@[reducible, inline]

abbrev Lean.Parser.mkAtom (info : Lean.SourceInfo) (val : String) : Lean.Syntax

Equations

• Lean.Parser.mkAtom info val = Lean.Syntax.atom info val

@[reducible, inline]

abbrev Lean.Parser.mkIdent (info : Lean.SourceInfo) (rawVal : Substring) (val : Lake.Name) : Lean.Syntax

Equations

• Lean.Parser.mkIdent info rawVal val = Lean.Syntax.ident info rawVal val []

def Lean.Parser.getNext (input : String) (pos : String.Pos) : Char

Return character after position pos

Equations

• Lean.Parser.getNext input pos = input.get (input.next pos)

def Lean.Parser.maxPrec : Nat

Maximal (and function application) precedence. In the standard lean language, no parser has precedence higher than maxPrec.

Note that nothing prevents users from using a higher precedence, but we strongly discourage them from doing it.

Equations

• Lean.Parser.maxPrec = 1024

def Lean.Parser.argPrec : Nat

Equations

• Lean.Parser.argPrec = 1023

def Lean.Parser.leadPrec : Nat

Equations

• Lean.Parser.leadPrec = 1022

def Lean.Parser.minPrec : Nat

Equations

• Lean.Parser.minPrec = 10

@[reducible, inline]

abbrev Lean.Parser.Token : Type

Equations

• Lean.Parser.Token = String

@[reducible, inline]

abbrev Lean.Parser.TokenTable : Type

Equations

• Lean.Parser.TokenTable = Lean.Data.Trie Lean.Parser.Token

@[reducible, inline]

abbrev Lean.Parser.SyntaxNodeKindSet : Type

Equations

• Lean.Parser.SyntaxNodeKindSet = Lean.PersistentHashMap Lean.SyntaxNodeKind Unit

def Lean.Parser.SyntaxNodeKindSet.insert (s : Lean.Parser.SyntaxNodeKindSet) (k : Lean.SyntaxNodeKind) : Lean.Parser.SyntaxNodeKindSet

Equations

• s.insert k = Lean.PersistentHashMap.insert s k ()

structure Lean.Parser.InputContext : Type

Input string and related data. Recall that the FileMap is a helper structure for mapping String.Pos in the input string to line/column information.

• input : String
• fileName : String
• fileMap : Lean.FileMap

Instances For

• Lean.Parser.instInhabitedInputContext

instance Lean.Parser.instInhabitedInputContext : Inhabited Lean.Parser.InputContext

Equations

• Lean.Parser.instInhabitedInputContext = { default := { input := default, fileName := default, fileMap := default } }

structure Lean.Parser.ParserModuleContext : Type

Input context derived from elaboration of previous commands.

• env : Lean.Environment
• options : Lean.Options
• currNamespace : Lake.Name
• openDecls : List Lean.OpenDecl

structure Lean.Parser.CacheableParserContext : Type

Parser context parts that can be updated without invalidating the parser cache.

• prec : Nat
• quotDepth : Nat
• suppressInsideQuot : Bool
• savedPos? : Option String.Pos
• forbiddenTk? : Option Lean.Parser.Token

Instances For

• Lean.Parser.instBEqCacheableParserContext

instance Lean.Parser.instBEqCacheableParserContext : BEq Lean.Parser.CacheableParserContext

Equations

• Lean.Parser.instBEqCacheableParserContext = { beq := Lean.Parser.beqCacheableParserContext✝ }

structure Lean.Parser.ParserContextCoreextends Lean.Parser.InputContext , Lean.Parser.ParserModuleContext , Lean.Parser.CacheableParserContext : Type

Parser context updateable in adaptUncacheableContextFn.

