Script Execution

For each non-coinbase input $i$, spend authorization is the predicate:

$$ \operatorname{Authorize}_{R}(tx,i,coin,u,H) \in {\top,\bot}, $$

where $u=(scriptSig,witness)$ is the unlocking data, $coin$ is the spent UTXO, $R$ is the active rule context, and $H$ is the candidate height and median-time context. Authorization chooses a spend form, constructs a script machine state, and evaluates the committed program.

Spend forms

Form	Required relation
Legacy	$Eval_R(scriptSig,BASE)$ then $Eval_R(scriptPubKey,BASE)$; witness empty; final stack top is true.
P2SH	$R$ includes P2SH; `scriptSig` is push-only; final pushed item is `redeemScript`; $HASH160(redeemScript)$ matches; $Eval_R(redeemScript,BASE)$ succeeds on the pushed stack.
Witness v0 key hash	Native witness program length 20; `scriptSig` empty unless P2SH-wrapped; witness stack is $(signature,pubkey)$; $HASH160(pubkey)$ matches; ECDSA verifies $M_wit0$.
Witness v0 script hash	Native witness program length 32; final witness item is `witnessScript`; $SHA256(witnessScript)$ matches; $Eval_R(witnessScript,WITNESS_V0)$ succeeds on the remaining witness stack.
Taproot key path	$R$ includes Taproot; witness stack, after optional annex removal, contains one Schnorr signature; BIP340 verifies $M_tr$ under the output key.
Taproot script path	Control block commits a tapleaf to the output key. Leaf version `0xc0` evaluates as Tapscript; unknown leaf versions succeed after commitment validation.
Unknown witness version	A syntactically valid witness program with no assigned meaning succeeds without execution.

Native witness spends require empty scriptSig; P2SH-wrapped witness spends require scriptSig to push exactly the witness program (sources: bip-0016,bip-0141,bip-0143,bip-0340,bip-0341,bip-0342).

Machine state

Script evaluation is a deterministic transition over:

$$ X=(tx,i,coin,script,pc,S,A,C,R,\sigma,k,\alpha,\beta). $$

Field	Meaning
`script`, `pc`	Program bytes and instruction cursor.
$S,A,C$	Main stack, altstack, and conditional-execution stack.
$R,\sigma$	Active rule context and signature version: $BASE$, $WITNESS_V0$, or $TAPSCRIPT$.
$k$	Last executed code-separator position for signature-message construction.
$\alpha$	Taproot annex, if present.
$\beta$	Tapscript validation-weight budget.

Legacy and witness-v0 execution enforce the script limits named in Appendix Constants. Tapscript removes the script-size and per-script-opcode limits, keeps the stack-item and stack-size limits, and sets:

$$ \beta = \text{\code{TAPSCRIPT_SIGOPS_BUDGET_BASE}}+ \operatorname{serializedWitnessSize}(input). $$

Each executed signature opcode with a nonempty signature subtracts TAPSCRIPT_SIGOPS_COST; negative $\beta$ fails.

Evaluation

$$ \operatorname{Eval}_{R}(script,\sigma,S_0)= \begin{cases} \top, & \text{execution halts successfully with required final stack,}\ \bot, & \text{parsing, execution, resource, or final-stack validation fails.} \end{cases} $$

If $\sigma=TAPSCRIPT$, the script is scanned for any OP_SUCCESSx index before ordinary execution; encountering one succeeds. Otherwise, instructions are decoded left to right and $Step$ is applied while all entries of $C$ are true. Non-control opcodes in inactive branches do not mutate $S$, but parse-stage failures and Tapscript OP_SUCCESSx detection still apply.

Successful termination requires an empty $C$. Legacy and witness-v0 require a nonempty $S$ whose top element casts to true. Tapscript requires exactly one stack element, and that element must cast to true.

Primitive relations

Relation	Definition
$CastToBool(x)$	False iff $x$ is empty, zero, or negative zero; true otherwise.
$Num(x,n,min)$	Signed-magnitude little-endian integer from byte vector $x$, length at most $n$; if $min$, nonzero encodings must be minimal.
$MinimalPush(op,x)$	True iff $op$ is the shortest permitted push form for $x$.
$LockTime(X,n)$	Units match `tx.lockTime`, $n<= tx.lockTime$, and the input sequence is nonfinal.
$Sequence(X,n)$	BIP68 is active in $R$, disable/type bits permit comparison, and the input sequence satisfies $n$.
$CheckSig(X,sig,key,h)$	Empty signatures return false. Legacy and witness-v0 use ECDSA over secp256k1; Taproot and Tapscript use BIP340 Schnorr. Tapscript key size 0 fails, size 32 verifies, and other nonzero key sizes are unknown key types that pass current consensus.

