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id-glossary.md

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title
Glossary

P n

  • A path graph or a path of n nodes.

${\left({b}{{0}},{b}{{1}},\ldots,{b}_{{{n}-{1}}}\right)}$

  • A sequence of bytes or byte array of length n

𝔹 n

  • A set of all byte arrays of length n

${I}={\left({B}{{n}}…{B}{{0}}\right)}_{{{256}}}$

  • A non-negative integer in base 256

${B}={\left({b}{{0}},{b}{{1}},…,{b}_{{n}}\right)}$

  • The little-endian representation of a non-negative interger ${I}={\left({B}{{n}}…{B}{{0}}\right)}{{{256}}}$ such that ${b}{{i}}≔{B}_{{i}}$

Enc L E

  • The little-endian encoding function.

C

  • A blockchain is defined as a directed path graph.

Block

  • A node of the directed path graph (blockchain) C

Genesis Block

  • The unique sink of blockchain C

Head

  • The source of blockchain C

P ( B )

  • The parent of block B

UNIX time

  • The number of milliseconds that have elapsed since the Unix epoch as a 64-bit integer

B T

  • The block tree of a blockchain

G

  • The genesis block, the root of the block tree BT

CHAIN ( B )

  • The path graph from G to B in B T .

H e a d ( C )

  • The head of chain C.

| C |

  • The length of chain C as a path graph

SubChain ( B , B )

  • The subgraph of C h a i n ( B ) path graph containing both B and B .

B ( B T )

  • The set of all subchains of B T rooted at block B .

, ( B T )

  • G ( B T ) i.e. the set of all chains of B T rooted at genesis block

Longest-Chain ( B T )

  • The longest sub path graph of B T i.e. ${C}:{\left|{C}\right|}=\max_{{{C}{{i}}∈ℂ}}{\left|{C}{{i}}\right|}$

Longest-Path ( B T )

  • The longest sub path graph of ( P ) B T with earliest block arrival time

Deepest-Leaf ( B T )

  • Head Longest-Path ( B T ) i.e. the head of Longest-Path ( B T )

B > B

  • B is a descendant of B in the block tree

StoredValue ( k )

  • The function to retrieve the value stored under a specific key in the state storage.

State trie, trie

  • The Merkle radix-16 Tree, which stores hashes of storage entries.

KeyEncode ( k )

  • The function to encode keys for labeling branches of the trie.

𝒩

  • The set of all nodes in the Polkadot state trie.

N

  • An individual node in the trie.

𝒩 b

  • A branch node of the trie which has at least one and at most 16 children

𝒩 l

  • A childless leaf node of the trie

p k N A g r

  • The aggregated prefix key of node N

p k N

  • The (suffix) partial key of node N

Index N

  • A function returning an integer in range of {0, . . . ,15} representing the index of a child node of node N among the children of N

v N

  • Node value containing the header of node N , its partial key and the digest of its childern values

H e a d N

  • The node header of trie node N storing information about the node’s type and kay

H ( N )

  • The Merkle value of node N .

ChildrenBitmap

  • The binary function indicates which child of a given node is present in the trie.

s v N

  • The subvalue of a trie node N .

Child storage

  • A sub storage of the state storage which has the same structure, although being stored separately

Child trie

  • State trie of a child storage

Transaction Queue

H p

  • The 32-byte Blake2b hash of the header of the parent of the block.

${H}{{i}},{H}{{i}}{\left({B}\right)}$

  • Block number, the incremental integer index of the current block in the chain.

H r

  • The hash of the root of the Merkle trie of the state storage at a given block

H e

  • An auxiliary field in the block header used by Runtime to validate the integrity of the extrinsics composing the block body.

${H}{{d}}$, ${H}{{d}}{\left({B}\right)}$

  • A block header used to store any chain-specific auxiliary data.

H h ( B )

  • The hash of the header of block B

B o d y ( B )

  • The body of block B consisting of a set of extrinsics

M v r , s t a g e

  • Vote message broadcasted by the voter v as part of the finality protocol

M v r , F i n ( B )

  • The commit message broadcasted by voter v indicating that they have finalized bock B in round r

v

  • GRANDPA voter node, which casts votes in the finality protocol

k v p r

  • The private key of voter v

v i d

  • The public key of voter v

𝕍 B , 𝕍

  • The set of all GRANDPA voters for at block B

G S

  • GRANDPA protocol state consisting of the set of voters, the number of times voters set has changed, and the current round number.

r

  • The voting round counter in the finality protocol

V B

  • A GRANDPA vote casted in favor of block B

V v r , p v

  • A GRANDPA vote casted by voter v during the pre-vote stage of round r

V v r , p c

  • A GRANDPA vote casted by voter v during the pre-commit stage of round r

J r , s t a g e ( B )

  • The justification for pre-committing or committing to block B in round r of finality protocol

${Sign}^{{{r},{stage}}}{\left\lbrace{v}{{i}}\right\rbrace}{\left({B}\right)}$

  • The signature of voter v on their vote to block B, broadcasted during the specified stage of finality round r

r , s t a g e

  • The set of all equivocator voters in sub-round ‘‘stage'' of round r

{ o b s ( v ) } r , s t a g e

  • The set of all equivocator voters in sub-round ‘‘stage'' of round r observed by voter v

V D { o b s ( v ) } r , s t a g e ( B )

  • The set of observed direct votes for block B in round r

V { o b s ( v ) } r , s t a g e

  • The set of total votes observed by voter v in sub-round ‘‘stage'' of round r

V { o b s ( v ) } r , s t a g e ( B )

  • The set of all observed votes by v in the sub-round “stage” of round r (directly or indirectly) for block B

B v r , p v

  • The currently pre-voted block in round r . The GRANDPA GHOST of round r

Account key, ( s k a , p k a )

  • A key pair of types accepted by the Polkadot protocol which can be used to sign transactions

E n c S C ( A )

  • SCALE encoding of value A

${T}≔{\left({A}{{1}},\ldots,{A}{{n}}\right)}$

  • A tuple of values A i 's each of different type

Varying Data Types $𝒯={\left\lbrace{T}{{1}},…,{T}{{n}}\right\rbrace}$

  • A data type representing any of varying types ${T}{{1}},…,{T}{{n}}$.

${S}≔{A}{{1}},…,{A}{{n}}$

  • Sequence of values A i of the same type

E n c { S C } L e n ( n )

  • SCALE length encoding, aka. compact encoding of non-negative interger n of arbitrary size.

E n c H E ( P K )

  • Hex encoding