• input : String
• fileName : String
• fileMap : Lean.FileMap
• env : Lean.Environment
• options : Lean.Options
• currNamespace : Lake.Name
• openDecls : List Lean.OpenDecl
• prec : Nat
• quotDepth : Nat
• suppressInsideQuot : Bool
• savedPos? : Option String.Pos
• forbiddenTk? : Option Lean.Parser.Token
• tokens : Lean.Parser.TokenTable

structure Lean.Parser.ParserContextextends Lean.Parser.ParserContextCore : Type

Opaque parser context updateable using adaptCacheableContextFn and adaptUncacheableContextFn.

structure Lean.Parser.Error : Type

• unexpectedTk : Lean.Syntax

  If not missing, used for lazily calculating unexpected message and range in mkErrorMessage. Otherwise, ParserState.pos is used as an empty range.

• unexpected : String
• expected : List String

Instances For

• Lean.Parser.Error.instToString
• Lean.Parser.instBEqError
• Lean.Parser.instInhabitedError

instance Lean.Parser.instInhabitedError : Inhabited Lean.Parser.Error

Equations

• Lean.Parser.instInhabitedError = { default := { unexpectedTk := default, unexpected := default, expected := default } }

instance Lean.Parser.instBEqError : BEq Lean.Parser.Error

Equations

• Lean.Parser.instBEqError = { beq := Lean.Parser.beqError✝ }

def Lean.Parser.Error.toString (e : Lean.Parser.Error) : String

Equations

• One or more equations did not get rendered due to their size.

instance Lean.Parser.Error.instToString : ToString Lean.Parser.Error

Equations

• Lean.Parser.Error.instToString = { toString := Lean.Parser.Error.toString }

def Lean.Parser.Error.merge (e₁ : Lean.Parser.Error) (e₂ : Lean.Parser.Error) : Lean.Parser.Error

Equations

• One or more equations did not get rendered due to their size.

structure Lean.Parser.TokenCacheEntry : Type

• startPos : String.Pos
• stopPos : String.Pos
• token : Lean.Syntax

structure Lean.Parser.ParserCacheKeyextends Lean.Parser.CacheableParserContext : Type

• prec : Nat
• quotDepth : Nat
• suppressInsideQuot : Bool
• savedPos? : Option String.Pos
• forbiddenTk? : Option Lean.Parser.Token
• parserName : Lake.Name
• pos : String.Pos

Instances For

• Lean.Parser.instBEqParserCacheKey
• Lean.Parser.instHashableParserCacheKey

instance Lean.Parser.instBEqParserCacheKey : BEq Lean.Parser.ParserCacheKey

Equations

• Lean.Parser.instBEqParserCacheKey = { beq := Lean.Parser.beqParserCacheKey✝ }

instance Lean.Parser.instHashableParserCacheKey : Hashable Lean.Parser.ParserCacheKey

Equations

• Lean.Parser.instHashableParserCacheKey = { hash := fun (k : Lean.Parser.ParserCacheKey) => hash (k.pos, k.parserName) }

structure Lean.Parser.ParserCacheEntry : Type

• stx : Lean.Syntax
• lhsPrec : Nat
• newPos : String.Pos
• errorMsg : Option Lean.Parser.Error

structure Lean.Parser.ParserCache : Type

• tokenCache : Lean.Parser.TokenCacheEntry
• parserCache : Lean.HashMap Lean.Parser.ParserCacheKey Lean.Parser.ParserCacheEntry

def Lean.Parser.initCacheForInput (input : String) : Lean.Parser.ParserCache

Equations

• Lean.Parser.initCacheForInput input = { tokenCache := { startPos := input.endPos + ' ', stopPos := 0, token := Lean.Syntax.missing }, parserCache := ∅ }

structure Lean.Parser.SyntaxStack : Type

A syntax array with an inaccessible prefix, used for sound caching.

