AILang/experiments/2026-05-12-cross-model-authoring/rendered/ail.md

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 AIL surface is parenthesised tagged-head Lisp-style notation. Every form begins with ( followed by a tag identifier; positional arguments follow; the form closes with ). There are no infix operators, no operator precedence, no implicit conversions.

A module starts with (module NAME ...) and contains import forms followed by definition forms. Whitespace and ;-prefixed line comments are insignificant; indentation is for readability only.

Identifier characters allowed: letters, digits, _, -, +, *, /, <, >, =, !, ?, %. An identifier may not start with a digit. String literals are double-quoted with \", \\, \n, \t escapes; integer literals are signed decimal; the (unit) keyword denotes the unit value.

The AIL form is the printed dual of the JSON form: ail parse file.ail produces the same canonical bytes as the JSON form would, and ail render file.ail.json produces the AIL text. Round-trip through this pair is gated by an integration test.

(module fn_returns_int
  (fn answer
    (doc "The simplest possible fn — no params, returns a fixed Int.")
    (type (fn-type (params) (ret (con Int))))
    (params)
    (body 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: Int, Bool, Str, Float, Unit, or a user type name. For parameterised types: (con List Int) reads "List of Int"; nested: (con Map (con Str) (con Int)).

Type::Var: a bare identifier alone in type position (no wrapper), e.g. a inside a (forall (a) ...). Type variables are syntactically distinguished from type constructors by being declared in the enclosing forall.

Type::Fn: (fn-type (params T1 T2) (ret RET) (effects E1 E2)). The parameter and effect lists may be empty. Modes wrap the relevant type: (own T) or (borrow T) — see section 4.

Type::Forall: (forall (a b) BODY-TYPE) quantifies over a and b. Class constraints attach as (forall (a) (constraints (Eq a)) BODY-TYPE).

(module forall_polymorphic
  (fn id
    (doc "The polymorphic identity function. Exercises Type::Forall and Type::Var.")
    (type (forall (vars a) (fn-type (params a) (ret a))))
    (params x)
    (body x)))

4. Mode annotations

Every function parameter carries a mode. The mode says how the callee may treat the value: implicit is the legacy default (treated as own), 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.

The mode also applies to the return value: ret_mode says whether the function transfers ownership to the caller (own) or returns a borrow (borrow). For most functions the return mode is own or implicit; borrow returns are rare and used only for accessor-style functions.

Modes are mandatory on every parameter and on the return position. The schema rejects unannotated fn signatures only when annotations are explicitly requested; for compatibility the legacy form (no mode field at all) is treated as all-implicit.

Modes are surface wrappers around the type in parameter and return position. Inside a (fn-type ...):

• (params (own T1) (borrow T2)) — T1 is owned, T2 is borrowed.
• (ret (own T)) — the function returns an owned value.
• A bare type with no mode wrapper is implicit (legacy default).

When all parameters and the return are implicit, the surface omits the mode wrappers entirely; this is the canonical form for fns that do not yet need explicit annotations. Adding modes is a forward change: an existing fn keeps the same canonical bytes as long as no annotation is added.

Writing (borrow T) on a parameter the typechecker wants own for surfaces as the over-strict-mode diagnostic — advisory, and suppressable via the fn def's suppress clause. The mode is part of the fn's signature and contributes to its content hash, so making the choice explicit at authoring time avoids surprise hash changes when the typechecker's defaults shift.

(module param_modes_all
  (fn f_implicit
    (doc "Implicit mode is the legacy default — `param_modes` is omitted from canonical JSON when every entry is Implicit, which is the case here. The visitor still observes ParamMode::Implicit via the (defaulted) ret_mode field on Type::Fn.")
    (type (fn-type (params (con Int)) (ret (con Int))))
    (params x)
    (body x))
  (fn f_own
    (doc "(own T) — caller transfers ownership; callee consumes.")
    (type (fn-type (params (own (con Int))) (ret (con Int))))
    (params x)
    (body x))
  (fn f_borrow
    (doc "(borrow T) — caller retains ownership; callee may not consume.")
    (type (fn-type (params (borrow (con Int))) (ret (con Int))))
    (params x)
    (body x)))

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: (fn NAME (doc STRING)? (type TYPE) (params NAME*) (body TERM)). The doc clause is optional but recommended.

