# AILang authoring reference

## 1. Header

AILang is a small data-as-source functional language designed for an
LLM author. This document is the complete authoring reference. Every
well-formed program is a module. Read the whole thing once before you
write code; the order of sections is the order of dependencies.

## 2. Modules and the on-disk form

A module is the top-level container. It has a name (matching the file
stem), an optional list of imports, and a flat list of definitions.
Every program you write is exactly one module. Cross-module imports
are out of scope for the tasks in this experiment — every task is a
single self-contained module with an empty `imports` array.

A definition is the unit that gets a content hash. There are five
kinds of definition: function, constant, data type, class, and
instance. Their order within the module is preserved on disk but is
not load-bearing semantically — forward references are legal.

The schema of the on-disk form is fixed. The toolchain rejects any
module that does not conform.

The on-disk form is a single JSON object with the following required
top-level fields, in canonical key order:

- `schema`: the string `"ailang/v0"`. Any other value is rejected at
  load time.
- `name`: the module name (matches the file stem on disk).
- `imports`: array of import objects. May be empty.
- `defs`: array of definition objects. Order is the declared order;
  the hash is computed over the canonical-keys-sorted byte form so
  inserting fields in source order is safe.

Canonical key order means object keys are emitted in sorted order
when the toolchain computes the canonical bytes for hashing; for
authoring you can write keys in whatever order is clearest. Numeric
literals are bare JSON numbers; strings are JSON strings. Every
definition object carries a `kind` discriminator (`fn`, `const`,
`type`, `class`, `instance`). Every term object carries a `t`
discriminator. Every type object carries a `k` discriminator. Every
pattern object carries a `p` discriminator. Every literal object
carries a `kind` discriminator.


```json
{
  "schema": "ailang/v0",
  "name": "fn_returns_int",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "answer",
      "doc": "The simplest possible fn — no params, returns a fixed Int.",
      "type": {
        "k": "fn",
        "params": [],
        "param_modes": [],
        "ret": { "k": "con", "name": "Int" },
        "ret_mode": "own",
        "effects": []
      },
      "params": [],
      "body": { "t": "lit", "lit": { "kind": "int", "value": 42 } }
    }
  ]
}
```

## 3. Types

A type is one of four shapes. Every type position in a function
signature must be filled in; there is no implicit type inference at
the binding form. Constructor types may carry type arguments.
Functions are first-class — function types appear as parameter and
return types.

A type constructor names a base type or a user-defined ADT. The
prelude provides `Int`, `Bool`, `Str`, `Float`, `Unit`. User ADTs are
introduced with the `data` form (see section 6); after declaration
their name is usable wherever a type constructor is expected.

A type variable is a placeholder introduced by `forall` at the top
of a function signature. Within the signature the variable behaves
as an opaque type; the toolchain instantiates it at each call site.

A function type names parameter types, parameter modes (see section
4), a return type, a return mode, and an effect row (see section 8).

A `forall` is universal quantification: it lists the type variables
bound and the body type they appear in. Forall is only valid at the
top of a function or constant signature.

Type::Con: `{"k": "con", "name": "Int"}` for a base type; for a
parameterised type, `{"k": "con", "name": "List", "args": [...]}`.
The `args` field is omitted when empty (canonical-bytes stable).

Type::Var: `{"k": "var", "name": "a"}`. Variable names are bare
identifiers; conventionally lower-case single letters.

Type::Fn: `{"k": "fn", "params": [...], "ret": ..., "effects": [...]}`
with optional `param_modes` and `ret_mode` fields. The `effects`
array is a set; sort and dedup at authoring time for readability.

Type::Forall: `{"k": "forall", "vars": [...], "body": ...}` with an
optional `constraints` array for class constraints (see section 10).


```json
{
  "schema": "ailang/v0",
  "name": "forall_polymorphic",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "id",
      "doc": "The polymorphic identity function. Exercises Type::Forall and Type::Var.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "body": {
          "k": "fn",
          "params": [ { "k": "var", "name": "a" } ],
          "param_modes": ["own"],
          "ret": { "k": "var", "name": "a" },
          "ret_mode": "own",
          "effects": []
        }
      },
      "params": ["x"],
      "body": { "t": "var", "name": "x" }
    }
  ]
}
```

## 4. Mode annotations

Every function parameter carries a mode, and so does the return
position. There are exactly two modes. `own` means the caller
transfers ownership and the callee consumes the value; `borrow`
means the caller retains ownership and the callee may inspect but
not consume. `borrow` is legal only over a boxed type (an algebraic
data type): unboxed value types (`Int`, `Bool`, `Float`, `Unit`)
are always `own`, and borrowing one is a `borrow-over-value` error.