• raw : Array Lean.Syntax
• drop : Nat

Instances For

• Lean.Parser.SyntaxStack.instHAppendArraySyntax

def Lean.Parser.SyntaxStack.toSubarray (stack : Lean.Parser.SyntaxStack) : Subarray Lean.Syntax

Equations

• stack.toSubarray = stack.raw.toSubarray stack.drop

def Lean.Parser.SyntaxStack.empty : Lean.Parser.SyntaxStack

Equations

• Lean.Parser.SyntaxStack.empty = { raw := #[], drop := 0 }

def Lean.Parser.SyntaxStack.size (stack : Lean.Parser.SyntaxStack) : Nat

Equations

• stack.size = stack.raw.size - stack.drop

def Lean.Parser.SyntaxStack.isEmpty (stack : Lean.Parser.SyntaxStack) : Bool

Equations

• stack.isEmpty = (stack.size == 0)

def Lean.Parser.SyntaxStack.shrink (stack : Lean.Parser.SyntaxStack) (n : Nat) : Lean.Parser.SyntaxStack

Equations

• stack.shrink n = { raw := stack.raw.shrink (stack.drop + n), drop := stack.drop }

def Lean.Parser.SyntaxStack.push (stack : Lean.Parser.SyntaxStack) (a : Lean.Syntax) : Lean.Parser.SyntaxStack

Equations

• stack.push a = { raw := stack.raw.push a, drop := stack.drop }

def Lean.Parser.SyntaxStack.pop (stack : Lean.Parser.SyntaxStack) : Lean.Parser.SyntaxStack

Equations

• stack.pop = if stack.size > 0 then { raw := stack.raw.pop, drop := stack.drop } else stack

def Lean.Parser.SyntaxStack.back (stack : Lean.Parser.SyntaxStack) : Lean.Syntax

Equations

• stack.back = if stack.size > 0 then stack.raw.back else panicWithPosWithDecl "Lean.Parser.Types" "Lean.Parser.SyntaxStack.back" 175 4 "SyntaxStack.back: element is inaccessible"

def Lean.Parser.SyntaxStack.get! (stack : Lean.Parser.SyntaxStack) (i : Nat) : Lean.Syntax

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.SyntaxStack.extract (stack : Lean.Parser.SyntaxStack) (start : Nat) (stop : Nat) : Array Lean.Syntax

Equations

• stack.extract start stop = stack.raw.extract (stack.drop + start) (stack.drop + stop)

instance Lean.Parser.SyntaxStack.instHAppendArraySyntax : HAppend Lean.Parser.SyntaxStack (Array Lean.Syntax) Lean.Parser.SyntaxStack

Equations

• Lean.Parser.SyntaxStack.instHAppendArraySyntax = { hAppend := fun (stack : Lean.Parser.SyntaxStack) (stxs : Array Lean.Syntax) => { raw := stack.raw ++ stxs, drop := stack.drop } }

structure Lean.Parser.ParserState : Type

• stxStack : Lean.Parser.SyntaxStack
• lhsPrec : Nat

  Set to the precedence of the preceding (not surrounding) parser by runLongestMatchParser for the use of checkLhsPrec in trailing parsers. Note that with chaining, the preceding parser can be another trailing parser: in 1 * 2 + 3, the preceding parser is '*' when '+' is executed.

• pos : String.Pos
• cache : Lean.Parser.ParserCache
• errorMsg : Option Lean.Parser.Error
• recoveredErrors : Array (String.Pos × Lean.Parser.SyntaxStack × Lean.Parser.Error)

@[inline]

def Lean.Parser.ParserState.hasError (s : Lean.Parser.ParserState) : Bool

Equations

• s.hasError = (s.errorMsg != none)

def Lean.Parser.ParserState.stackSize (s : Lean.Parser.ParserState) : Nat

Equations

• s.stackSize = s.stxStack.size

def Lean.Parser.ParserState.restore (s : Lean.Parser.ParserState) (iniStackSz : Nat) (iniPos : String.Pos) : Lean.Parser.ParserState

Equations

• s.restore iniStackSz iniPos = { stxStack := s.stxStack.shrink iniStackSz, lhsPrec := s.lhsPrec, pos := iniPos, cache := s.cache, errorMsg := none, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.setPos (s : Lean.Parser.ParserState) (pos : String.Pos) : Lean.Parser.ParserState

Equations

• s.setPos pos = { stxStack := s.stxStack, lhsPrec := s.lhsPrec, pos := pos, cache := s.cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.setCache (s : Lean.Parser.ParserState) (cache : Lean.Parser.ParserCache) : Lean.Parser.ParserState