Signature messages

Signature checks verify exactly one digest:

$$ \begin{aligned} M_{\mathrm{legacy}} &= \operatorname{SigMsg}{\mathrm{legacy}}(tx,i,k,h),\ M{\mathrm{wit0}} &= \operatorname{SigMsg}{\mathrm{wit0}}(tx,i,coin,k,h),\ M{\mathrm{tr}} &= \operatorname{SigMsg}_{\mathrm{tr}}(tx,i,coin,\alpha,k,h). \end{aligned} $$

Hash type bytes are 0x00 DEFAULT for Taproot, 0x01 ALL, 0x02 NONE, 0x03 SINGLE, and 0x80 ANYONECANPAY ORed with non-default forms. ALL, NONE, and SINGLE select the output commitment set; ANYONECANPAY restricts input commitment to the signed input. Legacy out-of-range SINGLE signs uint256::ONE; Taproot out-of-range SINGLE fails (sources: bip-0143,bip-0341,bip-0342).

Opcode classes

Effects use (before -- after) for stack transitions, with the rightmost item at the top of $S$. Parameterized direct byte pushes are represented as a single family; every named opcode is listed separately.

Index	Opcode	Effect
`0`	`OP_0 / OP_FALSE`	Push empty vector.
`1-75`	`OP_PUSHBYTES_n`	Push the next $n$ script bytes.
`76`	`OP_PUSHDATA1`	Next `uint8` gives pushed byte length.
`77`	`OP_PUSHDATA2`	Next little-endian `uint16` gives pushed byte length.
`78`	`OP_PUSHDATA4`	Next little-endian `uint32` gives pushed byte length.
`79`	`OP_1NEGATE`	Push $-1$.
`81`	`OP_1`	Push integer $1$.
`82`	`OP_2`	Push integer $2$.
`83`	`OP_3`	Push integer $3$.
`84`	`OP_4`	Push integer $4$.
`85`	`OP_5`	Push integer $5$.
`86`	`OP_6`	Push integer $6$.
`87`	`OP_7`	Push integer $7$.
`88`	`OP_8`	Push integer $8$.
`89`	`OP_9`	Push integer $9$.
`90`	`OP_10`	Push integer $10$.
`91`	`OP_11`	Push integer $11$.
`92`	`OP_12`	Push integer $12$.
`93`	`OP_13`	Push integer $13$.
`94`	`OP_14`	Push integer $14$.
`95`	`OP_15`	Push integer $15$.
`96`	`OP_16`	Push integer $16$.

Index	Opcode	Effect
`97`	`OP_NOP`	No effect.
`99`	`OP_IF`	`(v --)`; push $CastToBool(v)$ to $C$.
`100`	`OP_NOTIF`	`(v --)`; push negated condition to $C$.
`101`	`OP_VERIF`	Fail.
`102`	`OP_VERNOTIF`	Fail.
`103`	`OP_ELSE`	Toggle top of $C$; unmatched `ELSE` fails.
`104`	`OP_ENDIF`	Pop top of $C$; unmatched `ENDIF` fails.
`105`	`OP_VERIFY`	`(v --)` if true; otherwise fail.
`106`	`OP_RETURN`	Fail.

Index	Opcode	Effect
`107`	`OP_TOALTSTACK`	Move top of $S$ to $A$.
`108`	`OP_FROMALTSTACK`	Move top of $A$ to $S$.
`109`	`OP_2DROP`	`(x1 x2 --)`.
`110`	`OP_2DUP`	`(x1 x2 -- x1 x2 x1 x2)`.
`111`	`OP_3DUP`	`(x1 x2 x3 -- x1 x2 x3 x1 x2 x3)`.
`112`	`OP_2OVER`	`(x1 x2 x3 x4 -- x1 x2 x3 x4 x1 x2)`.
`113`	`OP_2ROT`	`(x1 x2 x3 x4 x5 x6 -- x3 x4 x5 x6 x1 x2)`.
`114`	`OP_2SWAP`	`(x1 x2 x3 x4 -- x3 x4 x1 x2)`.
`115`	`OP_IFDUP`	Duplicate top item iff it casts true.
`116`	`OP_DEPTH`	Push stack depth.
`117`	`OP_DROP`	`(x --)`.
`118`	`OP_DUP`	`(x -- x x)`.
`119`	`OP_NIP`	`(x1 x2 -- x2)`.
`120`	`OP_OVER`	`(x1 x2 -- x1 x2 x1)`.
`121`	`OP_PICK`	`(n -- x)`; copy stack item $n$ to the top.
`122`	`OP_ROLL`	`(n -- x)`; move stack item $n$ to the top.
`123`	`OP_ROT`	`(x1 x2 x3 -- x2 x3 x1)`.
`124`	`OP_SWAP`	`(x1 x2 -- x2 x1)`.
`125`	`OP_TUCK`	`(x1 x2 -- x2 x1 x2)`.
`130`	`OP_SIZE`	`(x -- x len(x))`.

