| Precedence Level | Associativity | Examples |
|---|---|---|
| Replication | left | σ Π ρ |
| Concatenation | list | ⋉ ⋊ ▷ ◁ ⨝ ⟕ ⟖ ⟗ ÷ ▵ X |
| Junctive and | list | ∩ ⩃ |
| Junctive or | list | ∪ ⩂ ⊖ \ |
| Chaining | chain |
∈ ∊ (elem)
∉
∋ ∍ (cont)
∌ ⊂ (<) ⊄ ⊃ (>) ⊆ (<=) ⊈ ⊇ (>=) ⊉ ≡ (==) ≢ |
Bool| is | is not | inverse | inverse not | Compare | |
|---|---|---|---|---|---|
| element of/contains | ∈ ∊ (elem) | ∉ | ∋ ∍ (cont) | ∌ | A Relation and a Tuple |
| (strict) subset/superset | ⊂ (<) | ⊄ | ⊃ (>) | ⊅ | Relations |
| subset/superset or equal | ⊆ (<=) | ⊈ | ⊇ (>=) | ⊉ | Relations |
| identity | ≡ (==) | ≢ | Relations |
TupleSetThe operators without a dot in them ensure each row is unique; the ones with a dot accept duplicates
| Operator | Set Theory Term | Comparitive Boolean Algebra Term |
Description |
|---|---|---|---|
| ∩ (U+2229) | Intersection | AND | |
| ∪ (U+222A) | Union | OR | |
| ⊖ (U+2296) | Symmetric Set Difference | XOR | |
| ∖ (-) | Set Difference | ||
| σ | Selection | Choose some Tuples; equivalent to the WHERE clause in SQL |
These operators don't make sense without the existence of a Universe set that encompasses both Relations. If there exists U such that A and B are subsets of U, then these operators will make sense. When performing these operations, it's required that the context variable $_ be a relation that's a superset of both operands.
| Operator | Set Theory Term | Comparitive Boolean Algebra Term |
Description |
|---|---|---|---|
| ⩃ (U+2229) | Intersection Complement | NAND | |
| ⩂ (U+2A42) | Union Complement | NOR | |
| Symmetric Set Difference Complement | XNOR | ||
| Set Difference Complement | |||
| Complement | NOT |
Array[TupleSet]| Operator | Set Theory Term | Comparitive Boolean Algebra Term |
Description |
|---|---|---|---|
| ℘ U+2118 | Power Set | Unary. Make a set whose members are all possible subsets of the Relation |
| Operator | Set Theory Term | Description |
|---|---|---|
Basic Operators | ||
| Π | Projection | Choose Fields; equivalent to the field selection clause in SQL; might be nice if we could also combine with subtraction, so we could go "all fields from Lot/Relation except..." |
| ρ | Rename | Rename fields; equivalent to the AS statement in SQL |
Sub-Join Operators | ||
| ⋉ U+22C9 | Left Semijoin | Includes the rows from the left table that match the right table (but no rows from the right table) |
| ⋊ U+22CA | Right Semijoin | vice versa |
| ▷ U+25B7 | Left Antijoin | Includes the rows from the left relation which do not have a match in the right relation |
| ◁ U+25C1 | Right Antijoin | vice versa |
Basic Join Operators | ||
| ⨝ U+2A1D | Inner Join | Only include the rows that appear in both relations (Left Semijoin + Right Semijoin). Mathematically, This symbol is the one for a Natural Join (see below) |
| ⟕ U+27D5 | Left Outer Join | Include all of the rows in the left relation, and any that match in the right relation |
| ⟖ U+27D6 | Right Outer Join | vice versa |
| ⟗ U+27D7 | Full Outer Join | Include all of the rows in both relations, matching up where possible |
Other Join Operators | ||
| ▷=◁ | Equjoin | Like an inner join, but the only comparison allowed is the = sign |
| ≜ U+225C | Natural Join | Like Equijoin, but the column names have to be the same in both tables |
| ÷ U+00F7 | Division | Creates a relation which lists every item in A that matches all elements in B. See Wikipedia for examples. |
| ▵ U+25B5 | Named Join | This is the symbol I chose to indicate that a join is being recalled; it's a unary prefix operator which takes a Join operand |
| X | Cross Join | This joins every record in the left operand to every record in the right operand |