The return position is always `own` — a function returns a fresh
owned value; borrow-returns are not permitted.

Modes are mandatory: every parameter and the return position carries
exactly one mode. There is no default or omitted mode.

On `Type::Fn`, two required fields carry modes:

- `param_modes`: an array of strings, each `"own"` or `"borrow"`,
  one per parameter, in the same order as `params`.
- `ret_mode`: a single string, always `"own"`.

Both are present on every fn type. Example — a fn that borrows a
boxed list and returns an int: `"param_modes": ["borrow"]`,
`"ret_mode": "own"`. A fn that consumes an int and returns an int:
`"param_modes": ["own"]`, `"ret_mode": "own"`.


```json
{"defs":[{"ctors":[{"fields":[],"name":"Nil"},{"fields":[{"k":"con","name":"Int"},{"k":"con","name":"List"}],"name":"Cons"}],"kind":"type","name":"List"},{"body":{"name":"x","t":"var"},"doc":"(own Int) — unboxed value types (Int/Bool/Float/Unit) are always own; borrow over them is a borrow-over-value error.","kind":"fn","name":"f_own_value","params":["x"],"type":{"effects":[],"k":"fn","param_modes":["own"],"params":[{"k":"con","name":"Int"}],"ret":{"k":"con","name":"Int"},"ret_mode":"own"}},{"body":{"arms":[{"body":{"lit":{"kind":"int","value":0},"t":"lit"},"pat":{"ctor":"Nil","fields":[],"p":"ctor"}},{"body":{"args":[{"lit":{"kind":"int","value":1},"t":"lit"},{"args":[{"name":"t","t":"var"}],"fn":{"name":"f_borrow_boxed","t":"var"},"t":"app"}],"fn":{"name":"+","t":"var"},"t":"app"},"pat":{"ctor":"Cons","fields":[{"name":"h","p":"var"},{"name":"t","p":"var"}],"p":"ctor"}}],"scrutinee":{"name":"xs","t":"var"},"t":"match"},"doc":"(borrow List) — boxed types may be borrowed; the callee reads without consuming.","kind":"fn","name":"f_borrow_boxed","params":["xs"],"type":{"effects":[],"k":"fn","param_modes":["borrow"],"params":[{"k":"con","name":"List"}],"ret":{"k":"con","name":"Int"},"ret_mode":"own"}}],"imports":[],"name":"param_modes_all","schema":"ailang/v0"}
```

## 5. Functions

A function definition binds a name to a body of code. The signature
declares the parameter types, the return type, and the effect set
(if any). The body is an expression — there is no statement form.
Functions are first-class values: they may be passed to other
functions, returned, stored in data structures.

Inside a function body, four term forms appear most often: a
variable reference (the name of a parameter, a local binding, or a
top-level definition); a function application (a callee plus
positional arguments); a lambda (an anonymous function with its
own signature); a literal value (see section 9).

Lambdas carry their own parameter list, parameter types, return
type, and effect set. Lambdas may close over names from the
enclosing lexical scope; the closure is captured by value (the
captured values are reference-counted under `--alloc=rc`).

A `let` binds a name to the value of one expression for the
duration of another expression. A `letrec` is the recursive variant:
the bound name is visible inside its own body. Both are
expressions, not statements — they have a value.

Function definition: `{"kind": "fn", "name": ..., "type": ...,
"params": [...], "body": ...}` plus optional `doc`.

Term variants relevant here:

- Variable reference: `{"t": "var", "name": "x"}`.
- Application: `{"t": "app", "fn": ..., "args": [...]}`.
- Lambda: `{"t": "lam", "params": [...], "paramTypes": [...],
  "retType": ..., "effects": [...], "body": ...}`.
- Let: `{"t": "let", "name": "x", "value": ..., "body": ...}`.
- Letrec: `{"t": "letrec", "name": "go", "type": ..., "params":
  [...], "body": ..., "in": ...}`.