Index	Opcode	Effect
`135`	`OP_EQUAL`	Byte-vector equality.
`136`	`OP_EQUALVERIFY`	Equality followed by `VERIFY`.
`139`	`OP_1ADD`	`(x -- x+1)` over $Num(x,4,min)$.
`140`	`OP_1SUB`	`(x -- x-1)` over $Num(x,4,min)$.
`143`	`OP_NEGATE`	`(x -- -x)` over $Num(x,4,min)$.
`144`	`OP_ABS`	`(x –
`145`	`OP_NOT`	Push $1$ iff numeric input is zero; otherwise push $0$.
`146`	`OP_0NOTEQUAL`	Push $0$ iff numeric input is zero; otherwise push $1$.
`147`	`OP_ADD`	`(x y -- x+y)` over script numbers.
`148`	`OP_SUB`	`(x y -- x-y)` over script numbers.
`154`	`OP_BOOLAND`	Push $1$ iff both numeric inputs are nonzero.
`155`	`OP_BOOLOR`	Push $1$ iff at least one numeric input is nonzero.
`156`	`OP_NUMEQUAL`	Numeric equality.
`157`	`OP_NUMEQUALVERIFY`	Numeric equality followed by `VERIFY`.
`158`	`OP_NUMNOTEQUAL`	Numeric inequality.
`159`	`OP_LESSTHAN`	Numeric less-than comparison.
`160`	`OP_GREATERTHAN`	Numeric greater-than comparison.
`161`	`OP_LESSTHANOREQUAL`	Numeric less-than-or-equal comparison.
`162`	`OP_GREATERTHANOREQUAL`	Numeric greater-than-or-equal comparison.
`163`	`OP_MIN`	Push the smaller numeric input.
`164`	`OP_MAX`	Push the larger numeric input.
`165`	`OP_WITHIN`	`(x min max -- ok)` where $min <= x < max$.

Index	Opcode	Effect
`166`	`OP_RIPEMD160`	`(x -- RIPEMD160(x))`.
`167`	`OP_SHA1`	`(x -- SHA1(x))`.
`168`	`OP_SHA256`	`(x -- SHA256(x))`.
`169`	`OP_HASH160`	`(x -- HASH160(x))`.
`170`	`OP_HASH256`	`(x -- H(x))`.
`171`	`OP_CODESEPARATOR`	Set $k$ to this opcode position.
`172`	`OP_CHECKSIG`	`(sig key -- ok)` using $CheckSig$.
`173`	`OP_CHECKSIGVERIFY`	`CHECKSIG` followed by `VERIFY`.
`174`	`OP_CHECKMULTISIG`	`(dummy sig[m] m key[n] n -- ok)`; enforces historical dummy rule when active; disabled in Tapscript.
`175`	`OP_CHECKMULTISIGVERIFY`	`CHECKMULTISIG` followed by `VERIFY`; disabled in Tapscript.
`186`	`OP_CHECKSIGADD`	Tapscript only: `(sig n key -- n+ok)`.

Index	Opcode	Effect
`176`	`OP_NOP1`	No effect.
`177`	`OP_CHECKLOCKTIMEVERIFY / OP_NOP2`	If active in $R$, require $LockTime(X,n)$; otherwise no effect.
`178`	`OP_CHECKSEQUENCEVERIFY / OP_NOP3`	If active in $R$, require $Sequence(X,n)$; otherwise no effect.
`179`	`OP_NOP4`	No effect unless redefined by active soft-fork rules.
`180`	`OP_NOP5`	No effect unless redefined by active soft-fork rules.
`181`	`OP_NOP6`	No effect unless redefined by active soft-fork rules.
`182`	`OP_NOP7`	No effect unless redefined by active soft-fork rules.
`183`	`OP_NOP8`	No effect unless redefined by active soft-fork rules.
`184`	`OP_NOP9`	No effect unless redefined by active soft-fork rules.
`185`	`OP_NOP10`	No effect unless redefined by active soft-fork rules.

