Proof theory
Proof theory is a branch of mathematics where we make assumptions and apply logic to prove something. For example, if a and b can be proven to be true, then a is true and so is b.
Logical connectives
The following table depicts logical connectives, in order of precedence:
Symbol | Math name | English name | Go operator | Example | Meaning |
¬ | Negation | NOT | ! | ¬a | not a |
∧ | Conjunction | AND | && | a ∧ b | a and b |
⊕ | Exclusive disjunction | exclusive or (XOR) | NA | a ⊕ b | either a or b (but not both) |
∨ | Disjunction | OR | || | a ∨ b | a or b |
∀ | Universal quantification | ∀ x: A(x) means A(x) is true for all x | NA | ∀a:A | all values a of type A |
∃ | Existential quantification | ∃ x: A(x) means there is at least one x such that A(x) is true | NA | ∃a:A | there exists some value a of type A |
⇒ | Material implication | Implies | NA | a ⇒ b | if a then b |
⇔ | Material equivalence | a ⇔ b is true only if both a and b are false, or both a and b are true | NA | a ⇔ b | a if and only if b |
≡ | Is defined as | a ≡ b means a is defined to be another name for b | NA | a ≡ b | a is logically equivalent to b |
⊢ | Turnstile | a ⊢ b means a... |
