Add safe simplify for expressions that compares random assignments

before and after.

crates/prover/src/constraint_framework/expr.rs

@@ -1,16 +1,20 @@
+use std::collections::{HashMap, HashSet};
 use std::ops::{Add, AddAssign, Index, Mul, MulAssign, Neg, Sub};
 
+use itertools::sorted;
 use num_traits::{One, Zero};
+use rand::rngs::SmallRng;
+use rand::{Rng, SeedableRng};
 
-use super::{EvalAtRow, Relation, RelationEntry, INTERACTION_TRACE_IDX};
+use super::{AssertEvaluator, EvalAtRow, Relation, RelationEntry, INTERACTION_TRACE_IDX};
 use crate::core::fields::cm31::CM31;
 use crate::core::fields::m31::{self, BaseField};
 use crate::core::fields::qm31::{SecureField, QM31};
 use crate::core::fields::FieldExpOps;
 use crate::core::lookups::utils::Fraction;
 
 /// A single base field column at index `idx` of interaction `interaction`, at mask offset `offset`.
-#[derive(Clone, Debug, PartialEq)]
+#[derive(Clone, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
 pub struct ColumnExpr {
     interaction: usize,
     idx: usize,
@@ -174,11 +178,14 @@ impl BaseExpr {
         }
     }
 
-    pub fn simplify(&self) -> Self {
+    /// Helper function, use [`simplify`] instead.
+    ///
+    /// Simplifies an expression by applying basic arithmetic rules.
+    fn unchecked_simplify(&self) -> Self {
         let simple = simplify_arithmetic!(self);
         match simple {
             Self::Inv(a) => {
-                let a = a.simplify();
+                let a = a.unchecked_simplify();
                 match a {
                     Self::Inv(inv_a) => *inv_a, // 1 / (1 / a) = a
                     Self::Const(c) => Self::Const(c.inverse()),
@@ -189,6 +196,14 @@ impl BaseExpr {
         }
     }
 
+    /// Simplifies an expression by applying basic arithmetic rules and ensures that the result is
+    /// equivalent to the original expression by assigning random values.
+    pub fn simplify(&self) -> Self {
+        let simplified = self.unchecked_simplify();
+        assert_eq!(self.random_eval(), simplified.random_eval());
+        simplified
+    }
+
     pub fn simplify_and_format(&self) -> String {
         self.simplify().format_expr()
     }
@@ -220,6 +235,25 @@ impl BaseExpr {
             Self::Inv(a) => a.eval_expr::<E, C, V>(columns, vars).inverse(),
         }
     }
+
+    pub fn collect_variables(&self) -> ExprVariables {
+        match self {
+            BaseExpr::Col(col) => ExprVariables::col(col.clone()),
+            BaseExpr::Const(_) => ExprVariables::default(),
+            BaseExpr::Param(param) => ExprVariables::param(param.to_string()),
+            BaseExpr::Add(a, b) => a.collect_variables() + b.collect_variables(),
+            BaseExpr::Sub(a, b) => a.collect_variables() + b.collect_variables(),
+            BaseExpr::Mul(a, b) => a.collect_variables() + b.collect_variables(),
+            BaseExpr::Neg(a) => a.collect_variables(),
+            BaseExpr::Inv(a) => a.collect_variables(),
+        }
+    }
+
+    pub fn random_eval(&self) -> BaseField {
+        let assignment = self.collect_variables().random_assignment();
+        assert!(assignment.2.is_empty());
+        self.eval_expr::<AssertEvaluator<'_>, _, _>(&assignment.0, &assignment.1)
+    }
 }
 
 impl ExtExpr {
@@ -256,14 +290,17 @@ impl ExtExpr {
         }
     }
 
-    pub fn simplify(&self) -> Self {
+    /// Helper function, use [`simplify`] instead.
+    ///
+    /// Simplifies an expression by applying basic arithmetic rules.
+    fn unchecked_simplify(&self) -> Self {
         let simple = simplify_arithmetic!(self);
         match simple {
             Self::SecureCol([a, b, c, d]) => {
-                let a = a.simplify();
-                let b = b.simplify();
-                let c = c.simplify();
-                let d = d.simplify();
+                let a = a.unchecked_simplify();
+                let b = b.unchecked_simplify();
+                let c = c.unchecked_simplify();
+                let d = d.unchecked_simplify();
                 match (a.clone(), b.clone(), c.clone(), d.clone()) {
                     (
                         BaseExpr::Const(a_val),
@@ -278,6 +315,14 @@ impl ExtExpr {
         }
     }
 