Index	Opcode	Effect
`80`	`OP_RESERVED / OP_SUCCESS80`	Reserved failure if executed outside Tapscript; Tapscript success.
`98`	`OP_VER / OP_SUCCESS98`	Reserved failure if executed outside Tapscript; Tapscript success.
`126`	`OP_CAT / OP_SUCCESS126`	Disabled failure outside Tapscript; Tapscript success.
`127`	`OP_SUBSTR / OP_SUCCESS127`	Disabled failure outside Tapscript; Tapscript success.
`128`	`OP_LEFT / OP_SUCCESS128`	Disabled failure outside Tapscript; Tapscript success.
`129`	`OP_RIGHT / OP_SUCCESS129`	Disabled failure outside Tapscript; Tapscript success.
`131`	`OP_INVERT / OP_SUCCESS131`	Disabled failure outside Tapscript; Tapscript success.
`132`	`OP_AND / OP_SUCCESS132`	Disabled failure outside Tapscript; Tapscript success.
`133`	`OP_OR / OP_SUCCESS133`	Disabled failure outside Tapscript; Tapscript success.
`134`	`OP_XOR / OP_SUCCESS134`	Disabled failure outside Tapscript; Tapscript success.
`137`	`OP_RESERVED1 / OP_SUCCESS137`	Reserved failure if executed outside Tapscript; Tapscript success.
`138`	`OP_RESERVED2 / OP_SUCCESS138`	Reserved failure if executed outside Tapscript; Tapscript success.
`141`	`OP_2MUL / OP_SUCCESS141`	Disabled failure outside Tapscript; Tapscript success.
`142`	`OP_2DIV / OP_SUCCESS142`	Disabled failure outside Tapscript; Tapscript success.
`149`	`OP_MUL / OP_SUCCESS149`	Disabled failure outside Tapscript; Tapscript success.
`150`	`OP_DIV / OP_SUCCESS150`	Disabled failure outside Tapscript; Tapscript success.
`151`	`OP_MOD / OP_SUCCESS151`	Disabled failure outside Tapscript; Tapscript success.
`152`	`OP_LSHIFT / OP_SUCCESS152`	Disabled failure outside Tapscript; Tapscript success.
`153`	`OP_RSHIFT / OP_SUCCESS153`	Disabled failure outside Tapscript; Tapscript success.
`187`	`OP_SUCCESS187`	Tapscript success; invalid outside Tapscript.
`188`	`OP_SUCCESS188`	Tapscript success; invalid outside Tapscript.
`189`	`OP_SUCCESS189`	Tapscript success; invalid outside Tapscript.
`190`	`OP_SUCCESS190`	Tapscript success; invalid outside Tapscript.
`191`	`OP_SUCCESS191`	Tapscript success; invalid outside Tapscript.
`192`	`OP_SUCCESS192`	Tapscript success; invalid outside Tapscript.
`193`	`OP_SUCCESS193`	Tapscript success; invalid outside Tapscript.
`194`	`OP_SUCCESS194`	Tapscript success; invalid outside Tapscript.
`195`	`OP_SUCCESS195`	Tapscript success; invalid outside Tapscript.
`196`	`OP_SUCCESS196`	Tapscript success; invalid outside Tapscript.
`197`	`OP_SUCCESS197`	Tapscript success; invalid outside Tapscript.
`198`	`OP_SUCCESS198`	Tapscript success; invalid outside Tapscript.
`199`	`OP_SUCCESS199`	Tapscript success; invalid outside Tapscript.
`200`	`OP_SUCCESS200`	Tapscript success; invalid outside Tapscript.
`201`	`OP_SUCCESS201`	Tapscript success; invalid outside Tapscript.
`202`	`OP_SUCCESS202`	Tapscript success; invalid outside Tapscript.
`203`	`OP_SUCCESS203`	Tapscript success; invalid outside Tapscript.
`204`	`OP_SUCCESS204`	Tapscript success; invalid outside Tapscript.
`205`	`OP_SUCCESS205`	Tapscript success; invalid outside Tapscript.
`206`	`OP_SUCCESS206`	Tapscript success; invalid outside Tapscript.
`207`	`OP_SUCCESS207`	Tapscript success; invalid outside Tapscript.
`208`	`OP_SUCCESS208`	Tapscript success; invalid outside Tapscript.
`209`	`OP_SUCCESS209`	Tapscript success; invalid outside Tapscript.
`210`	`OP_SUCCESS210`	Tapscript success; invalid outside Tapscript.
