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merged 2 commits into from
Nov 11, 2025
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feat: remove legacy type proofs #1316

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03a5788
feat: remove legacy type proofs
DavePearce Nov 11, 2025
f853bcb
ensure minimal range constraint is u16
DavePearce Nov 11, 2025
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301 changes: 4 additions & 297 deletions pkg/ir/air/gadgets/bitwidth.go
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Original file line number Diff line number Diff line change
Expand Up @@ -29,7 +29,6 @@ import (
"github.com/consensys/go-corset/pkg/util/collection/hash"
"github.com/consensys/go-corset/pkg/util/field"
"github.com/consensys/go-corset/pkg/util/source/sexp"
"github.com/consensys/go-corset/pkg/util/word"
)

// BitwidthGadget is a general-purpose mechanism for enforcing type constraints
Expand All @@ -41,19 +40,14 @@ type BitwidthGadget[F field.Element[F]] struct {
// translated into AIR range constraints, versus using a horizontal
// bitwidth gadget.
maxRangeConstraint uint
// Enables the use of type proofs which exploit the
// limitless prover. Specifically, modules with a recursive structure are
// created specifically for the purpose of checking types.
limitless bool
// Schema into which constraints are placed.
schema *air.SchemaBuilder[F]
}

// NewBitwidthGadget constructs a new bitwidth gadget.
func NewBitwidthGadget[F field.Element[F]](schema *air.SchemaBuilder[F]) *BitwidthGadget[F] {
return &BitwidthGadget[F]{
maxRangeConstraint: 8,
limitless: false,
maxRangeConstraint: 16,
schema: schema,
}
}
Expand All @@ -64,12 +58,6 @@ func (p *BitwidthGadget[F]) WithMaxRangeConstraint(width uint) *BitwidthGadget[F
return p
}

// WithLimitless enables or disables use of limitless type proofs.
func (p *BitwidthGadget[F]) WithLimitless(flag bool) *BitwidthGadget[F] {
p.limitless = flag
return p
}

// Constrain ensures all values in a given register fit within a given bitwidth.
func (p *BitwidthGadget[F]) Constrain(ref register.Ref, bitwidth uint) {
var (
Expand All @@ -92,12 +80,8 @@ func (p *BitwidthGadget[F]) Constrain(ref register.Ref, bitwidth uint) {
[]*term.RegisterAccess[F, air.Term[F]]{access}, []uint{bitwidth}))
// Done
return
case p.limitless:
p.applyRecursiveBitwidthGadget(ref, bitwidth)
default:
// NOTE: this should be deprecated once the limitless prover is well
// established.
p.applyHorizontalBitwidthGadget(ref, bitwidth)
p.applyRecursiveBitwidthGadget(ref, bitwidth)
}
}

Expand Down Expand Up @@ -139,32 +123,6 @@ func (p *BitwidthGadget[F]) applyBinaryGadget(ref register.Ref) {
air.NewVanishingConstraint(handle, module.Id(), util.None[int](), X_X_m1))
}

// ApplyHorizontalBitwidthGadget ensures all values in a given column fit within
// a given bitwidth. This is implemented using a *horizontal byte
// decomposition* which adds n columns and a vanishing constraint (where n*8 >=
// bitwidth).
func (p *BitwidthGadget[F]) applyHorizontalBitwidthGadget(ref register.Ref, bitwidth uint) {
var (
module = p.schema.Module(ref.Module())
reg = module.Register(ref.Register())
lookupHandle = fmt.Sprintf("%s:u%d", reg.Name, bitwidth)
)
// Allocate computed byte registers in the given module, and add required
// range constraints.
byteRegisters := allocateByteRegisters(reg.Name, bitwidth, module)
// Build up the decomposition sum
sum := buildDecompositionTerm[F](bitwidth, byteRegisters)
// Construct X == (X:0 * 1) + ... + (X:n * 2^n)
X := term.NewRegisterAccess[F, air.Term[F]](ref.Register(), reg.Width, 0)
//
eq := term.Subtract(X, sum)
// Construct column name
module.AddConstraint(
air.NewVanishingConstraint(lookupHandle, module.Id(), util.None[int](), eq))
// Add decomposition assignment
module.AddAssignment(&byteDecomposition[F]{reg.Name, bitwidth, ref, byteRegisters})
}

