rs, off) = rro(args);
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("tmp1 <=X= wrap({rs} + {off});"),
-                    "addr <=X= and(tmp1, 0xfffffffc);".to_string(),
-                    "tmp2 <=X= and(tmp1, 0x3);".to_string(),
-                    format!("{rd} <=X= mload();"),
-                    format!("{rd} <=X= shr({rd}, 8 * tmp2);"),
-                    format!("{rd} <=X= sign_extend_byte({rd});"),
+                    format!("tmp1 <== wrap({rs} + {off});"),
+                    "addr <== and(tmp1, 0xfffffffc);".to_string(),
+                    "tmp2 <== and(tmp1, 0x3);".to_string(),
+                    format!("{rd} <== mload();"),
+                    format!("{rd} <== shr({rd}, 8 * tmp2);"),
+                    format!("{rd} <== sign_extend_byte({rd});"),
                 ],
                 rd,
             )
@@ -1252,12 +1252,12 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             let (rd, rs, off) = rro(args);
             only_if_no_write_to_zero_vec(
                 vec![
-                    format!("tmp1 <=X= wrap({rs} + {off});"),
-                    "addr <=X= and(tmp1, 0xfffffffc);".to_string(),
-                    "tmp2 <=X= and(tmp1, 0x3);".to_string(),
-                    format!("{rd} <=X= mload();"),
-                    format!("{rd} <=X= shr({rd}, 8 * tmp2);"),
-                    format!("{rd} <=X= and({rd}, 0xff);"),
+                    format!("tmp1 <== wrap({rs} + {off});"),
+                    "addr <== and(tmp1, 0xfffffffc);".to_string(),
+                    "tmp2 <== and(tmp1, 0x3);".to_string(),
+                    format!("{rd} <== mload();"),
+                    format!("{rd} <== shr({rd}, 8 * tmp2);"),
+                    format!("{rd} <== and({rd}, 0xff);"),
                 ],
                 rd,
             )
@@ -1265,7 +1265,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         "sw" => {
             let (r1, r2, off) = rro(args);
             vec![
-                format!("addr <=X= wrap({r2} + {off});"),
+                format!("addr <== wrap({r2} + {off});"),
                 format!("mstore {r1};"),
             ]
         }
@@ -1276,16 +1276,16 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
 
             let (rs, rd, off) = rro(args);
             vec![
-                format!("tmp1 <=X= wrap({rd} + {off});"),
-                "addr <=X= and(tmp1, 0xfffffffc);".to_string(),
-                "tmp2 <=X= and(tmp1, 0x3);".to_string(),
-                "tmp1 <=X= mload();".to_string(),
-                "tmp3 <=X= shl(0xffff, 8 * tmp2);".to_string(),
-                "tmp3 <=X= xor(tmp3, 0xffffffff);".to_string(),
-                "tmp1 <=X= and(tmp1, tmp3);".to_string(),
-                format!("tmp3 <=X= and({rs}, 0xffff);"),
-                "tmp3 <=X= shl(tmp3, 8 * tmp2);".to_string(),
-                "tmp1 <=X= or(tmp1, tmp3);".to_string(),
+                format!("tmp1 <== wrap({rd} + {off});"),
+                "addr <== and(tmp1, 0xfffffffc);".to_string(),
+                "tmp2 <== and(tmp1, 0x3);".to_string(),
+                "tmp1 <== mload();".to_string(),
+                "tmp3 <== shl(0xffff, 8 * tmp2);".to_string(),
+                "tmp3 <== xor(tmp3, 0xffffffff);".to_string(),
+                "tmp1 <== and(tmp1, tmp3);".to_string(),
+                format!("tmp3 <== and({rs}, 0xffff);"),
+                "tmp3 <== shl(tmp3, 8 * tmp2);".to_string(),
+                "tmp1 <== or(tmp1, tmp3);".to_string(),
                 "mstore tmp1;".to_string(),
             ]
         }
@@ -1293,16 +1293,16 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
             // store byte
             let (rs, rd, off) = rro(args);
             vec![
-                format!("tmp1 <=X= wrap({rd} + {off});"),
-                "addr <=X= and(tmp1, 0xfffffffc);".to_string(),
-                "tmp2 <=X= and(tmp1, 0x3);".to_string(),
-                "tmp1 <=X= mload();".to_string(),
-                "tmp3 <=X= shl(0xff, 8 * tmp2);".to_string(),
-                "tmp3 <=X= xor(tmp3, 0xffffffff);".to_string(),
-                "tmp1 <=X= and(tmp1, tmp3);".to_string(),
-                format!("tmp3 <=X= and({rs}, 0xff);"),
-                "tmp3 <=X= shl(tmp3, 8 * tmp2);".to_string(),
-                "tmp1 <=X= or(tmp1, tmp3);".to_string(),
+                format!("tmp1 <== wrap({rd} + {off});"),
+                "addr <== and(tmp1, 0xfffffffc);".to_string(),
+                "tmp2 <== and(tmp1, 0x3);".to_string(),
+                "tmp1 <== mload();".to_string(),
+                "tmp3 <== shl(0xff, 8 * tmp2);".to_string(),
+                "tmp3 <== xor(tmp3, 0xffffffff);".to_string(),
+                "tmp1 <== and(tmp1, tmp3);".to_string(),
+                format!("tmp3 <== and({rs}, 0xff);"),
+                "tmp3 <== shl(tmp3, 8 * tmp2);".to_string(),
+                "tmp1 <== or(tmp1, tmp3);".to_string(),
                 "mstore tmp1;".to_string(),
             ]
         }
@@ -1312,7 +1312,7 @@ fn process_instruction(instr: &str, args: &[Argument]) -> Vec<String> {
         // Special instruction that is inserted to allow dynamic label references
         "load_dynamic" => {
             let (rd, label) = rl(args);
-            only_if_no_write_to_zero(format!("{rd} <=X= load_label({label});"), rd)
+            only_if_no_write_to_zero(format!("{rd} <== load_label({label});"), rd)
         }
 
         _ => {
diff --git a/test_data/asm/book/function.asm b/test_data/asm/book/function.asm
index 64ed7c58e..517cad4ea 100644
--- a/test_data/asm/book/function.asm
+++ b/test_data/asm/book/function.asm
@@ -50,7 +50,7 @@ machine Machine {
         // ANCHOR_END: read_register
         // square `A`
         // ANCHOR: instruction
-        A <=Y= square(A);
+        A <== square(A);
         // ANCHOR_END: instruction
         // jump back to `start`
         jmp start;
diff --git a/test_data/asm/book/hello_world.asm b/test_data/asm/book/hello_world.asm
index 9868140b5..1f9ce1f91 100644
--- a/test_data/asm/book/hello_world.asm
+++ b/test_data/asm/book/hello_world.asm
@@ -33,8 +33,8 @@ machine HelloWorld {
     // the main function assigns the first prover input to A, increments it, decrements it, and loops forever
     function main {
         A <=X= ${ ("input", 0) };
-        A <=Y= incr(A);
-        A <=Y= decr(A);
+        A <== incr(A);
+        A <== decr(A);
         assert_zero A;
         loop;
     }