diff --git a/pkg/air/gadgets/column_sort.go b/pkg/air/gadgets/column_sort.go
index 1d11426..d50a479 100644
--- a/pkg/air/gadgets/column_sort.go
+++ b/pkg/air/gadgets/column_sort.go
@@ -43,7 +43,7 @@ func ApplyColumnSortGadget(col uint, sign bool, bitwidth uint, schema *air.Schem
 	// Add new column (if it does not already exist)
 	if !ok {
 		deltaIndex = schema.AddAssignment(
-			assignment.NewComputedColumn(column.Context, deltaName, Xdiff))
+			assignment.NewComputedColumn[air.Expr](column.Context, deltaName, Xdiff))
 	}
 	// Add necessary bitwidth constraints
 	ApplyBitwidthGadget(deltaIndex, bitwidth, schema)
diff --git a/pkg/air/gadgets/expand.go b/pkg/air/gadgets/expand.go
index e29da64..7f27a15 100644
--- a/pkg/air/gadgets/expand.go
+++ b/pkg/air/gadgets/expand.go
@@ -29,7 +29,7 @@ func Expand(ctx trace.Context, e air.Expr, schema *air.Schema) uint {
 	// Add new column (if it does not already exist)
 	if !ok {
 		// Add computed column
-		index = schema.AddAssignment(assignment.NewComputedColumn(ctx, name, e))
+		index = schema.AddAssignment(assignment.NewComputedColumn[air.Expr](ctx, name, e))
 		// Construct v == [e]
 		v := air.NewColumnAccess(index, 0)
 		// Construct 1 == e/e
diff --git a/pkg/air/gadgets/normalisation.go b/pkg/air/gadgets/normalisation.go
index 10d08ee..f781de1 100644
--- a/pkg/air/gadgets/normalisation.go
+++ b/pkg/air/gadgets/normalisation.go
@@ -44,7 +44,7 @@ func ApplyPseudoInverseGadget(e air.Expr, schema *air.Schema) air.Expr {
 	// Add new column (if it does not already exist)
 	if !ok {
 		// Add computed column
-		index = schema.AddAssignment(assignment.NewComputedColumn(ctx, name, ie))
+		index = schema.AddAssignment(assignment.NewComputedColumn[air.Expr](ctx, name, ie))
 		// Construct 1/e
 		inv_e := air.NewColumnAccess(index, 0)
 		// Construct e/e
@@ -82,6 +82,23 @@ func (e *Inverse) EvalAt(k int, tbl tr.Trace) fr.Element {
 	return inv
 }
 
+// Add two expressions together, producing a third.
+func (e *Inverse) Add(other air.Expr) air.Expr { panic("unreachable") }
+
+// Sub (subtract) one expression from another.
+func (e *Inverse) Sub(other air.Expr) air.Expr { panic("unreachable") }
+
+// Mul (multiply) two expressions together, producing a third.
+func (e *Inverse) Mul(other air.Expr) air.Expr { panic("unreachable") }
+
+// Equate one expression with another (equivalent to subtraction).
+func (e *Inverse) Equate(other air.Expr) air.Expr { panic("unreachable") }
+
+// AsConstant determines whether or not this is a constant expression.  If
+// so, the constant is returned; otherwise, nil is returned.  NOTE: this
+// does not perform any form of simplification to determine this.
+func (e *Inverse) AsConstant() *fr.Element { return nil }
+
 // Bounds returns max shift in either the negative (left) or positive
 // direction (right).
 func (e *Inverse) Bounds() util.Bounds { return e.Expr.Bounds() }
diff --git a/pkg/cmd/debug.go b/pkg/cmd/debug.go
index d497078..b1ded80 100644
--- a/pkg/cmd/debug.go
+++ b/pkg/cmd/debug.go
@@ -4,11 +4,13 @@ import (
 	"fmt"
 	"os"
 	"reflect"
-	"strings"
 