The `paramTypes` and `retType` keys in `lam` use camelCase; the rest
use snake_case. This is historical and the canonical bytes preserve
the difference.


```json
{
  "schema": "ailang/v0",
  "name": "fn_calls_prelude",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "add",
      "doc": "Add two Ints via the polymorphic prelude `+`. Also exercises TermLet by binding the sum to a local name before returning it, and TermClone by re-using the let-bound value.",
      "type": {
        "k": "fn",
        "params": [
          { "k": "con", "name": "Int" },
          { "k": "con", "name": "Int" }
        ],
        "param_modes": ["own", "own"],
        "ret": { "k": "con", "name": "Int" },
        "ret_mode": "own",
        "effects": []
      },
      "params": ["x", "y"],
      "body": {
        "t": "let",
        "name": "s",
        "value": {
          "t": "app",
          "fn": { "t": "var", "name": "+" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        },
        "body": { "t": "clone", "value": { "t": "var", "name": "s" } }
      }
    }
  ]
}
```

```json
{
  "schema": "ailang/v0",
  "name": "fn_with_lambda",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "make_adder",
      "doc": "Curried adder: takes an Int and returns an Int -> Int closure. Exercises TermLam and Type::Fn appearing as a return type.",
      "type": {
        "k": "fn",
        "params": [ { "k": "con", "name": "Int" } ],
        "param_modes": ["own"],
        "ret": {
          "k": "fn",
          "params": [ { "k": "con", "name": "Int" } ],
          "param_modes": ["own"],
          "ret": { "k": "con", "name": "Int" },
          "ret_mode": "own",
          "effects": []
        },
        "ret_mode": "own",
        "effects": []
      },
      "params": ["x"],
      "body": {
        "t": "lam",
        "params": ["y"],
        "param-types": [ { "k": "con", "name": "Int" } ],
        "ret-type": { "k": "con", "name": "Int" },
        "effects": [],
        "body": {
          "t": "app",
          "fn": { "t": "var", "name": "+" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        }
      }
    }
  ]
}
```

## 6. Algebraic data types

A data type declaration introduces a new named type with one or
more constructors. Each constructor takes zero or more positional
argument types and produces a value of the declared type. ADTs may
be parameterised by type variables; the variables are listed before
the constructors and may appear in the constructor argument types.

A constructor is invoked at the term level by naming the type and
the constructor plus the positional arguments. The runtime
representation under `--alloc=rc` is a tagged heap cell with one
slot per constructor field; the tag identifies which constructor
was used.

Constructor names live in their own namespace, separate from
function names. The same identifier may be a function and a
constructor without conflict, though for readability the convention
is constructors are capitalised and functions are lower-case.

Type definition: `{"kind": "type", "name": ..., "vars": [...],
"doc": ..., "ctors": [...]}`. The `vars` array is the list of type
parameter names; omitted when empty.

Each ctor: `{"name": "Cons", "fields": [TYPE, TYPE, ...]}`.
`fields` is a positional list of field types.

Constructor invocation: `{"t": "ctor", "type": "List", "ctor":
"Cons", "args": [...]}`. The `type` field disambiguates which ADT
the constructor belongs to (necessary because constructor names are
not globally unique). `args` is positional and matches the
constructor's declared `fields` in order; nullary constructors
carry `"args": []`.


```json
{"defs":[{"ctors":[{"fields":[{"k":"var","name":"a"}],"name":"MkBox"}],"kind":"type","name":"Box","vars":["a"]},{"body":{"arms":[{"body":{"body":{"args":[{"lit":{"kind":"int","value":1},"t":"lit"}],"ctor":"MkBox","t":"ctor","type":"Box"},"source":{"name":"src","t":"var"},"t":"reuse-as"},"pat":{"ctor":"MkBox","fields":[{"name":"v","p":"var"}],"p":"ctor"}}],"scrutinee":{"name":"src","t":"var"},"t":"match"},"kind":"fn","name":"wrap_one","params":["src"],"type":{"effects":[],"k":"fn","param_modes":["own"],"params":[{"args":[{"k":"con","name":"Int"}],"k":"con","name":"Box"}],"ret":{"args":[{"k":"con","name":"Int"}],"k":"con","name":"Box"},"ret_mode":"own"}}],"imports":[],"name":"data_simple","schema":"ailang/v0"}
```

## 7. Pattern matching

Pattern matching is the way to inspect an ADT value. A `match`
form takes a scrutinee expression plus one or more arms; each arm
pairs a pattern with a body. Arms are tried top-to-bottom; the
first matching arm's body is evaluated. The toolchain checks
exhaustiveness: every constructor of the scrutinee's type must be
reachable through some arm, otherwise the typechecker errors.

