1. Relational Operators
2. Logical Operators
3. Logical Expressions
4. Conditional Expressions
5. Conditional Structures
6. Binary Parameters

Lower[r] <= sum {i in INGREDIENTS} Contributes[r, i] * Amount[i]

sum {s in SURFBOARDS} Recipe[m, s] * Production[s] <= Supply[m];

1. <e> in <SET> is true if <e> is a member of <SET>;
2. <e> not in <SET> is false if <e> is a member of <SET>;
3. exists {<e> in <SET>} <expression> is true if some <e> in <SET> has <expression> being true;
4. forall {<e> in <SET>} <expression> is true if all <e> in <SET> have <expression> being true;
5. <SUBSET> within <SET> is true if all the elements in <SUBSET> are in <SET>;
6. <SUBSET> not within <SET> is true if some element in <SUBSET> is not in <SET>.

param ifvalue := if <some logical expression> then
                   <a value>
                [else
                   <another value>];

if <logical expression> then
  <a statement>;
[else
  <another statement>;]

Note here that even if the else keyword is present you need to end <a statement> with ;. If you want to include more than one statement within the conditional structures you can use { and } to enclose your statements:

if <logical expression> then
{
  <some statements>
}
[else
{
  <some other statements>
}]

param stillSearching binary;

param isGreater binary;

let isGreater := if 4 > 5 then 1 else 0; # isGreater = 0 (false)
let isGreater := if 6 > 5 then 1; # else 0 is the default, isGreater = 1 (true)

let <binary parameter> := if <expression> then 1;

binary <binary parameter>;

if <expression> then
  let <binary parameter> := 1;
else
  let <binary parameter> := 0;

Some example from depth first searching or column generation

Some example from depth first searching or column generation