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Decompose multisig signer pubkeys for p-token #1018

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automergerpr-permission-manager merged 1 commit into from
Apr 8, 2026
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Decompose multisig signer pubkeys for p-token #1018

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101 changes: 92 additions & 9 deletions kmir/src/kmir/kdist/mir-semantics/symbolic/p-token.md
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Original file line number Diff line number Diff line change
Expand Up @@ -110,6 +110,39 @@ The code uses some helper sorts for better readability.
rule allBytes( ListItem(Integer(_, 8, false)) REST:List) => allBytes(REST)
rule allBytes( ListItem(_OTHER) _:List) => false [owise]

// Construct a 32-byte pubkey List from individual Int variables.
// When used with existential variables (?Var:Int), this produces a concrete List structure
// that ==K can decompose element-wise, avoiding opaque symbolic List equality in SMT.
syntax List ::= #mkPubkey (
Int , Int , Int , Int , Int , Int , Int , Int ,
Int , Int , Int , Int , Int , Int , Int , Int ,
Int , Int , Int , Int , Int , Int , Int , Int ,
Int , Int , Int , Int , Int , Int , Int , Int ) [macro]
rule #mkPubkey(
B0, B1, B2, B3, B4, B5, B6, B7,
B8, B9, B10, B11, B12, B13, B14, B15,
B16, B17, B18, B19, B20, B21, B22, B23,
B24, B25, B26, B27, B28, B29, B30, B31 ) =>
ListItem(Integer(B0, 8, false)) ListItem(Integer(B1, 8, false))
ListItem(Integer(B2, 8, false)) ListItem(Integer(B3, 8, false))
ListItem(Integer(B4, 8, false)) ListItem(Integer(B5, 8, false))
ListItem(Integer(B6, 8, false)) ListItem(Integer(B7, 8, false))
ListItem(Integer(B8, 8, false)) ListItem(Integer(B9, 8, false))
ListItem(Integer(B10, 8, false)) ListItem(Integer(B11, 8, false))
ListItem(Integer(B12, 8, false)) ListItem(Integer(B13, 8, false))
ListItem(Integer(B14, 8, false)) ListItem(Integer(B15, 8, false))
ListItem(Integer(B16, 8, false)) ListItem(Integer(B17, 8, false))
ListItem(Integer(B18, 8, false)) ListItem(Integer(B19, 8, false))
ListItem(Integer(B20, 8, false)) ListItem(Integer(B21, 8, false))
ListItem(Integer(B22, 8, false)) ListItem(Integer(B23, 8, false))
ListItem(Integer(B24, 8, false)) ListItem(Integer(B25, 8, false))
ListItem(Integer(B26, 8, false)) ListItem(Integer(B27, 8, false))
ListItem(Integer(B28, 8, false)) ListItem(Integer(B29, 8, false))
ListItem(Integer(B30, 8, false)) ListItem(Integer(B31, 8, false))

syntax Bool ::= #isPByte ( Int ) [macro]
rule #isPByte(X) => 0 <=Int X andBool X <Int 256