There are four pattern shapes. A wildcard matches anything and
binds nothing. A variable pattern matches anything and binds the
matched value to the named identifier for use inside the arm body.
A literal pattern matches only when the scrutinee is bit-equal to
the literal value; literal patterns work on Int, Bool, Str, and
Unit (Float patterns are rejected at typecheck — see section 9).
A constructor pattern matches when the scrutinee is built by the
named constructor and recursively matches the constructor's
fields.

Match expression: `{"t": "match", "scrutinee": ..., "arms": [...]}`.
Each arm: `{"pat": PATTERN, "body": TERM}`.

Pattern variants:
- Wildcard: `{"p": "wild"}` — no other fields.
- Variable: `{"p": "var", "name": "h"}` — binds the scrutinee to
  `h`.
- Literal: `{"p": "lit", "lit": LITERAL}` — same `lit` shape as a
  term literal.
- Constructor: `{"p": "ctor", "ctor": "Cons", "fields": [PATTERN,
  PATTERN, ...]}` — positional sub-patterns matching the
  constructor's declared field types.

Pattern variables are linear: each name appears at most once in a
single pattern. Repeating a name is a typecheck error.


```json
{
  "schema": "ailang/v0",
  "name": "data_with_match",
  "imports": [],
  "defs": [
    {
      "kind": "type",
      "name": "List",
      "doc": "Monomorphic singly-linked Int list \u2014 boxed, recursive.",
      "ctors": [
        {
          "name": "Nil",
          "fields": []
        },
        {
          "name": "Cons",
          "fields": [
            {
              "k": "con",
              "name": "Int"
            },
            {
              "k": "con",
              "name": "List"
            }
          ]
        }
      ]
    },
    {
      "kind": "fn",
      "name": "head_or_zero",
      "doc": "Return the head of xs, or 0 if empty. Exercises TermMatch with two arms, PatternCtor (both nullary Nil and binary Cons), and PatternWild on the tail field.",
      "type": {
        "k": "fn",
        "params": [
          {
            "k": "con",
            "name": "List"
          }
        ],
        "param_modes": [
          "borrow"
        ],
        "ret": {
          "k": "con",
          "name": "Int"
        },
        "ret_mode": "own",
        "effects": []
      },
      "params": [
        "xs"
      ],
      "body": {
        "t": "match",
        "scrutinee": {
          "t": "var",
          "name": "xs"
        },
        "arms": [
          {
            "pat": {
              "p": "ctor",
              "ctor": "Nil",
              "fields": []
            },
            "body": {
              "t": "lit",
              "lit": {
                "kind": "int",
                "value": 0
              }
            }
          },
          {
            "pat": {
              "p": "ctor",
              "ctor": "Cons",
              "fields": [
                {
                  "p": "var",
                  "name": "h"
                },
                {
                  "p": "wild"
                }
              ]
            },
            "body": {
              "t": "var",
              "name": "h"
            }
          }
        ]
      }
    },
    {
      "kind": "fn",
      "name": "count_via_letrec",
      "doc": "Walk xs counting nodes using a local recursive let. Exercises TermLetRec and TermVar; the recursive `go` is bound locally.",
      "type": {
        "k": "fn",
        "params": [
          {
            "k": "con",
            "name": "List"
          }
        ],
        "param_modes": [
          "own"
        ],
        "ret": {
          "k": "con",
          "name": "Int"
        },
        "ret_mode": "own",
        "effects": []
      },
      "params": [
        "xs"
      ],
      "body": {
        "t": "letrec",
        "name": "go",
        "type": {
          "k": "fn",
          "params": [
            {
              "k": "con",
              "name": "List"
            }
          ],
          "param_modes": [
            "own"
          ],
          "ret": {
            "k": "con",
            "name": "Int"
          },
          "ret_mode": "own",
          "effects": []
        },
        "params": [
          "ys"
        ],
        "body": {
          "t": "match",
          "scrutinee": {
            "t": "var",
            "name": "ys"
          },
          "arms": [
            {
              "pat": {
                "p": "ctor",
                "ctor": "Nil",
                "fields": []
              },
