The following table shows a list of some common symbols or abbreviations and their meaning. Please feel free to add, modify or correct this list.
| Serial | Symbol/Abbreviation | Meaning |
|---|---|---|
| 1 | i.e. | that is or in other words |
| 2 | e.g. | for example |
| 3 | etc. | and so forth or and so on |
| 4 | ∅ | null pattern or empty set {} |
| 5 | ε | Empty |
| 6 | δ | Delta |
| 7 | γ | Gamma |
| 8 | ρ (Rho) | represents Environment |
| 9 | κ (Kappa) | represents continuation |
| 10 | σ (sigma - lowercase) | represents store |
| 11 | Σ (Sigma - uppercase) | represents State type of machine |
| 12 | ς (varsigma) | refers to State |
| 13 | := | Left hand side (LHS) is being defined to be what is on the Right hand side (RHS) |
| 14 | ∈ | in or is an element of, for example, X ∈ R, means X is an element of R |
| 15 | ∋ | such that |
| 16 | ∃ | there exists |
| 17 | ∀ | for all |
| 18 | ≡ | identical to, indicating equivalence of two different things |
| 19 | ≜ | delta over equals, occasionally used to define a new variable or function |
| 20 | ::= | is defined as |
| 21 | ℕ (Double-Struck Capital N) | used to denote the set of all natural numbers, (0 to infinity) |
| 22 | ℤ | Represents the set of integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} |
| 23 | ⊆ | read as is a subset of |
| 24 | ⊂ | read as is a proper subset of |
| 25 | ∪ | union |
| 26 | iff | read as if and only if |
| 27 | ⇐⇒ | read as if and only if |
| 28 | ⇝ | transitions/leads to. In solving a problem, it denotes the next step is |
| 29 | ⇓ | evaluates to/turns into/returns (for Big Step semantics) |
| 30 | → | evaluates to/turns into/returns (for Small Step semantics) |
| 31 | ⇒ | logically implies that |
| 32 | ∧ | and / conjunction |
| 33 | ∨ | or / disjunction |
| 34 | ⊢ | for example, P ⊢ Q, read as, From P, we can conclude Q, or P entails Q |
| 35 | : | For example, v:V1, means, term v has type V1 |
| 36 | ∴ | therefore |
| 37 | ∎ or □ | Used to denote the end of a proof |