syntax Value ::= fromKey ( Key ) [function, total]
// -----------------------------------------------
// We assume that the Key always contains valid data, because it is constructed via toKey.
Expand Down Expand Up @@ -659,24 +692,74 @@ An `AccountInfo` reference is passed to the function.
#### `#addMultisig`

```{.k .symbolic}
// Multisig cheatcode: decompose signer pubkeys into individual byte variables.
// Each ?SiNBj:Int is a single byte (0..255), giving 32 concrete ListItems per signer.
// This allows ==K on pubkey Lists to decompose into integer equalities (fast for SMT),
// instead of opaque symbolic List equality (causes Z3 timeout at scale).
rule #addMultisig(Aggregate(variantIdx(0), _:List ListItem(Integer(DATA_LEN, 64, false))) #as P_ACC)
=> PAccountMultisig(
#toPAcc(P_ACC),
IMulti(U8(?M),
U8(?N),
U8(?INITIALISED),
Signers( ListItem(Key(?Signer0))
ListItem(Key(?Signer1))
ListItem(Key(?Signer2))
Signers( ListItem(Key(#mkPubkey(
?Si0B0:Int, ?Si0B1:Int, ?Si0B2:Int, ?Si0B3:Int,
?Si0B4:Int, ?Si0B5:Int, ?Si0B6:Int, ?Si0B7:Int,
?Si0B8:Int, ?Si0B9:Int, ?Si0B10:Int, ?Si0B11:Int,
?Si0B12:Int, ?Si0B13:Int, ?Si0B14:Int, ?Si0B15:Int,
?Si0B16:Int, ?Si0B17:Int, ?Si0B18:Int, ?Si0B19:Int,
?Si0B20:Int, ?Si0B21:Int, ?Si0B22:Int, ?Si0B23:Int,
?Si0B24:Int, ?Si0B25:Int, ?Si0B26:Int, ?Si0B27:Int,
?Si0B28:Int, ?Si0B29:Int, ?Si0B30:Int, ?Si0B31:Int)))
ListItem(Key(#mkPubkey(
?Si1B0:Int, ?Si1B1:Int, ?Si1B2:Int, ?Si1B3:Int,
?Si1B4:Int, ?Si1B5:Int, ?Si1B6:Int, ?Si1B7:Int,
?Si1B8:Int, ?Si1B9:Int, ?Si1B10:Int, ?Si1B11:Int,
?Si1B12:Int, ?Si1B13:Int, ?Si1B14:Int, ?Si1B15:Int,
?Si1B16:Int, ?Si1B17:Int, ?Si1B18:Int, ?Si1B19:Int,
?Si1B20:Int, ?Si1B21:Int, ?Si1B22:Int, ?Si1B23:Int,
?Si1B24:Int, ?Si1B25:Int, ?Si1B26:Int, ?Si1B27:Int,
?Si1B28:Int, ?Si1B29:Int, ?Si1B30:Int, ?Si1B31:Int)))
ListItem(Key(#mkPubkey(
?Si2B0:Int, ?Si2B1:Int, ?Si2B2:Int, ?Si2B3:Int,
?Si2B4:Int, ?Si2B5:Int, ?Si2B6:Int, ?Si2B7:Int,
?Si2B8:Int, ?Si2B9:Int, ?Si2B10:Int, ?Si2B11:Int,
?Si2B12:Int, ?Si2B13:Int, ?Si2B14:Int, ?Si2B15:Int,
?Si2B16:Int, ?Si2B17:Int, ?Si2B18:Int, ?Si2B19:Int,
?Si2B20:Int, ?Si2B21:Int, ?Si2B22:Int, ?Si2B23:Int,
?Si2B24:Int, ?Si2B25:Int, ?Si2B26:Int, ?Si2B27:Int,
?Si2B28:Int, ?Si2B29:Int, ?Si2B30:Int, ?Si2B31:Int)))
)
)
)
ensures 0 <=Int ?M andBool ?M <=Int 256
andBool 0 <=Int ?N andBool ?N <=Int 256
andBool 0 <=Int ?INITIALISED andBool ?INITIALISED <=Int 256
andBool size(?Signer0) ==Int 32 andBool allBytes(?Signer0)
andBool size(?Signer1) ==Int 32 andBool allBytes(?Signer1)
andBool size(?Signer2) ==Int 32 andBool allBytes(?Signer2)
ensures #isPByte(?M) andBool #isPByte(?N) andBool #isPByte(?INITIALISED)
// signer 0