              "body": {
                "t": "lit",
                "lit": {
                  "kind": "int",
                  "value": 0
                }
              }
            },
            {
              "pat": {
                "p": "ctor",
                "ctor": "Cons",
                "fields": [
                  {
                    "p": "wild"
                  },
                  {
                    "p": "var",
                    "name": "t"
                  }
                ]
              },
              "body": {
                "t": "app",
                "fn": {
                  "t": "var",
                  "name": "+"
                },
                "args": [
                  {
                    "t": "lit",
                    "lit": {
                      "kind": "int",
                      "value": 1
                    }
                  },
                  {
                    "t": "app",
                    "fn": {
                      "t": "var",
                      "name": "go"
                    },
                    "args": [
                      {
                        "t": "var",
                        "name": "t"
                      }
                    ]
                  }
                ]
              }
            }
          ]
        },
        "in": {
          "t": "app",
          "fn": {
            "t": "var",
            "name": "go"
          },
          "args": [
            {
              "t": "var",
              "name": "xs"
            }
          ]
        }
      }
    }
  ]
}
```

```json
{
  "schema": "ailang/v0",
  "name": "match_literal_pattern",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "classify",
      "doc": "Classify an Int via literal patterns plus a wildcard fallback. Exercises PatternLit and PatternWild.",
      "type": {
        "k": "fn",
        "params": [ { "k": "con", "name": "Int" } ],
        "param_modes": ["own"],
        "ret": { "k": "con", "name": "Int" },
        "ret_mode": "own",
        "effects": []
      },
      "params": ["n"],
      "body": {
        "t": "match",
        "scrutinee": { "t": "var", "name": "n" },
        "arms": [
          {
            "pat": { "p": "lit", "lit": { "kind": "int", "value": 0 } },
            "body": { "t": "lit", "lit": { "kind": "int", "value": 100 } }
          },
          {
            "pat": { "p": "wild" },
            "body": { "t": "lit", "lit": { "kind": "int", "value": 200 } }
          }
        ]
      }
    },
    {
      "kind": "fn",
      "name": "sign_if",
      "doc": "Return -1 / 0 / 1 for the sign of n using nested TermIf. Exercises TermIf in both then/else positions plus TermApp on the polymorphic comparison.",
      "type": {
        "k": "fn",
        "params": [ { "k": "con", "name": "Int" } ],
        "param_modes": ["own"],
        "ret": { "k": "con", "name": "Int" },
        "ret_mode": "own",
        "effects": []
      },
      "params": ["n"],
      "body": {
        "t": "if",
        "cond": {
          "t": "app",
          "fn": { "t": "var", "name": "lt" },
          "args": [
            { "t": "var", "name": "n" },
            { "t": "lit", "lit": { "kind": "int", "value": 0 } }
          ]
        },
        "then": { "t": "lit", "lit": { "kind": "int", "value": -1 } },
        "else": {
          "t": "if",
          "cond": {
            "t": "app",
            "fn": { "t": "var", "name": "eq" },
            "args": [
              { "t": "var", "name": "n" },
              { "t": "lit", "lit": { "kind": "int", "value": 0 } }
            ]
          },
          "then": { "t": "lit", "lit": { "kind": "int", "value": 0 } },
          "else": { "t": "lit", "lit": { "kind": "int", "value": 1 } }
        }
      }
    }
  ]
}
```

## 8. Effects

Every function type carries an effect row — a set of effect labels
that the function may raise. The two currently wired effects are
`IO` (required to call effect operations like `io/print_int`) and
`Diverge` (used for functions that may not terminate). An empty
effect row marks the function as pure.

Effect operations are reached through the `do` term, not through a
regular function application. The `do` form names the operation
(e.g. `io/print_int`) and lists the operation's arguments; the
typechecker resolves the operation against the prelude's effect-op
table, checks the arguments, and accumulates the operation's
effect label into the enclosing function's effect row.