+	"github.com/consensys/go-corset/pkg/air"
 	"github.com/consensys/go-corset/pkg/hir"
+	"github.com/consensys/go-corset/pkg/mir"
 	"github.com/consensys/go-corset/pkg/schema"
 	sc "github.com/consensys/go-corset/pkg/schema"
+	"github.com/consensys/go-corset/pkg/schema/assignment"
 	"github.com/consensys/go-corset/pkg/util"
 	log "github.com/sirupsen/logrus"
 	"github.com/spf13/cobra"
@@ -133,19 +135,20 @@ type schemaSummariser struct {
 
 var schemaSummarisers []schemaSummariser = []schemaSummariser{
 	// Constraints
-	constraintCounter("Constraints", "*constraint.VanishingConstraint"),
-	constraintCounter("Lookups", "*constraint.LookupConstraint"),
-	constraintCounter("Permutations", "*constraint.PermutationConstraint"),
-	constraintCounter("Types", "*constraint.TypeConstraint"),
-	constraintCounter("Range", "*constraint.RangeConstraint"),
+	constraintCounter("Constraints", vanishingConstraints...),
+	constraintCounter("Lookups", lookupConstraints...),
+	constraintCounter("Permutations", permutationConstraints...),
+	constraintCounter("Range", rangeConstraints...),
 	// Assignments
-	assignmentCounter("Decompositions", "*assignment.ByteDecomposition"),
-	assignmentCounter("Computed Columns", "*assignment.ComputedColumn"),
-	assignmentCounter("Committed Columns", "*assignment.DataColumn"),
-	assignmentCounter("Interleavings", "*assignment.Interleaving"),
-	assignmentCounter("Lexicographic Orderings", "*assignment.LexicographicSort"),
-	assignmentCounter("Sorted Permutations", "*assignment.SortedPermutation"),
-	// Column Width
+	assignmentCounter("Decompositions", reflect.TypeOf((*assignment.ByteDecomposition)(nil))),
+	assignmentCounter("Committed Columns", reflect.TypeOf((*assignment.DataColumn)(nil))),
+	assignmentCounter("Computed Columns", computedColumns...),
+	assignmentCounter("Computation Columns", reflect.TypeOf((*assignment.Computation)(nil))),
+	assignmentCounter("Interleavings", reflect.TypeOf((*assignment.Interleaving)(nil))),
+	assignmentCounter("Lexicographic Orderings", reflect.TypeOf((*assignment.LexicographicSort)(nil))),
+	assignmentCounter("Sorted Permutations", reflect.TypeOf((*assignment.SortedPermutation)(nil))),
+	// Columns
+	columnCounter(),
 	columnWidthSummariser(1, 1),
 	columnWidthSummariser(2, 4),
 	columnWidthSummariser(5, 8),
@@ -156,30 +159,61 @@ var schemaSummarisers []schemaSummariser = []schemaSummariser{
 	columnWidthSummariser(129, 256),
 }
 
-func constraintCounter(title string, prefix string) schemaSummariser {
+var vanishingConstraints = []reflect.Type{
+	reflect.TypeOf((hir.VanishingConstraint)(nil)),
+	reflect.TypeOf((mir.VanishingConstraint)(nil)),
+	reflect.TypeOf((air.VanishingConstraint)(nil))}
+
+var lookupConstraints = []reflect.Type{
+	reflect.TypeOf((hir.LookupConstraint)(nil)),
+	reflect.TypeOf((mir.LookupConstraint)(nil)),
+	reflect.TypeOf((air.LookupConstraint)(nil))}
+
+var rangeConstraints = []reflect.Type{
+	reflect.TypeOf((hir.RangeConstraint)(nil)),
+	reflect.TypeOf((mir.RangeConstraint)(nil)),
+	reflect.TypeOf((air.RangeConstraint)(nil))}
+
+var permutationConstraints = []reflect.Type{
+	// permutation constraints only exist at AIR level
+	reflect.TypeOf((air.PermutationConstraint)(nil))}
+
+var computedColumns = []reflect.Type{
+	// permutation constraints only exist at AIR level
+	reflect.TypeOf((*assignment.ComputedColumn[air.Expr])(nil))}
+
+func constraintCounter(title string, types ...reflect.Type) schemaSummariser {
 	return schemaSummariser{
 		name: title,
 		summary: func(schema sc.Schema) int {
-			return typeOfCounter(schema.Constraints(), prefix)
+			sum := 0
+			for _, t := range types {
+				sum += typeOfCounter(schema.Constraints(), t)
+			}
+			return sum
 		},
 	}
 }
 
-func assignmentCounter(title string, prefix string) schemaSummariser {
+func assignmentCounter(title string, types ...reflect.Type) schemaSummariser {
 	return schemaSummariser{
 		name: title,
 		summary: func(schema sc.Schema) int {
-			return typeOfCounter(schema.Declarations(), prefix)
+			sum := 0
+			for _, t := range types {
+				sum += typeOfCounter(schema.Declarations(), t)
+			}
+			return sum
 		},
 	}
 }
 
