Expressions
Everything in the Algosim language is an expression. An expression is made up of symbols, function calls, and operators; however, every operator is mapped to (or “implemented by”) a function, so when an expression has been parsed, it consists only of symbols and function calls. When evaluated, an expression returns an object (or “value”).
Operators
Algosim supports many operators:
Sometimes, special brackets are also considered as circumfix operators:
Some symbols are mapped to different operators depending on the context. For instance, − can be both a prefix (unary) and an infix (binary) operator:
−2^10
5264 − 1054
In order of precedence, the available (non-circumfix) operators are
| 1 . (infix) | 2 ‰ (postfix) | 3 ° (postfix) | 4 ! (postfix) | 5 ? (postfix) |
| 6 % (postfix) | 7 * (postfix) | 8 # (postfix) | 9 ∁ (prefix) | 10 ¬ (prefix) |
| 11 # (prefix) | 12 § (prefix) | 13 & (prefix) | 14 − (prefix) | 15 √ (prefix) |
| 16 + (prefix) | 17 ^ (infix) | 18 + (prefix) | 19 − (prefix) | 20 ⋅ (infix) |
| 21 ∘ (infix) | 22 × (infix) | 23 @ (infix) | 24 / (infix) | 25 ⊗ (infix) |
| 26 ⊙ (infix) | 27 ⊕ (infix) | 28 + (infix) | 29 − (infix) | 30 ∆ (infix) |
| 31 ∩ (infix) | 32 ∖ (infix) | 33 ∪ (infix) | 34 ∼ (infix) | 35 ∉ (infix) |
| 36 ∌ (infix) | 37 ∈ (infix) | 38 ∋ (infix) | 39 ⊊ (infix) | 40 ∤ (infix) |
| 41 ∥ (infix) | 42 ∦ (infix) | 43 ⟂ (infix) | 44 ⊃ (infix) | 45 ⊇ (infix) |
| 46 ⊋ (infix) | 47 ∣ (infix) | 48 ⊆ (infix) | 49 = (infix) | 50 ≥ (infix) |
| 51 > (infix) | 52 ≤ (infix) | 53 < (infix) | 54 ≠ (infix) | 55 ⊂ (infix) |
| 56 → (infix) | 57 ≈ (infix) | 58 ⊼ (infix) | 59 ∧ (infix) | 60 ⊻ (infix) |
| 61 ∨ (infix) | 62 ⊽ (infix) | 63 ⇔ (infix) | 64 ⇐ (infix) | 65 ⇒ (infix) |
| 66 : (infix) | 67 ↦ (infix) | 68 \ (infix) | 69 | (infix) | 70 ≔ (infix) |
| 71 ; (infix) |
Collapsing operators
Some infix operators are effectively n-ary, meaning that they can take any number of operands. One typical example is <, which can be used like this:
3 < π < 4
true
This is parsed as FCN_LessThan(3, π, 4) and returns true since 3 < π and π < 4.
Classically, most computer languages would treat < as a pure binary operator, so that 3 < π would first evaluate to true and then true < 4 would yield a type error.
Algosim’s use of true n-ary operators like this mimics the notation used in ordinary mathematics and this can be used in all contexts; for instance, you may plot
plot(arctan(x) < y < 1 + cos(x^2), 0, π / 2)
Operators that, like <, can collapse a sequence of binary operations to a single n-ary function call are called “collapsing”. The following operators are collapsing:
| + | ⋅ | × | ; | < | ≤ | > | ≥ | = | ∧ | ∨ | ⊕ | ∼ |
Notice that you can prevent a sequence of collapsing operators from combining into a single function call by using parentheses:
(3 < π) < 4
will be parsed as FCN_LessThan(FCN_LessThan(3, π), 4) and yield a type error.