A `seq` term sequences two effectful expressions: the left-hand
side is evaluated for its effects and its result discarded, then
the right-hand side is evaluated and its value is the value of the
whole expression. `seq` is the canonical way to perform multiple
IO operations one after the other inside a function body.

Effect row on `Type::Fn`: the `effects` field is a JSON array of
strings (the effect labels). `[]` means pure. `["IO"]` is the
common effectful case. The toolchain compares effect rows modulo
order; for readability sort the array alphabetically.

Effect operation invocation: `{"t": "do", "op": "io/print_int",
"args": [INT-TERM]}`. The `op` is a string naming the prelude
operation. The `args` list matches the operation's declared
parameter types.

Sequencing: `{"t": "seq", "lhs": EFFECT-TERM, "rhs": EFFECT-TERM}`.
The value of the `seq` is the value of `rhs`; `lhs`'s value is
discarded but its effects count toward the enclosing fn's row.


```json
{
  "schema": "ailang/v0",
  "name": "fn_with_do_seq",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "main",
      "doc": "Print two Ints in sequence. Exercises TermDo, TermSeq, and the IO effect on a fn type. The trailing unit return is implicit in the last Do (op returns Unit).",
      "type": {
        "k": "fn",
        "params": [],
        "param_modes": [],
        "ret": {
          "k": "con",
          "name": "Unit"
        },
        "ret_mode": "own",
        "effects": [
          "IO"
        ]
      },
      "params": [],
      "body": {
        "t": "seq",
        "lhs": {
          "t": "seq",
          "lhs": {
            "t": "do",
            "op": "io/print_str",
            "args": [
              {
                "t": "app",
                "fn": {
                  "t": "var",
                  "name": "int_to_str"
                },
                "args": [
                  {
                    "t": "lit",
                    "lit": {
                      "kind": "int",
                      "value": 1
                    }
                  }
                ]
              }
            ]
          },
          "rhs": {
            "t": "do",
            "op": "io/print_str",
            "args": [
              {
                "t": "lit",
                "lit": {
                  "kind": "str",
                  "value": "\n"
                }
              }
            ]
          }
        },
        "rhs": {
          "t": "seq",
          "lhs": {
            "t": "do",
            "op": "io/print_str",
            "args": [
              {
                "t": "app",
                "fn": {
                  "t": "var",
                  "name": "int_to_str"
                },
                "args": [
                  {
                    "t": "lit",
                    "lit": {
                      "kind": "int",
                      "value": 2
                    }
                  }
                ]
              }
            ]
          },
          "rhs": {
            "t": "do",
            "op": "io/print_str",
            "args": [
              {
                "t": "lit",
                "lit": {
                  "kind": "str",
                  "value": "\n"
                }
              }
            ]
          }
        }
      }
    }
  ]
}
```

## 9. Literals

There are five literal shapes. An integer literal is a signed
64-bit decimal. A boolean literal is `true` or `false`. A string
literal is a UTF-8 sequence in double quotes; AILang restricts the
authored byte set to ASCII printable (Decision 6 Constraint 3) — non-
ASCII bytes are an authoring error. A unit literal is the value of
type Unit, written `(unit)` in AIL and `{"kind": "unit"}` in JSON.

A Float literal is an IEEE-754 binary64 value. When you author
Floats, write the decimal form (`3.14`) — the AIL parser converts
to the 64-bit bit pattern and emits the canonical 16-character
lowercase hex string into the JSON. You never author the hex
encoding by hand; the toolchain owns that representation. NaN and
±Inf are representable through the prelude constants `nan`, `inf`,
and `neg_inf` (see section 11).

Float pattern matching is rejected at typecheck. IEEE-`==` makes
Float patterns semantically dubious (NaN never matches; equality
is bit-exact, not approximate), so the language hard-rejects them
to push authors toward comparison-based dispatch.

