# Prelude (built-in) classes

## Prelude (built-in) classes

The prelude ships the `Ordering` ADT, the `Eq` and `Ord`
[classes](typeclasses.md), primitive `Eq Int/Bool/Str` and
`Ord Int/Bool/Str` instances, and the five polymorphic free-fn
helpers `ne`/`lt`/`le`/`gt`/`ge`. Float has neither `Eq` nor `Ord`
instance per [Float semantics](float-semantics.md); a polymorphic
helper invoked at Float fires `NoInstance` at typecheck with a
Float-aware diagnostic cross-referencing this section. The lookup
machinery that turns a `show x` call site into the right monomorphic
instance is documented in [method dispatch](method-dispatch.md).

The prelude ships `class Show a where show : (a borrow) -> Str` and
primitive `Show Int`, `Show Bool`, `Show Str`, `Show Float`
instances. Float **is** included in Show (unlike Eq/Ord) — IEEE-754
makes structural equality and total ordering semantically dubious,
but textual representation of a Float is well-defined modulo the
NaN-spelling caveat in [Float semantics](float-semantics.md). Each
`Show <T>` instance body is a single-application lambda invoking the
corresponding runtime primitive (`int_to_str`, `bool_to_str`,
`str_clone`, `float_to_str`; see [Str ABI](str-abi.md) for the
heap-Str primitives); no codegen intercept is required. The
polymorphic helper `print : forall a. Show a => a -> () !IO` has body
`\x -> let s = show x in do io/print_str s` (explicit let-binder for
heap-Str RC discipline per the Str carve-out in
[Str ABI](str-abi.md)). The let-binder is
structurally pinned by `crates/ail/tests/print_mono_body_shape.rs`.
Routing through `print` is the path for non-`Str` primitives;
`io/print_str` is the only built-in direct-output effect-op.

Ratified by: `crates/ail/tests/show_no_instance_e2e.rs`.