-func typeOfCounter[T any](iter util.Iterator[T], prefix string) int {
+func typeOfCounter[T any](iter util.Iterator[T], dyntype reflect.Type) int {
 	count := 0
 
 	for iter.HasNext() {
 		ith := iter.Next()
-		if isTypeOf(ith, prefix) {
+		if dyntype == reflect.TypeOf(ith) {
 			count++
 		}
 	}
@@ -187,10 +221,18 @@ func typeOfCounter[T any](iter util.Iterator[T], prefix string) int {
 	return count
 }
 
-func isTypeOf(obj any, prefix string) bool {
-	dyntype := reflect.TypeOf(obj)
-	// Check whether dynamic type matches prefix
-	return strings.HasPrefix(dyntype.String(), prefix)
+func columnCounter() schemaSummariser {
+	return schemaSummariser{
+		name: "Columns (all)",
+		summary: func(sc schema.Schema) int {
+			count := 0
+			for i := sc.Columns(); i.HasNext(); {
+				i.Next()
+				count++
+			}
+			return count
+		},
+	}
 }
 
 func columnWidthSummariser(lowWidth uint, highWidth uint) schemaSummariser {
diff --git a/pkg/corset/compiler/translator.go b/pkg/corset/compiler/translator.go
index 6f87e4f..e40dba1 100644
--- a/pkg/corset/compiler/translator.go
+++ b/pkg/corset/compiler/translator.go
@@ -291,10 +291,13 @@ func (t *translator) translateDefConstraint(decl *ast.DefConstraint, module util
 	}
 	// Apply guard (if applicable)
 	if guard != nil {
-		constraint = &hir.Mul{Args: []hir.Expr{guard, constraint}}
+		constraint = &hir.IfZero{Condition: guard, TrueBranch: nil, FalseBranch: constraint}
 	}
 	// Apply perspective selector (if applicable)
 	if selector != nil {
+		// NOTE: using an ifnot (as above) would be preferable here.  However,
+		// this is currently done just to ensure constraints identical to the
+		// original are generated.
 		constraint = &hir.Mul{Args: []hir.Expr{selector, constraint}}
 	}
 	//
diff --git a/pkg/corset/stdlib.lisp b/pkg/corset/stdlib.lisp
index 44e356e..f429b3c 100644
--- a/pkg/corset/stdlib.lisp
+++ b/pkg/corset/stdlib.lisp
@@ -21,12 +21,10 @@
 
 (defpurefun ((not :binary@bool :force) (x :binary)) (- 1 x))
 
-(defpurefun ((eq! :binary@loob :force) (x :binary) (y :binary)) (^ (- x y) 2))
 (defpurefun ((eq! :@loob) x y) (- x y))
 (defpurefun ((neq! :binary@loob :force) x y) (not (~ (eq! x y))))
 (defunalias = eq!)
 
-(defpurefun ((eq :binary@bool :force) (x :binary) (y :binary)) (- 1 (^ (- x y) 2)))
 (defpurefun ((eq :binary@bool :force) x y) (- 1 (~ (eq! x y))))
 (defpurefun ((neq :binary@bool :force) x y) (eq! x y))
 
diff --git a/pkg/hir/lower.go b/pkg/hir/lower.go
index 8fa56f8..74a5b69 100644
--- a/pkg/hir/lower.go
+++ b/pkg/hir/lower.go
@@ -299,7 +299,17 @@ func extractBodies(es []Expr, schema *mir.Schema) []mir.Expr {
 func expand(e Expr, schema sc.Schema) []Expr {
 	if p, ok := e.(*Add); ok {
 		return expandWithNaryConstructor(p.Args, func(nargs []Expr) Expr {
-			return &Add{Args: nargs}
+			var args []Expr
+			// Flatten nested sums
+			for _, e := range nargs {
+				if a, ok := e.(*Add); ok {
+					args = append(args, a.Args...)
+				} else {
+					args = append(args, e)
+				}
+			}
+			// Done
+			return &Add{Args: args}
 		}, schema)
 	} else if _, ok := e.(*Constant); ok {
 		return []Expr{e}
@@ -307,7 +317,17 @@ func expand(e Expr, schema sc.Schema) []Expr {
 		return []Expr{e}
 	} else if p, ok := e.(*Mul); ok {
 		return expandWithNaryConstructor(p.Args, func(nargs []Expr) Expr {
-			return &Mul{Args: nargs}
+			var args []Expr
+			// Flatten nested products
+			for _, e := range nargs {
+				if a, ok := e.(*Mul); ok {
+					args = append(args, a.Args...)
+				} else {
+					args = append(args, e)
+				}
+			}
+			// Done
+			return &Mul{Args: args}
 		}, schema)
 	} else if p, ok := e.(*List); ok {
 		ees := make([]Expr, 0)
diff --git a/pkg/mir/const.go b/pkg/mir/const.go
index b5854cd..f84407a 100644
--- a/pkg/mir/const.go
+++ b/pkg/mir/const.go
@@ -32,7 +32,7 @@ func applyConstantPropagation(e Expr, schema sc.Schema) Expr {
 