`211`	`OP_SUCCESS211`	Tapscript success; invalid outside Tapscript.
`212`	`OP_SUCCESS212`	Tapscript success; invalid outside Tapscript.
`213`	`OP_SUCCESS213`	Tapscript success; invalid outside Tapscript.
`214`	`OP_SUCCESS214`	Tapscript success; invalid outside Tapscript.
`215`	`OP_SUCCESS215`	Tapscript success; invalid outside Tapscript.
`216`	`OP_SUCCESS216`	Tapscript success; invalid outside Tapscript.
`217`	`OP_SUCCESS217`	Tapscript success; invalid outside Tapscript.
`218`	`OP_SUCCESS218`	Tapscript success; invalid outside Tapscript.
`219`	`OP_SUCCESS219`	Tapscript success; invalid outside Tapscript.
`220`	`OP_SUCCESS220`	Tapscript success; invalid outside Tapscript.
`221`	`OP_SUCCESS221`	Tapscript success; invalid outside Tapscript.
`222`	`OP_SUCCESS222`	Tapscript success; invalid outside Tapscript.
`223`	`OP_SUCCESS223`	Tapscript success; invalid outside Tapscript.
`224`	`OP_SUCCESS224`	Tapscript success; invalid outside Tapscript.
`225`	`OP_SUCCESS225`	Tapscript success; invalid outside Tapscript.
`226`	`OP_SUCCESS226`	Tapscript success; invalid outside Tapscript.
`227`	`OP_SUCCESS227`	Tapscript success; invalid outside Tapscript.
`228`	`OP_SUCCESS228`	Tapscript success; invalid outside Tapscript.
`229`	`OP_SUCCESS229`	Tapscript success; invalid outside Tapscript.
`230`	`OP_SUCCESS230`	Tapscript success; invalid outside Tapscript.
`231`	`OP_SUCCESS231`	Tapscript success; invalid outside Tapscript.
`232`	`OP_SUCCESS232`	Tapscript success; invalid outside Tapscript.
`233`	`OP_SUCCESS233`	Tapscript success; invalid outside Tapscript.
`234`	`OP_SUCCESS234`	Tapscript success; invalid outside Tapscript.
`235`	`OP_SUCCESS235`	Tapscript success; invalid outside Tapscript.
`236`	`OP_SUCCESS236`	Tapscript success; invalid outside Tapscript.
`237`	`OP_SUCCESS237`	Tapscript success; invalid outside Tapscript.
`238`	`OP_SUCCESS238`	Tapscript success; invalid outside Tapscript.
`239`	`OP_SUCCESS239`	Tapscript success; invalid outside Tapscript.
`240`	`OP_SUCCESS240`	Tapscript success; invalid outside Tapscript.
`241`	`OP_SUCCESS241`	Tapscript success; invalid outside Tapscript.
`242`	`OP_SUCCESS242`	Tapscript success; invalid outside Tapscript.
`243`	`OP_SUCCESS243`	Tapscript success; invalid outside Tapscript.
`244`	`OP_SUCCESS244`	Tapscript success; invalid outside Tapscript.
`245`	`OP_SUCCESS245`	Tapscript success; invalid outside Tapscript.
`246`	`OP_SUCCESS246`	Tapscript success; invalid outside Tapscript.
`247`	`OP_SUCCESS247`	Tapscript success; invalid outside Tapscript.
`248`	`OP_SUCCESS248`	Tapscript success; invalid outside Tapscript.
`249`	`OP_SUCCESS249`	Tapscript success; invalid outside Tapscript.
`250`	`OP_SUCCESS250`	Tapscript success; invalid outside Tapscript.
`251`	`OP_SUCCESS251`	Tapscript success; invalid outside Tapscript.
`252`	`OP_SUCCESS252`	Tapscript success; invalid outside Tapscript.
`253`	`OP_SUCCESS253`	Tapscript success; invalid outside Tapscript.
`254`	`OP_SUCCESS254`	Tapscript success; invalid outside Tapscript.
`255`	`OP_INVALIDOPCODE`	Fail.

Consensus script behavior is defined by the active P2SH, DER, locktime, sequence, NULLDUMMY, SegWit, Taproot, and Tapscript rules (sources: bip-0065,bip-0066,bip-0068,bip-0112,bip-0113,bip-0147,bip-0341,bip-0342,bitcoin-core-v31).

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