// ApplyRecursiveBitwidthGadget ensures all values in a given column fit within
// a given bitwidth. This is implemented using a combination of reference tables
// and lookups. Specifically, if the width is below 16bits, then a static
Expand Down Expand Up @@ -357,117 +315,7 @@ func (p *typeDecomposition[F]) Lisp(schema sc.AnySchema[F]) sexp.SExp {
}

// ============================================================================
// Byte Decomposition Assignment
// ============================================================================

// byteDecomposition is part of a range constraint for wide columns (e.g. u32)
// implemented using a byte decomposition.
type byteDecomposition[F field.Element[F]] struct {
// Handle for identifying this assignment
handle string
// Width of decomposition.
bitwidth uint
// The source register being decomposed
source register.Ref
// Target registers holding the decomposition
targets []register.Ref
}

// Compute computes the values of columns defined by this assignment.
// This requires computing the value of each byte column in the decomposition.
func (p *byteDecomposition[F]) Compute(tr trace.Trace[F], schema sc.AnySchema[F],
) ([]array.MutArray[F], error) {
var n = uint(len(p.targets))
// Read inputs
sources := assignment.ReadRegistersRef(tr, p.source)
// Apply native function
data := byteDecompositionNativeFunction(n, sources, tr.Builder())
//
return data, nil
}

// Bounds determines the well-definedness bounds for this assignment for both
// the negative (left) or positive (right) directions. For example, consider an
// expression such as "(shift X -1)". This is technically undefined for the
// first row of any trace and, by association, any constraint evaluating this
// expression on that first row is also undefined (and hence must pass).
func (p *byteDecomposition[F]) Bounds(_ sc.ModuleId) util.Bounds {
return util.EMPTY_BOUND
}

// Consistent performs some simple checks that the given schema is consistent.
// This provides a double check of certain key properties, such as that
// registers used for assignments are large enough, etc.
func (p *byteDecomposition[F]) Consistent(schema sc.AnySchema[F]) []error {
var (
bitwidth = schema.Register(p.source).Width
total = uint(0)
errors []error
)
//
for _, ref := range p.targets {
reg := schema.Module(ref.Module()).Register(ref.Register())
total += reg.Width
}
//
if total != bitwidth {
err := fmt.Errorf("inconsistent byte decomposition (decomposed %d bits, but expected %d)", total, bitwidth)
errors = append(errors, err)
}
//
return errors
}

// RegistersExpanded identifies registers expanded by this assignment.
func (p *byteDecomposition[F]) RegistersExpanded() []register.Ref {
return nil
}

// RegistersRead returns the set of columns that this assignment depends upon.
// That can include both input columns, as well as other computed columns.
func (p *byteDecomposition[F]) RegistersRead() []register.Ref {
return []register.Ref{p.source}
}

// RegistersWritten identifies registers assigned by this assignment.
func (p *byteDecomposition[F]) RegistersWritten() []register.Ref {
return p.targets
}

// Substitute any matchined labelled constants within this assignment
func (p *byteDecomposition[F]) Substitute(mapping map[string]F) {
// Nothing to do here.
}

// Lisp converts this schema element into a simple S-Expression, for example
// so it can be printed.
func (p *byteDecomposition[F]) Lisp(schema sc.AnySchema[F]) sexp.SExp {
var (
srcModule = schema.Module(p.source.Module())
source = srcModule.Register(p.source.Register())
targets = sexp.EmptyList()
)
//
for _, t := range p.targets {
tgtModule := schema.Module(t.Module())
reg := tgtModule.Register(t.Register())
targets.Append(sexp.NewList([]sexp.SExp{
// name
sexp.NewSymbol(reg.QualifiedName(tgtModule)),
// type
sexp.NewSymbol(fmt.Sprintf("u%d", reg.Width)),
}))
}

return sexp.NewList(
[]sexp.SExp{sexp.NewSymbol("decompose"),
targets,
sexp.NewSymbol(source.QualifiedName(srcModule)),
})
}

// ============================================================================
// Helpers (for recursive)
// Helpers
// ============================================================================

