Browsable Logic Grammar

Grammar extracted by Vadim Zaytsev, see the Grammar Zoo entry for details: markup/scientific/logic/concrete/extracted
Source used for this grammar: Jurgen Vinju, lang::logic::syntax::Booleans, 2011 [GitHub]
Source used for this grammar: Jurgen Vinju, lang::logic::syntax::Propositions, 2011 [GitHub]
Source used for this grammar: Jurgen Vinju, lang::logic::syntax::Truths, 2011 [GitHub]

Summary

• Total 23 production rules with 23 top alternatives and 158 symbols.
• Vocabulary: 34 = 3 nonterminals + 13 terminals + 18 labels + 0 markers.
• Total 3 nonterminal symbols: 3 defined (Formula, False, True), 0 root (—), 0 top (—), 0 bottom (—).
• Total 13 terminal symbols: 5 keywords ("true" ², "false" ², "not" ², "and" ⁴, "or" ⁴), 0 letters (—), 0 numerics (—), 8 signs ("!", "&", "|", "<=", "=>", "<=>", "(" ², ")" ²).
• Total 18 labels: [arg], [not], [true], [false], [lhs] ⁵, [rhs] ⁵, [and], [or], [fi], [if], [iff], [id], [t], [lf] ⁴, [rt] ⁴, [rf] ⁴, [lt] ⁴, [f].

Syntax

Formula ::=
	[not]::("!" [arg]::Formula)

Formula ::=
	[true]::"true"

Formula ::=
	[false]::"false"

Formula ::=
	[and]::([lhs]::Formula "&" [rhs]::Formula)

Formula ::=
	[or]::([lhs]::Formula "|" [rhs]::Formula)

Formula ::=
	[fi]::([lhs]::Formula "<=" [rhs]::Formula)

Formula ::=
	[if]::([lhs]::Formula "=>" [rhs]::Formula)

Formula ::=
	[iff]::([lhs]::Formula "<=>" [rhs]::Formula)

Formula ::=
	[id]::ε

False ::=
	"false"

False ::=
	"not" [t]::True

False ::=
	"(" False ")"

False ::=
	[lf]::False "and" [rt]::True

False ::=
	[lf]::False "and" [rf]::False

False ::=
	[lt]::True "and" [rf]::False

False ::=
	[lf]::False "or" [rf]::False

True ::=
	"(" True ")"

True ::=
	"true"

True ::=
	"not" [f]::False

True ::=
	[lt]::True "and" [rt]::True

True ::=
	[lt]::True "or" [rt]::True

True ::=
	[lt]::True "or" [rf]::False

True ::=
	[lf]::False "or" [rt]::True

Maintained by Dr. Vadim Zaytsev a.k.a. @grammarware. Last updated in September 2015. [↑]