fix: several typos in the documentation (#943)

* fix typo groth16.go

* fix typo main.go

* fix typo circuit_test.go

* fix typo operator.go

* fix typos rollup_test.go

* fix typos api.go

* fix typo builder.go

* fix typo heap.go

* fix typo api.go

* fix typo builder.go

* fix typo coeff_table.go

backend/groth16/groth16.go

@@ -200,7 +200,7 @@ func Prove(r1cs constraint.ConstraintSystem, pk ProvingKey, fullWitness witness.
 
 // Setup runs groth16.Setup with provided R1CS and outputs a key pair associated with the circuit.
 //
-// Note that careful consideration must be given to this step in production environment.
+// Note that careful consideration must be given to this step in a production environment.
 // groth16.Setup uses some randomness to precompute the Proving and Verifying keys. If the process
 // or machine leaks this randomness, an attacker could break the ZKP protocol.
 //

examples/plonk/main.go

@@ -108,7 +108,7 @@ func main() {
 			log.Fatal(err)
 		}
 
-		// public data consists the polynomials describing the constants involved
+		// public data consists of the polynomials describing the constants involved
 		// in the constraints, the polynomial describing the permutation ("grand
 		// product argument"), and the FFT domains.
 		pk, vk, err := plonk.Setup(ccs, srs)
@@ -149,7 +149,7 @@ func main() {
 			log.Fatal(err)
 		}
 
-		// public data consists the polynomials describing the constants involved
+		// public data consists of the polynomials describing the constants involved
 		// in the constraints, the polynomial describing the permutation ("grand
 		// product argument"), and the FFT domains.
 		pk, vk, err := plonk.Setup(ccs, srs)

examples/rollup/circuit_test.go

@@ -28,7 +28,7 @@ import (
 
 type circuitSignature Circuit
 
-// Circuit implements part of the rollup circuit only by delcaring a subset of the constraints
+// Circuit implements part of the rollup circuit only by declaring a subset of the constraints
 func (t *circuitSignature) Define(api frontend.API) error {
 	if err := (*Circuit)(t).postInit(api); err != nil {
 		return err

examples/rollup/operator.go

@@ -35,7 +35,7 @@ type Queue struct {
 	listTransfers chan Transfer
 }
 
-// NewQueue creates a new queue, BatchSizeCircuit is the capaciy
+// NewQueue creates a new queue, BatchSizeCircuit is the capacity
 func NewQueue(BatchSizeCircuit int) Queue {
 	resChan := make(chan Transfer, BatchSizeCircuit)
 	var res Queue
@@ -52,7 +52,7 @@ type Operator struct {
 	h          hash.Hash         // hash function used to build the Merkle Tree
 	q          Queue             // queue of transfers
 	batch      int               // current number of transactions in a batch
-	witnesses  Circuit           // witnesses for the snark cicruit
+	witnesses  Circuit           // witnesses for the snark circuit
 }
 
 // NewOperator creates a new operator.

examples/rollup/rollup_test.go

@@ -33,7 +33,7 @@ func TestOperatorReadAccount(t *testing.T) {
 	// create operator with 10 accounts
 	operator, _ := createOperator(10)
 
-	// check if the account read from the operator are correct
+	// check if the account read from the operator is correct
 	for i := 0; i < 10; i++ {
 		opAccount, err := operator.readAccount(uint64(i))
 		if err != nil {
@@ -168,7 +168,7 @@ func createAccount(i int) (Account, eddsa.PrivateKey) {
 	return acc, privkey
 }
 
-// Returns a newly created operator and tha private keys of the associated accounts
+// Returns a newly created operator and the private keys of the associated accounts
 func createOperator(nbAccounts int) (Operator, []eddsa.PrivateKey) {
 
 	operator := NewOperator(nbAccounts)

frontend/cs/coeff_table.go

@@ -33,7 +33,7 @@ func NewCoeffTable() CoeffTable {
 	return st
 }
 
-// CoeffID tries to fetch the entry where b is if it exits, otherwise appends b to
+// CoeffID tries to fetch the entry where b is if it exists, otherwise appends b to
 // the list of Coeffs and returns the corresponding entry
 func (t *CoeffTable) CoeffID(v *big.Int) int {
 

frontend/cs/r1cs/api.go

@@ -91,7 +91,7 @@ func (builder *builder) MulAcc(a, b, c frontend.Variable) frontend.Variable {
 		// it fits, no mem alloc
 		_a = append(_a, builder.mbuf2...)
 	} else {
-		// allocate a expression linear with extended capacity
+		// allocate an expression linear with extended capacity
 		_a = make(expr.LinearExpression, len(builder.mbuf2), len(builder.mbuf2)*3)
 		copy(_a, builder.mbuf2)
 	}
@@ -350,7 +350,7 @@ func (builder *builder) Inverse(i1 frontend.Variable) frontend.Variable {
 // n is the number of bits to select (starting from lsb)
 // n default value is fr.Bits the number of bits needed to represent a field element
 //
-// The result in in little endian (first bit= lsb)
+// The result is in little endian (first bit= lsb)
 func (builder *builder) ToBinary(i1 frontend.Variable, n ...int) []frontend.Variable {
 	// nbBits
 	nbBits := builder.cs.FieldBitLen()

frontend/cs/r1cs/builder.go

@@ -316,7 +316,7 @@ func (builder *builder) constantValue(v frontend.Variable) (constraint.Element,
 	return builder.cs.FromInterface(v), true
 }
 
-// toVariable will return (and allocate if neccesary) a linearExpression from given value
+// toVariable will return (and allocate if necessary) a linearExpression from given value
 //
 // if input is already a linearExpression, does nothing
 // else, attempts to convert input to a big.Int (see utils.FromInterface) and returns a toVariable linearExpression

frontend/cs/r1cs/heap.go

@@ -79,7 +79,7 @@ func (h *minHeap) down(i0, n int) bool {
 	return i > i0
 }
 
-// linMeta stores meta data to iterate over a linear expression
+// linMeta stores metadata to iterate over a linear expression
 type linMeta struct {
 	lID int // argument ID to retrieve the position of the list in the argument
 	tID int // termID current iteration position (starts at 0)

frontend/cs/scs/api.go

@@ -232,7 +232,7 @@ func (builder *builder) Inverse(i1 frontend.Variable) frontend.Variable {
 // n is the number of bits to select (starting from lsb)
 // n default value is fr.Bits the number of bits needed to represent a field element
 //
-// The result in in little endian (first bit= lsb)
+// The result is in little endian (first bit= lsb)
 func (builder *builder) ToBinary(i1 frontend.Variable, n ...int) []frontend.Variable {
 	// nbBits
 	nbBits := builder.cs.FieldBitLen()

frontend/cs/scs/builder.go

@@ -56,7 +56,7 @@ type builder struct {
 	// map for recording boolean constrained variables (to not constrain them twice)
 	mtBooleans map[expr.Term]struct{}
 
-	// records multiplications constraint to avoid duplicate.
+	// records multiplications constraint to avoid duplicates.
 	// see mulConstraintExist(...)
 	mMulInstructions map[uint64]int