Term forms relevant here:

• Variable reference: a bare identifier, e.g. x or +.
• Application: (app CALLEE ARG*) — head is app, then the callee term, then positional arguments.
• Lambda: (lam (params NAME*) (paramTypes TYPE*) (ret TYPE) (effects EFFECT*) BODY).
• Let: (let (NAME VALUE) BODY) — binds NAME to VALUE in BODY.
• Letrec: (letrec NAME (type FN-TYPE) (params NAME*) BODY IN-BODY) — NAME is recursively visible inside BODY.

Inside any term position, an integer literal is a bare decimal number, a string is a double-quoted string, a bool is true or false, unit is (unit).

(module fn_calls_prelude
  (fn 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 (fn-type (params (con Int) (con Int)) (ret (con Int))))
    (params x y)
    (body (let s (app + x y) (clone s)))))

(module fn_with_lambda
  (fn 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 (fn-type (params (con Int)) (ret (fn-type (params (con Int)) (ret (con Int))))))
    (params x)
    (body (lam (params (typed y (con Int))) (ret (con Int)) (body (app + x 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: (data NAME (vars TYVAR*)? (doc STRING)? (ctor CTOR-NAME ARG-TYPE*)*). The vars clause is optional; nullary constructors have an empty argument list.

Example: (data List (ctor Nil) (ctor Cons Int (con List))) is a monomorphic Int list with a Nil and a Cons constructor.

Constructor invocation: (ctor TYPE-NAME CTOR-NAME ARG*). The TYPE-NAME precedes the constructor name so the parser does not need a separate registry to resolve overlapping constructor names across ADTs. Example: (ctor List Cons 1 (ctor List Nil)) builds a single-element list.

(module data_simple
  (data Box (vars a)
    (doc "A unary box around a polymorphic value.")
    (ctor MkBox a))
  (fn wrap_one
    (doc "Construct a Box Int via MkBox. The body uses (reuse-as src body) — a hint that the freshly-allocated Box should reuse the source's memory slot under --alloc=rc. Exercises TermCtor, ReuseAs, and Type::Var inside a ctor field position.")
    (type (fn-type (params (own (con Box (con Int)))) (ret (own (con Box (con Int))))))
    (params src)
    (body (reuse-as src (term-ctor Box MkBox 1)))))

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: (match SCRUT (case PAT BODY) (case PAT BODY) ...). Arms are introduced by (case ...); the order matters (top- to-bottom).

Pattern shapes:

• Wildcard: _ — bare underscore is the wildcard pattern.
• Variable: a bare identifier alone, e.g. h, binds the scrutinee.
• Literal: a literal value alone, e.g. 0, true, "abc", (unit), matches bit-equal scrutinees.
• Constructor: (ctor CTOR-NAME SUBPAT*) — note no type slot here, because the constructor name is resolved against the scrutinee's type.

Pattern variables introduced by a (case PAT BODY) are in scope inside BODY and bind there only. They do not leak into sibling arms or into code outside the match.

(module data_with_match
  (data List
    (doc "Monomorphic singly-linked Int list — boxed, recursive.")
    (ctor Nil)
    (ctor Cons (con Int) (con List)))
  (fn 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 (fn-type (params (borrow (con List))) (ret (con Int))))
    (params xs)
    (body (match xs
      (case (pat-ctor Nil) 0)
      (case (pat-ctor Cons h _) h))))
  (fn count_via_letrec
    (doc "Walk xs counting nodes using a local recursive let. Exercises TermLetRec and TermVar; the recursive `go` is bound locally.")
    (type (fn-type (params (borrow (con List))) (ret (con Int))))
    (params xs)
    (body (let-rec go (params ys) (type (fn-type (params (borrow (con List))) (ret (con Int)))) (body (match ys
      (case (pat-ctor Nil) 0)
      (case (pat-ctor Cons _ t) (app + 1 (app go t))))) (in (app go xs))))))