Equations

• s.setCache cache = { stxStack := s.stxStack, lhsPrec := s.lhsPrec, pos := s.pos, cache := cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.pushSyntax (s : Lean.Parser.ParserState) (n : Lean.Syntax) : Lean.Parser.ParserState

Equations

• s.pushSyntax n = { stxStack := s.stxStack.push n, lhsPrec := s.lhsPrec, pos := s.pos, cache := s.cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.popSyntax (s : Lean.Parser.ParserState) : Lean.Parser.ParserState

Equations

• s.popSyntax = { stxStack := s.stxStack.pop, lhsPrec := s.lhsPrec, pos := s.pos, cache := s.cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.shrinkStack (s : Lean.Parser.ParserState) (iniStackSz : Nat) : Lean.Parser.ParserState

Equations

• s.shrinkStack iniStackSz = { stxStack := s.stxStack.shrink iniStackSz, lhsPrec := s.lhsPrec, pos := s.pos, cache := s.cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.next (s : Lean.Parser.ParserState) (input : String) (pos : String.Pos) : Lean.Parser.ParserState

Equations

• s.next input pos = { stxStack := s.stxStack, lhsPrec := s.lhsPrec, pos := input.next pos, cache := s.cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.next' (s : Lean.Parser.ParserState) (input : String) (pos : String.Pos) (h : ¬input.atEnd pos = true) : Lean.Parser.ParserState

Equations

• s.next' input pos h = { stxStack := s.stxStack, lhsPrec := s.lhsPrec, pos := input.next' pos h, cache := s.cache, errorMsg := s.errorMsg, recoveredErrors := s.recoveredErrors }

def Lean.Parser.ParserState.mkNode (s : Lean.Parser.ParserState) (k : Lean.SyntaxNodeKind) (iniStackSz : Nat) : Lean.Parser.ParserState

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserState.mkTrailingNode (s : Lean.Parser.ParserState) (k : Lean.SyntaxNodeKind) (iniStackSz : Nat) : Lean.Parser.ParserState

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserState.allErrors (s : Lean.Parser.ParserState) : Array (String.Pos × Lean.Parser.SyntaxStack × Lean.Parser.Error)

Equations

• s.allErrors = s.recoveredErrors ++ (Option.map (fun (e : Lean.Parser.Error) => #[(s.pos, s.stxStack, e)]) s.errorMsg).getD #[]

@[inline]

def Lean.Parser.ParserState.setError (s : Lean.Parser.ParserState) (e : Lean.Parser.Error) : Lean.Parser.ParserState

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserState.mkError (s : Lean.Parser.ParserState) (msg : String) : Lean.Parser.ParserState

Equations

• s.mkError msg = (s.setError { unexpectedTk := Lean.Syntax.missing, unexpected := "", expected := [msg] }).pushSyntax Lean.Syntax.missing

def Lean.Parser.ParserState.mkUnexpectedError (s : Lean.Parser.ParserState) (msg : String) (expected : optParam (List String) []) (pushMissing : optParam Bool true) : Lean.Parser.ParserState

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserState.mkEOIError (s : Lean.Parser.ParserState) (expected : optParam (List String) []) : Lean.Parser.ParserState

Equations

• s.mkEOIError expected = s.mkUnexpectedError "unexpected end of input" expected

def Lean.Parser.ParserState.mkErrorsAt (s : Lean.Parser.ParserState) (ex : List String) (pos : String.Pos) (initStackSz? : optParam (Option Nat) none) : Lean.Parser.ParserState

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserState.mkErrorAt (s : Lean.Parser.ParserState) (msg : String) (pos : String.Pos) (initStackSz? : optParam (Option Nat) none) : Lean.Parser.ParserState

Equations

• s.mkErrorAt msg pos initStackSz? = s.mkErrorsAt [msg] pos initStackSz?

def Lean.Parser.ParserState.mkUnexpectedTokenErrors (s : Lean.Parser.ParserState) (ex : List String) (iniPos : optParam String.Pos 0) : Lean.Parser.ParserState

Reports given 'expected' messages at range of top stack element (assumed to be a single token). Replaces the element with missing and resets position to the token position. iniPos can be specified to avoid this position lookup but still must be identical to the token position.