Literal variants and their JSON shapes:

- Int: `{"kind": "int", "value": 42}` — value is a JSON number.
- Bool: `{"kind": "bool", "value": true}` — value is a JSON bool.
- Str: `{"kind": "str", "value": "hi"}` — value is a JSON string.
- Unit: `{"kind": "unit"}` — no value payload.
- Float: `{"kind": "float", "bits": "400921fb54442d18"}` — the
  `bits` field is a 16-character lowercase hex string of the IEEE-
  754 binary64 bit pattern. The hex-string path keeps NaN and ±Inf
  representable (JSON numbers cannot encode them) and avoids
  serialisation drift across `serde_json` versions.

Float bit patterns are computed by the toolchain on `ail parse`,
not by the author. When you write `3.14` in AIL, the parser emits
`"bits": "40091eb851eb851f"` in the JSON form.


```json
{
  "schema": "ailang/v0",
  "name": "floats",
  "imports": [],
  "defs": [
    {
      "kind": "const",
      "name": "pi",
      "doc": "Pi as a Float constant. Exercises Def::Const and Literal::Float — the bit pattern below is f64::to_bits(3.14).",
      "type": { "k": "con", "name": "Float" },
      "value": { "t": "lit", "lit": { "kind": "float", "bits": "40091eb851eb851f" } }
    }
  ]
}
```

```json
{
  "schema": "ailang/v0",
  "name": "bool_str",
  "imports": [],
  "defs": [
    {
      "kind": "fn",
      "name": "is_true",
      "doc": "Trivial Bool literal. Exercises Literal::Bool.",
      "type": {
        "k": "fn",
        "params": [],
        "param_modes": [],
        "ret": { "k": "con", "name": "Bool" },
        "ret_mode": "own",
        "effects": []
      },
      "params": [],
      "body": { "t": "lit", "lit": { "kind": "bool", "value": true } }
    },
    {
      "kind": "fn",
      "name": "greeting",
      "doc": "Trivial Str literal. Exercises Literal::Str.",
      "type": {
        "k": "fn",
        "params": [],
        "param_modes": [],
        "ret": { "k": "con", "name": "Str" },
        "ret_mode": "own",
        "effects": []
      },
      "params": [],
      "body": { "t": "lit", "lit": { "kind": "str", "value": "hi" } }
    },
    {
      "kind": "fn",
      "name": "unit_value",
      "doc": "Trivial Unit literal — needed so Literal::Unit appears at least once in the corpus.",
      "type": {
        "k": "fn",
        "params": [],
        "param_modes": [],
        "ret": { "k": "con", "name": "Unit" },
        "ret_mode": "own",
        "effects": []
      },
      "params": [],
      "body": { "t": "lit", "lit": { "kind": "unit" } }
    }
  ]
}
```

## 10. Typeclasses

A typeclass is a named bundle of operations that may be
implemented for multiple types. The class declaration lists the
methods; each instance declaration provides the bodies for a
specific type. The compiler resolves method calls at the call site
and monomorphises the implementation: there is no runtime dispatch.

A class is parameterised by a single type variable (multi-parameter
classes are not supported in v1). Methods are declared with their
full type signature; the class parameter appears as a type variable
inside the method type. Methods may carry an optional default body
that instances inherit unless they explicitly override.

Class constraints attach to polymorphic function types: a function
`forall a. (Eq a) => (a, a) -> Bool` requires its callers to
provide an `Eq` instance for `a` at the call site. The constraint
appears inside the `forall` quantifier, in the `constraints` slot.

The prelude provides four built-in classes: `Eq` (equality), `Ord`
(ordering with `<`, `<=`, `>`, `>=`), `Num` (arithmetic — `+`, `-`,
`*`, `/`, `neg`), and `Bounded`. Their instances for Int, Bool,
Str, Float, and Unit are built in; you do not declare them.

Class declaration: `{"kind": "class", "name": "Show", "param": "a",
"methods": [...]}`. Each method: `{"name": "show", "type": ...,
"default": ...}` — `type` is the method's full signature with the
class parameter appearing as a `Type::Var`; `default` is an
optional body (omit when the method is abstract-required).

Instance declaration: `{"kind": "instance", "class": "Show",
"type": ..., "methods": [...]}`. The `type` field is the concrete
type the class is applied to. Each method: `{"name": "show",
"body": TERM}`.