// Determine the split of limbs for the given bitwidth. For example, 33bits
Expand Down Expand Up @@ -564,7 +412,7 @@ func decompose[F field.Element[F]](loWidth uint, ith F) (F, F) {
)
// Sanity check assumption
if loWidth%8 != 0 {
panic("unreachable")
panic(fmt.Sprintf("unreachable (u%d)", loWidth))
}
//
if loByteWidth >= n {
Expand All @@ -580,144 +428,3 @@ func decompose[F field.Element[F]](loWidth uint, ith F) (F, F) {
//
return loFr, hiFr
}

// ============================================================================
// Helpers (for horizontal)
// ============================================================================

// Allocate n byte registers, each of which requires a suitable range
// constraint.
func allocateByteRegisters[F field.Element[F]](prefix string, bitwidth uint, module *air.ModuleBuilder[F],
) []register.Ref {
var (
n = bitwidth / 8
zero big.Int
)
//
if bitwidth == 0 {
panic("zero byte decomposition encountered")
}
// Account for asymetric case
if bitwidth%8 != 0 {
n++
}
// Allocate target register ids
targets := make([]register.Ref, n)
// Allocate byte registers
for i := uint(0); i < n; i++ {
name := fmt.Sprintf("%s:%d", prefix, i)
byteRegister := register.NewComputed(name, min(8, bitwidth), zero)
// Allocate byte register
rid := module.NewRegister(byteRegister)
targets[i] = register.NewRef(module.Id(), rid)
// Add suitable range constraint
ith_access := term.RawRegisterAccess[F, air.Term[F]](rid, byteRegister.Width, 0)
//
module.AddConstraint(
air.NewRangeConstraint(name, module.Id(),
[]*term.RegisterAccess[F, air.Term[F]]{ith_access},
[]uint{byteRegister.Width}))
//
bitwidth -= 8
}
//
return targets
}

func buildDecompositionTerm[F field.Element[F]](bitwidth uint, byteRegisters []register.Ref) air.Term[F] {
var (
// Determine ranges required for the give bitwidth
ranges = splitColumnRanges[F](bitwidth)
// Initialise array of terms
terms = make([]air.Term[F], len(byteRegisters))
// Initialise coefficient
coefficient F = field.One[F]()
)
// Construct Columns
for i, ref := range byteRegisters {
// Create Column + Constraint
reg := term.NewRegisterAccess[F, air.Term[F]](ref.Register(), 8, 0)
terms[i] = term.Product(reg, term.Const[F, air.Term[F]](coefficient))
// Update coefficient
coefficient = coefficient.Mul(ranges[i])
}
// Construct (X:0 * 1) + ... + (X:n * 2^n)
return term.Sum(terms...)
}

func splitColumnRanges[F field.Element[F]](nbits uint) []F {
var (
n = nbits / 8
m = nbits % 8
ranges []F
// FIXME: following fails for very small fields like GF251!
two8 F = field.Uint64[F](256)
)
//
if m == 0 {
ranges = make([]F, n)
} else {
// Most significant column has smaller range.
ranges = make([]F, n+1)
// Determine final range
ranges[n] = field.TwoPowN[F](m)
}
//
for i := range n {
ranges[i] = two8
}
//
return ranges
}

func byteDecompositionNativeFunction[F field.Element[F]](n uint, sources []array.Array[F],
builder array.Builder[F]) []array.MutArray[F] {
//
var (
source = sources[0]
targets = make([]array.MutArray[F], n)
height = source.Len()
)
// Sanity check
if len(sources) != 1 {
panic("too many source columns for byte decomposition")
}
// Initialise columns
for i := range n {
// Construct a byte array for ith byte
targets[i] = builder.NewArray(height, 8)
}
// Decompose each row of each column
for i := range height {
ith := decomposeIntoBytes(source.Get(i), n)
for j := uint(0); j < n; j++ {
targets[j].Set(i, ith[j])
}
}
//
return targets
}

// Decompose a given element into n bytes in little endian form. For example,
// decomposing 41b into 2 bytes gives [0x1b,0x04].
func decomposeIntoBytes[W word.Word[W]](val W, n uint) []W {
// Construct return array
elements := make([]W, n)
// Determine bytes of this value (in big endian form).
bytes := val.Bytes()
//
l := uint(len(bytes))
//
m := min(n, l)
// Convert each byte into a field element
for i := range m {
var (
ith W
j = l - i - 1
)
//
elements[i] = ith.SetUint64(uint64(bytes[j]))
}
// Done
return elements
}
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