 func applyConstantPropagationAdd(es []Expr, schema sc.Schema) Expr {
 	sum := fr.NewElement(0)
-	is_const := true
+	count := 0
 	rs := make([]Expr, len(es))
 	//
 	for i, e := range es {
@@ -40,16 +40,18 @@ func applyConstantPropagationAdd(es []Expr, schema sc.Schema) Expr {
 		// Check for constant
 		c, ok := rs[i].(*Constant)
 		// Try to continue sum
-		if ok && is_const {
+		if ok {
 			sum.Add(&sum, &c.Value)
-		} else {
-			is_const = false
+			// Increase count of constants
+			count++
 		}
 	}
 	// Check if constant
-	if is_const {
+	if count == len(es) {
 		// Propagate constant
 		return &Constant{sum}
+	} else if count > 1 {
+		rs = mergeConstants(sum, rs)
 	}
 	// Done
 	return &Add{rs}
@@ -85,10 +87,10 @@ func applyConstantPropagationSub(es []Expr, schema sc.Schema) Expr {
 
 func applyConstantPropagationMul(es []Expr, schema sc.Schema) Expr {
 	one := fr.NewElement(1)
-	is_const := true
 	prod := one
 	rs := make([]Expr, len(es))
 	ones := 0
+	consts := 0
 	//
 	for i, e := range es {
 		rs[i] = applyConstantPropagation(e, schema)
@@ -100,16 +102,17 @@ func applyConstantPropagationMul(es []Expr, schema sc.Schema) Expr {
 			return &Constant{c.Value}
 		} else if ok && c.Value.IsOne() {
 			ones++
+			consts++
 			rs[i] = nil
-		} else if ok && is_const {
+		} else if ok {
 			// Continue building constant
 			prod.Mul(&prod, &c.Value)
-		} else {
-			is_const = false
+			//
+			consts++
 		}
 	}
 	// Check if constant
-	if is_const {
+	if consts == len(es) {
 		return &Constant{prod}
 	} else if ones > 0 {
 		rs = util.RemoveMatching[Expr](rs, func(item Expr) bool { return item == nil })
@@ -117,6 +120,9 @@ func applyConstantPropagationMul(es []Expr, schema sc.Schema) Expr {
 	// Sanity check what's left.
 	if len(rs) == 1 {
 		return rs[0]
+	} else if consts-ones > 1 {
+		// Combine constants
+		rs = mergeConstants(prod, rs)
 	}
 	// Done
 	return &Mul{rs}
@@ -155,3 +161,26 @@ func applyConstantPropagationNorm(arg Expr, schema sc.Schema) Expr {
 	//
 	return &Normalise{arg}
 }
+
+// Replace all constants within a given sequence of expressions with a single
+// constant (whose value has been precomputed from those constants).  The new
+// value replaces the first constant in the list.
+func mergeConstants(constant fr.Element, es []Expr) []Expr {
+	j := 0
+	first := true
+	//
+	for i := range es {
+		// Check for constant
+		if _, ok := es[i].(*Constant); ok && first {
+			es[j] = &Constant{constant}
+			first = false
+			j++
+		} else if !ok {
+			// Retain non-constant expression
+			es[j] = es[i]
+			j++
+		}
+	}
+	// Return slice
+	return es[0:j]
+}
diff --git a/pkg/schema/assignment/computation.go b/pkg/schema/assignment/computation.go
index 1346b51..014ecea 100644
--- a/pkg/schema/assignment/computation.go
+++ b/pkg/schema/assignment/computation.go
@@ -230,7 +230,6 @@ func mapIfNativeFunction(trace tr.Trace, sources []uint) []util.FrArray {
 				rhs := fmt.Sprintf("%v=>%s", ith_row, val.String())
 				panic(fmt.Sprintf("conflicting values in source map (row %d): %s vs %s", i, lhs, rhs))
 			} else if !ok {
-				fmt.Printf("Inserting source key (row %d): %v\n", i, extractIthColumns(i, source_keys))
 				// Item not previously in map
 				source_map.Insert(ith_key, ith_value)
 			}