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserState.mkUnexpectedTokenError (s : Lean.Parser.ParserState) (msg : String) (iniPos : optParam String.Pos 0) : Lean.Parser.ParserState

Reports given 'expected' message at range of top stack element (assumed to be a single token). Replaces the element with missing and resets position to the token position. iniPos can be specified to avoid this position lookup but still must be identical to the token position.

Equations

• s.mkUnexpectedTokenError msg iniPos = s.mkUnexpectedTokenErrors [msg] iniPos

def Lean.Parser.ParserState.mkUnexpectedErrorAt (s : Lean.Parser.ParserState) (msg : String) (pos : String.Pos) : Lean.Parser.ParserState

Equations

• s.mkUnexpectedErrorAt msg pos = (s.setPos pos).mkUnexpectedError msg []

def Lean.Parser.ParserState.toErrorMsg (ctx : Lean.Parser.InputContext) (s : Lean.Parser.ParserState) : String

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.ParserFn : Type

Equations

• Lean.Parser.ParserFn = (Lean.Parser.ParserContext → Lean.Parser.ParserState → Lean.Parser.ParserState)

Instances For

• Lean.Parser.instInhabitedParserFn

instance Lean.Parser.instInhabitedParserFn : Inhabited Lean.Parser.ParserFn

Equations

• Lean.Parser.instInhabitedParserFn = { default := fun (x : Lean.Parser.ParserContext) (s : Lean.Parser.ParserState) => s }

inductive Lean.Parser.FirstTokens : Type

• epsilon: Lean.Parser.FirstTokens
• unknown: Lean.Parser.FirstTokens
• tokens: List Lean.Parser.Token → Lean.Parser.FirstTokens
• optTokens: List Lean.Parser.Token → Lean.Parser.FirstTokens

Instances For

• Lean.Parser.FirstTokens.instToString
• Lean.Parser.instInhabitedFirstTokens

instance Lean.Parser.instInhabitedFirstTokens : Inhabited Lean.Parser.FirstTokens

Equations

• Lean.Parser.instInhabitedFirstTokens = { default := Lean.Parser.FirstTokens.epsilon }

def Lean.Parser.FirstTokens.seq : Lean.Parser.FirstTokens → Lean.Parser.FirstTokens → Lean.Parser.FirstTokens

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.FirstTokens.toOptional : Lean.Parser.FirstTokens → Lean.Parser.FirstTokens

Equations

• x.toOptional = match x with | Lean.Parser.FirstTokens.tokens tks => Lean.Parser.FirstTokens.optTokens tks | tks => tks

def Lean.Parser.FirstTokens.merge : Lean.Parser.FirstTokens → Lean.Parser.FirstTokens → Lean.Parser.FirstTokens

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.FirstTokens.toStr : Lean.Parser.FirstTokens → String

Equations

• One or more equations did not get rendered due to their size.

instance Lean.Parser.FirstTokens.instToString : ToString Lean.Parser.FirstTokens

Equations

• Lean.Parser.FirstTokens.instToString = { toString := Lean.Parser.FirstTokens.toStr }

structure Lean.Parser.ParserInfo : Type

• collectTokens : List Lean.Parser.Token → List Lean.Parser.Token
• collectKinds : Lean.Parser.SyntaxNodeKindSet → Lean.Parser.SyntaxNodeKindSet
• firstTokens : Lean.Parser.FirstTokens