Constraint on a polymorphic fn: inside `Type::Forall`, the
`constraints` field is an array of constraint objects: `{"class":
"Eq", "type": TYPE}`. Empty when the polymorphic fn has no class
constraints; omitted from canonical bytes when empty.


```json
{
  "schema": "ailang/v0",
  "name": "class_def",
  "imports": [],
  "defs": [
    {
      "kind": "class",
      "name": "MyShow",
      "param": "a",
      "doc": "A toy single-method class. The instance in instance_def.ail.json provides a body for `show` at type Int.",
      "methods": [
        {
          "name": "show",
          "type": {
            "k": "fn",
            "params": [ { "k": "var", "name": "a" } ],
            "param_modes": ["own"],
            "ret": { "k": "con", "name": "Str" },
            "ret_mode": "own",
            "effects": []
          }
        }
      ]
    }
  ]
}
```

```json
{
  "schema": "ailang/v0",
  "name": "instance_def",
  "imports": [],
  "defs": [
    {
      "kind": "class",
      "name": "MyShow",
      "param": "a",
      "doc": "Re-declared here so this fixture is self-contained; class_def.ail.json declares the same class verbatim.",
      "methods": [
        {
          "name": "show",
          "type": {
            "k": "fn",
            "params": [ { "k": "var", "name": "a" } ],
            "param_modes": ["own"],
            "ret": { "k": "con", "name": "Str" },
            "ret_mode": "own",
            "effects": []
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "MyShow",
      "type": { "k": "con", "name": "Int" },
      "doc": "Trivial MyShow Int — show always returns the fixed string \"int\".",
      "methods": [
        {
          "name": "show",
          "body": { "t": "lit", "lit": { "kind": "str", "value": "int" } }
        }
      ]
    }
  ]
}
```

## 11. The prelude

The prelude provides a fixed set of operators, conversion functions,
and effect operations that are in scope without any import. The
operators are polymorphic over a small set of types and resolve at
the call site by the resolved argument type.

| Name | Type | Notes |
|------|------|------|
| `+` `-` `*` `/` | `forall a. (a, a) -> a` | Int and Float; codegen filters at use site |
| `%` | `(Int, Int) -> Int` | Int only |
| `==` `!=` `<` `<=` `>` `>=` | `forall a. (a, a) -> Bool` | Int, Bool, Str, Float, Unit |
| `not` | `(Bool) -> Bool` | Boolean negation |
| `neg` | `forall a. (a) -> a` | Int and Float negation |
| `int_to_float` | `(Int) -> Float` | Widening; codegen uses `sitofp` |
| `float_to_int_truncate` | `(Float) -> Int` | Saturating truncation to zero |
| `float_to_str` | `(Float) -> Str` | Formatted decimal |
| `is_nan` | `(Float) -> Bool` | True only for NaN bit patterns |
| `nan` `inf` `neg_inf` | `Float` | Bare-value constants |
| `__unreachable__` | `forall a. a` | Polymorphic bottom; LLVM `unreachable` |

Effect operations (reached through `do`, not `app`):

| Op | Signature | Effect |
|----|----------|-------|
| `io/print_int` | `(Int) -> Unit` | `IO` |
| `io/print_bool` | `(Bool) -> Unit` | `IO` |
| `io/print_str` | `(Str) -> Unit` | `IO` |
| `io/print_float` | `(Float) -> Unit` | `IO` |

`int_to_str` is intentionally NOT in the prelude — it is type-
installed in a future milestone but codegen-deferred pending the
heap-Str ABI work. Do not call it.

## 12. Content addressing

AILang has content-addressed identity: every top-level definition
has a 16-character hash derived from its canonical bytes. The
toolchain computes hashes on `ail parse` and `ail check`; the
author writes no hash literal in either form, and the JSON form
has no `hash` field. This is symmetric across forms and removes
hash as a form-distinguishing factor. You author code; the
toolchain owns the identity.

## 13. Out of scope, and closing directive

This reference does NOT teach: cross-module imports (every task is
a single self-contained module with an empty `imports` array),
refinement types (reserved in the schema but pass-through in this
version), point-free style (cut by Decision 6), operator
overloading (cut), syntactic sugar of any kind (cut). The four
tasks you will be given do not need any of these features.

When asked to write a module, return the complete module text and
nothing else. No markdown fences. No prose explanation. No
preamble. The harness parses your response verbatim; any wrapping
text is treated as a parse error.