andBool #isPByte(?Si0B0) andBool #isPByte(?Si0B1) andBool #isPByte(?Si0B2) andBool #isPByte(?Si0B3)
andBool #isPByte(?Si0B4) andBool #isPByte(?Si0B5) andBool #isPByte(?Si0B6) andBool #isPByte(?Si0B7)
andBool #isPByte(?Si0B8) andBool #isPByte(?Si0B9) andBool #isPByte(?Si0B10) andBool #isPByte(?Si0B11)
andBool #isPByte(?Si0B12) andBool #isPByte(?Si0B13) andBool #isPByte(?Si0B14) andBool #isPByte(?Si0B15)
andBool #isPByte(?Si0B16) andBool #isPByte(?Si0B17) andBool #isPByte(?Si0B18) andBool #isPByte(?Si0B19)
andBool #isPByte(?Si0B20) andBool #isPByte(?Si0B21) andBool #isPByte(?Si0B22) andBool #isPByte(?Si0B23)
andBool #isPByte(?Si0B24) andBool #isPByte(?Si0B25) andBool #isPByte(?Si0B26) andBool #isPByte(?Si0B27)
andBool #isPByte(?Si0B28) andBool #isPByte(?Si0B29) andBool #isPByte(?Si0B30) andBool #isPByte(?Si0B31)
// signer 1
andBool #isPByte(?Si1B0) andBool #isPByte(?Si1B1) andBool #isPByte(?Si1B2) andBool #isPByte(?Si1B3)
andBool #isPByte(?Si1B4) andBool #isPByte(?Si1B5) andBool #isPByte(?Si1B6) andBool #isPByte(?Si1B7)
andBool #isPByte(?Si1B8) andBool #isPByte(?Si1B9) andBool #isPByte(?Si1B10) andBool #isPByte(?Si1B11)
andBool #isPByte(?Si1B12) andBool #isPByte(?Si1B13) andBool #isPByte(?Si1B14) andBool #isPByte(?Si1B15)
andBool #isPByte(?Si1B16) andBool #isPByte(?Si1B17) andBool #isPByte(?Si1B18) andBool #isPByte(?Si1B19)
andBool #isPByte(?Si1B20) andBool #isPByte(?Si1B21) andBool #isPByte(?Si1B22) andBool #isPByte(?Si1B23)
andBool #isPByte(?Si1B24) andBool #isPByte(?Si1B25) andBool #isPByte(?Si1B26) andBool #isPByte(?Si1B27)
andBool #isPByte(?Si1B28) andBool #isPByte(?Si1B29) andBool #isPByte(?Si1B30) andBool #isPByte(?Si1B31)
// signer 2
andBool #isPByte(?Si2B0) andBool #isPByte(?Si2B1) andBool #isPByte(?Si2B2) andBool #isPByte(?Si2B3)
andBool #isPByte(?Si2B4) andBool #isPByte(?Si2B5) andBool #isPByte(?Si2B6) andBool #isPByte(?Si2B7)
andBool #isPByte(?Si2B8) andBool #isPByte(?Si2B9) andBool #isPByte(?Si2B10) andBool #isPByte(?Si2B11)
andBool #isPByte(?Si2B12) andBool #isPByte(?Si2B13) andBool #isPByte(?Si2B14) andBool #isPByte(?Si2B15)
andBool #isPByte(?Si2B16) andBool #isPByte(?Si2B17) andBool #isPByte(?Si2B18) andBool #isPByte(?Si2B19)
andBool #isPByte(?Si2B20) andBool #isPByte(?Si2B21) andBool #isPByte(?Si2B22) andBool #isPByte(?Si2B23)
andBool #isPByte(?Si2B24) andBool #isPByte(?Si2B25) andBool #isPByte(?Si2B26) andBool #isPByte(?Si2B27)
andBool #isPByte(?Si2B28) andBool #isPByte(?Si2B29) andBool #isPByte(?Si2B30) andBool #isPByte(?Si2B31)
andBool DATA_LEN ==Int 99 // size_of(Multisig), see pinocchio_token_interface::state::Transmutable instance
```

Expand Down
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