Instances For

• Lean.Parser.instInhabitedParserInfo

instance Lean.Parser.instInhabitedParserInfo : Inhabited Lean.Parser.ParserInfo

Equations

• Lean.Parser.instInhabitedParserInfo = { default := { collectTokens := default, collectKinds := default, firstTokens := default } }

structure Lean.Parser.Parser : Type

• info : Lean.Parser.ParserInfo
• fn : Lean.Parser.ParserFn

Instances For

• Lean.Parser.instAndThenParser
• Lean.Parser.instCoeParserParserAliasValue
• Lean.Parser.instCoeStringParser
• Lean.Parser.instInhabitedParser
• Lean.Parser.instOrElseParser

instance Lean.Parser.instInhabitedParser : Inhabited Lean.Parser.Parser

Equations

• Lean.Parser.instInhabitedParser = { default := { info := default, fn := default } }

@[reducible, inline]

abbrev Lean.Parser.TrailingParser : Type

Equations

• Lean.Parser.TrailingParser = Lean.Parser.Parser

@[inline]

def Lean.Parser.withFn (f : Lean.Parser.ParserFn → Lean.Parser.ParserFn) (p : Lean.Parser.Parser) : Lean.Parser.Parser

Create a simple parser combinator that inherits the info of the nested parser.

Equations

• Lean.Parser.withFn f p = { info := p.info, fn := f p.fn }

def Lean.Parser.adaptCacheableContextFn (f : Lean.Parser.CacheableParserContext → Lean.Parser.CacheableParserContext) (p : Lean.Parser.ParserFn) : Lean.Parser.ParserFn

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.adaptCacheableContext (f : Lean.Parser.CacheableParserContext → Lean.Parser.CacheableParserContext) : Lean.Parser.Parser → Lean.Parser.Parser

Equations

• Lean.Parser.adaptCacheableContext f = Lean.Parser.withFn (Lean.Parser.adaptCacheableContextFn f)

def Lean.Parser.withResetCacheFn (p : Lean.Parser.ParserFn) : Lean.Parser.ParserFn

Run p with a fresh cache, restore outer cache afterwards. p may access the entire syntax stack.

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.withResetCache : Lean.Parser.Parser → Lean.Parser.Parser

Run p with a fresh cache, restore outer cache afterwards. p may access the entire syntax stack.

Equations

• Lean.Parser.withResetCache = Lean.Parser.withFn Lean.Parser.withResetCacheFn

def Lean.Parser.adaptUncacheableContextFn (f : Lean.Parser.ParserContextCore → Lean.Parser.ParserContextCore) (p : Lean.Parser.ParserFn) : Lean.Parser.ParserFn

Run p under the given context transformation with a fresh cache (see also withResetCacheFn).

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.withCacheFn (parserName : Lake.Name) (p : Lean.Parser.ParserFn) : Lean.Parser.ParserFn

Run p and record result in parser cache for any further invocation with this parserName, parser context, and parser state. p cannot access syntax stack elements pushed before the invocation in order to make caching independent of parser history. As this excludes trailing parsers from being cached, we also reset lhsPrec, which is not read but set by leading parsers, to 0 in order to increase cache hits. Finally, errorMsg is also reset to none as a leading parser should not be called in the first place if there was an error.

Equations

• One or more equations did not get rendered due to their size.

def Lean.Parser.withCache (parserName : Lake.Name) : Lean.Parser.Parser → Lean.Parser.Parser

Run p and record result in parser cache for any further invocation with this parserName, parser context, and parser state. p cannot access syntax stack elements pushed before the invocation in order to make caching independent of parser history. As this excludes trailing parsers from being cached, we also reset lhsPrec, which is not read but set by leading parsers, to 0 in order to increase cache hits. Finally, errorMsg is also reset to none as a leading parser should not be called in the first place if there was an error.

Equations

• Lean.Parser.withCache parserName = Lean.Parser.withFn (Lean.Parser.withCacheFn parserName)

def Lean.Parser.ParserFn.run (p : Lean.Parser.ParserFn) (ictx : Lean.Parser.InputContext) (pmctx : Lean.Parser.ParserModuleContext) (tokens : Lean.Parser.TokenTable) (s : Lean.Parser.ParserState) : Lean.Parser.ParserState

Equations

• One or more equations did not get rendered due to their size.