(module match_literal_pattern
  (fn classify
    (doc "Classify an Int via literal patterns plus a wildcard fallback. Exercises PatternLit and PatternWild.")
    (type (fn-type (params (con Int)) (ret (con Int))))
    (params n)
    (body (match n
      (case (pat-lit 0) 100)
      (case _ 200))))
  (fn 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 (fn-type (params (con Int)) (ret (con Int))))
    (params n)
    (body (if (app < n 0) -1 (if (app == n 0) 0 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 a fn type: (effects E1 E2 ...) inside the (fn-type ...). Empty row: omit the (effects) clause or write (effects). Common effectful row: (effects IO). Order is sorted in canonical output.

Effect operation: (do OP-NAME ARG*) — the leading do head is the parser's signal that the next identifier is an effect op, not a function. Example: (do io/print_int 42) prints the integer 42 and raises the IO effect.

Sequencing: (seq LHS RHS). The value of (seq X Y) is Y's value; X's value is discarded. Chains of sequencing are written nested: (seq A (seq B C)) runs A, then B, then yields C's value.

(module fn_with_do_seq
  (fn 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 (fn-type (params) (ret (con Unit)) (effects IO)))
    (params)
    (body (seq (do io/print_int 1) (do io/print_int 2)))))

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 surface forms:

• Int: bare signed decimal, e.g. 42, -7, 0.
• Bool: true or false as bare keywords.
• Str: double-quoted with \", \\, \n, \t escapes, e.g. "hello". Bytes outside ASCII printable are rejected by the authoring rule (Decision 6 Constraint 3).
• Unit: the keyword (unit).
• Float: bare decimal with at least one digit on each side of the point, e.g. 3.14, 0.5, -2.0. The parser converts to the bit-pattern hex string when emitting JSON; you never author the hex form.

There is no separate syntax for exponent-form floats in the v1 authoring surface; for non-finite values use the prelude constants nan, inf, neg_inf.

(module floats
  (const pi
    (doc "Pi as a Float constant. Exercises Def::Const and Literal::Float — the bit pattern below is f64::to_bits(3.14).")
    (type (con Float))
    (body 3.14)))

(module bool_str
  (fn is_true
    (doc "Trivial Bool literal. Exercises Literal::Bool.")
    (type (fn-type (params) (ret (con Bool))))
    (params)
    (body true))
  (fn greeting
    (doc "Trivial Str literal. Exercises Literal::Str.")
    (type (fn-type (params) (ret (con Str))))
    (params)
    (body "hi"))
  (fn unit_value
    (doc "Trivial Unit literal — needed so Literal::Unit appears at least once in the corpus.")
    (type (fn-type (params) (ret (con Unit))))
    (params)
    (body (lit-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: (class NAME (param TYVAR) (method NAME (type METHOD-TYPE) (default BODY)?)*). The default clause is optional; methods without a default must be supplied by every instance.

Instance declaration: (instance NAME (type CONCRETE-TYPE) (method NAME BODY)*). The method bodies must match the class's method signatures with the class parameter substituted to the concrete type.

Constraints inside a forall: (forall (a) (constraints (Eq a) (Ord a)) BODY-TYPE). Each constraint is (CLASS-NAME TYPE) — usually the type is a single bound type variable but a concrete type is also legal (typically a typecheck error unless an instance exists).

(module class_def
  (class MyShow
    (param a)
    (doc "A toy single-method class. The instance in instance_def.ail.json provides a body for `show` at type Int.")
    (method show
      (type (fn-type (params a) (ret (con Str)))))))

(module instance_def
  (class MyShow
    (param a)
    (doc "Re-declared here so this fixture is self-contained; class_def.ail.json declares the same class verbatim.")
    (method show
      (type (fn-type (params a) (ret (con Str))))))
  (instance
    (class MyShow)
    (type (con Int))
    (doc "Trivial MyShow Int — show always returns the fixed string \"int\".")
    (method show
      (body "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.