+    /// Simplifies an expression by applying basic arithmetic rules and ensures that the result is
+    /// equivalent to the original expression by assigning random values.
+    pub fn simplify(&self) -> Self {
+        let simplified = self.unchecked_simplify();
+        assert_eq!(self.random_eval(), simplified.random_eval());
+        simplified
+    }
+
     pub fn simplify_and_format(&self) -> String {
         self.simplify().format_expr()
     }
@@ -319,6 +364,104 @@ impl ExtExpr {
             Self::Neg(a) => -a.eval_expr::<E, C, V, EV>(columns, vars, ext_vars),
         }
     }
+
+    pub fn collect_variables(&self) -> ExprVariables {
+        match self {
+            ExtExpr::SecureCol([a, b, c, d]) => {
+                a.collect_variables()
+                    + b.collect_variables()
+                    + c.collect_variables()
+                    + d.collect_variables()
+            }
+            ExtExpr::Const(_) => ExprVariables::default(),
+            ExtExpr::Param(param) => ExprVariables::ext_param(param.to_string()),
+            ExtExpr::Add(a, b) => a.collect_variables() + b.collect_variables(),
+            ExtExpr::Sub(a, b) => a.collect_variables() + b.collect_variables(),
+            ExtExpr::Mul(a, b) => a.collect_variables() + b.collect_variables(),
+            ExtExpr::Neg(a) => a.collect_variables(),
+        }
+    }
+
+    pub fn random_eval(&self) -> SecureField {
+        let assignment = self.collect_variables().random_assignment();
+        self.eval_expr::<AssertEvaluator<'_>, _, _, _>(&assignment.0, &assignment.1, &assignment.2)
+    }
+}
+
+/// An assignment to the variables that may appear in an expression.
+pub type ExprVarAssignment = (
+    HashMap<(usize, usize, isize), BaseField>,
+    HashMap<String, BaseField>,
+    HashMap<String, SecureField>,
+);
+
+/// Three sets representing all the variables that can appear in an expression:
+///    * `cols`: The columns of the AIR.
+///    * `params`: The formal parameters to the AIR.
+///    * `ext_params`: The extension field parameters to the AIR.
+#[derive(Default)]
+pub struct ExprVariables {
+    pub cols: HashSet<ColumnExpr>,
+    pub params: HashSet<String>,
+    pub ext_params: HashSet<String>,
+}
+
+impl ExprVariables {
+    pub fn col(col: ColumnExpr) -> Self {
+        Self {
+            cols: vec![col].into_iter().collect(),
+            params: HashSet::new(),
+            ext_params: HashSet::new(),
+        }
+    }
+
+    pub fn param(param: String) -> Self {
+        Self {
+            cols: HashSet::new(),
+            params: vec![param].into_iter().collect(),
+            ext_params: HashSet::new(),
+        }
+    }
+
+    pub fn ext_param(param: String) -> Self {
+        Self {
+            cols: HashSet::new(),
+            params: HashSet::new(),
+            ext_params: vec![param].into_iter().collect(),
+        }
+    }
+
+    /// Generates a random assignment to the variables.
+    /// Note that the assignment is deterministic in the sets of variables (disregarding their
+    /// order), and this is required.
+    pub fn random_assignment(&self) -> ExprVarAssignment {
+        let mut rng = SmallRng::seed_from_u64(0);
+
+        let cols = sorted(self.cols.iter())
+            .map(|col| ((col.interaction, col.idx, col.offset), rng.gen()))
+            .collect();
+
+        let params = sorted(self.params.iter())
+            .map(|param| (param.clone(), rng.gen()))
+            .collect();
+
+        let ext_params = sorted(self.ext_params.iter())
+            .map(|param| (param.clone(), rng.gen()))
+            .collect();
+
+        (cols, params, ext_params)
+    }
+}
+
+impl Add for ExprVariables {
+    type Output = Self;
+    fn add(self, rhs: Self) -> Self {
+        Self {
+            cols: self.cols.union(&rhs.cols).cloned().collect(),
+            params: self.params.union(&rhs.params).cloned().collect(),
+            ext_params: self.ext_params.union(&rhs.ext_params).cloned().collect(),
+        }
+    }
 }
 
 impl From<BaseField> for BaseExpr {