# Comparisons

{% hint style="warning" %}
Type signatures are provisional and may contain errors.
{% endhint %}

### LT

```
(LT)
> Nat
```

Represents "less than" in ordering comparisons.

```sire
LT == 0
```

### EQ

```
(EQ)
> Nat
```

Represents "equal to" in ordering comparisons.

```sire
EQ == 1
```

### GT

```
(GT)
> Nat
```

Represents "greater than" in ordering comparisons.

```sire
GT == 2
```

### ordWeld

```
(ordWeld x y)
> x : Nat
> y : Nat
> Nat
```

Combines two ordering results, giving precedence to the first non-EQ result.

```sire
ordWeld LT EQ    == 0    ; LT
ordWeld EQ GT    == 2    ; GT
ordWeld EQ EQ    == 1    ; EQ
ordWeld LT GT    == 0    ; LT
```

### isZero

```
(isZero x)
> x : Nat
> Bool
```

Checks if a value is zero.

```sire
isZero 0      == 1
isZero 1      == 0
isZero 100    == 0
```

### isOne

```
(isOne x)
> x : Nat
> Bool
```

Checks if a value is one.

```sire
isOne 1      == 1
isOne 100    == 0
```

### cmp

```
(cmp x y)
> x : a
> y : a
> Nat
```

Compares two values, returning LT, EQ, or GT.

```sire
cmp 1 2            == LT
cmp 2 2            == EQ
cmp 3 2            == GT
cmp [1 2] [1 3]    == LT
cmp [1 2] [1 2]    == EQ
```

### eql

```
(eql x y)
> x : a
> y : a
> Bool
```

Checks if two values are equal.

```sire
eql 1 1            == 1
eql 1 2            == 0
eql [1 2] [1 2]    == 1
eql [1 2] [1 3]    == 0
```

### neq

```
(neq x y)
> x : a
> y : a
> Bool
```

Checks if two values are not equal.

```sire
neq 1 2            == 1
neq 1 1            == 0
neq [1 2] [1 3]    == 1
neq [1 2] [1 2]    == 0
```

### lth

```
(lth x y)
> x : a
> y : a
> Bool
```

Checks if the first value is less than the second.

```sire
lth 1 2    == 1
lth 2 1    == 0
lth 1 1    == 0
```

### lte

```
(lte x y)
> x : a
> y : a
> Bool
```

Checks if the first value is less than or equal to the second.

```sire
lte 1 2    == 1
lte 1 1    == 1
lte 2 1    == 0
```

### gth

```
(gth x y)
> x : a
> y : a
> Bool
```

Checks if the first value is greater than the second.

```sire
gth 2 1    == 1
gth 1 2    == 0
gth 1 1    == 0
```

### gte

```
(gte x y)
> x : a
> y : a
> Bool
```

Checks if the first value is greater than or equal to the second.

```sire
gte 2 1    == 1
gte 1 1    == 1
gte 1 2    == 0
```

### min

```
(min x y)
> x : a
> y : a
> a
```

Returns the minimum of two values.

```sire
min 1 2    == 1
min 2 1    == 1
min 1 1    == 1
```

### max

```
(max x y)
> x : a
> y : a
> a
```

Returns the maximum of two values.

```sire
max 1 2    == 2
max 2 1    == 2
max 1 1    == 1
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://opfn.gitbook.io/pallas/sire-reference/wip-standard-library/comparisons.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.