AILang/crates/ailang-core/specs/form_a.md

AILang Form-A — LLM authoring specification

Form-A is the canonical textual surface of AILang. It is the form that LLMs generate when asked to produce or edit AILang code, and the form that ail parse <file>.ail reads. The inverse direction — printing JSON-AST as Form-A — is ail render <file>.ail.json. Round-trip through this pair is the gating contract: parse(render(m)) == m for every well-formed module.

This document is the complete LLM-targeted specification. If you are an LLM and this is in your context, you have everything you need to produce valid Form-A. The file lives at crates/ailang-core/specs/form_a.md next to the AST definitions, and a unit test (tests/spec_drift.rs) walks every AST enum variant and asserts its serde tag appears here — so this document cannot silently fall behind the language.

Why Form-A and not JSON

The hashable artefact is .ail.json, but no human or LLM should write that directly. JSON-AST is a mechanical serialization with high boilerplate ({"k": "con", "name": "Int"} per type reference, mandatory field tags, every term wrapped). Form-A is the same information in a Lisp-style S-expression dress that:

• omits structural noise (no field tags; positions carry meaning)
• has a real parser with positional error messages
• round-trips through ail render ↔ ail parse losslessly
• is the form every existing examples/*.ail is written in

LLMs generate Form-A; the toolchain converts to JSON.

Conventions

• NAME is a bare identifier: letters, digits, _, -, +, *, /, <, >, =, !, ?, %. Cannot start with a digit.
• STRING is a double-quoted UTF-8 literal: "hello". Backslash escapes: \", \\, \n, \t.
• INT is a signed decimal integer; leading - is allowed.
• Whitespace and ;-prefixed line comments are insignificant.
• ? after a clause means optional. * means zero or more.

Module structure

(module NAME
  IMPORT*
  DEF*)

The module name MUST equal the file stem (bench_list_sum.ail → (module bench_list_sum ...)).

Imports

(import MODULE-NAME)
(import MODULE-NAME (as ALIAS))

The alias clause is optional. Imported modules are resolved relative to the entry file's directory.

Definitions

Five kinds, matched on the leading keyword:

Function — (fn ...)

(fn NAME
  (doc STRING)?
  (export STRING)?
  (suppress (code STRING) (because STRING))*
  (type FN-TYPE)
  (params NAME*)
  (body TERM))

doc is optional but recommended — it appears in the prose projection and helps downstream readers (human and LLM).

export is optional. When present, the string is the C symbol under which codegen's --emit=staticlib mode exposes this fn as an externally-callable entrypoint (Embedding ABI M1). The symbol is author-chosen and decoupled from the internal ail_<module>_<def> mangling. M1 requires the fn's parameter and return types to be scalar (Int/Float) and its effect set to be empty — see design/contracts/0003-embedding-abi.md.

suppress clauses silence advisory diagnostics for this def. The code MUST be one of the registered codes (today: over-strict-mode). The because MUST be a non-empty justification — empty / whitespace- only because is itself an error (empty-suppress-reason).

type is a (fn-type ...) (possibly wrapped in (forall ...) for polymorphic defs). A heap-shaped parameter or return of a (fn ...) MUST carry a mode annotation; a scalar (non-heap-shaped: (con Int), (con Bool), (con Unit), (con Str)) takes no mode and is written bare — see Modes below.

params is a list of bare names that bind the parameters in body. The list length must match the number of params in type.

Data type — (data ...)

(data NAME
  (vars TYVAR+)?
  (doc STRING)?
  (ctor CTOR-NAME ARG-TYPE*)*)

vars makes the type polymorphic; absent means monomorphic. Each ctor clause is one variant. ARG-TYPE is a TYPE — see below.

Constant — (const ...)

(const NAME
  (doc STRING)?
  (type TYPE)
  (body TERM))

Class — (class ...)

(class NAME
  (param TYVAR)
  (doc STRING)?
  (superclass (class CLASS-REF) (type TYVAR))?
  (method NAME (type FN-TYPE) (default TERM)?)*)

A class declaration introduces a typeclass with one type parameter (param) and a list of method signatures.

CLASS-REF in the optional superclass clause follows the canonical-form rule (see Types below): bare for same-module, MODULE.CLASS for cross-module. The superclass slot is at most one — multi-superclass chains are not yet supported.

Each method carries a function-typed signature. The bound type variable named in param is in scope throughout the method's (type ...). A (default ...) clause provides a fallback implementation; absent means the method is abstract-required (every instance MUST implement it).

Example (examples/test_22c_user_class_e2e.ail):

(class Foo
  (param a)
  (method foo
    (type (fn-type (params (borrow a)) (ret (con Int))))))

Instance — (instance ...)

(instance
  (class CLASS-REF)
  (type TYPE)
  (doc STRING)?
  (method NAME (body LAM-TERM))*)

An instance declaration provides method implementations of CLASS-REF at the concrete TYPE.

CLASS-REF follows the canonical-form rule: bare for same-module-to- class (the instance and the class live in the same module), MODULE.CLASS for cross-module (the class lives in another module — most commonly prelude.Show, prelude.Eq, etc.).

Each method body is a (lam ...) term. The class's type parameter is substituted for TYPE throughout the method body's parameter types and return type; method bodies are type-checked under that substitution and walk through the same identifier-resolution path as (fn ...) bodies, so an unbound name inside a method body fires [unbound-var] at ail check.

Two examples.

Same-module class + instance (examples/mq3_class_eq_vs_fn_eq_classmod.ail, abbreviated):

(class MyEq (param a)
  (method myeq (type (fn-type (params (borrow a) (borrow a)) (ret (con Bool))))))
(instance
  (class MyEq)
  (type (con Int))
  (method myeq
    (body (lam (params (typed x (con Int)) (typed y (con Int))) (ret (con Bool)) (body true)))))

Cross-module qualified class (examples/show_user_adt.ail, abbreviated):

(instance
  (class prelude.Show)
  (type (con IntBox))
  (method show
    (body (lam (params (typed x (con IntBox))) (ret (con Str))
      (body (match x (case (pat-ctor MkIntBox n) (app int_to_str n))))))))

The prelude.Show qualifier is required here because Show is declared in the prelude module, not the entry module. Writing (class Show) bare would fail with bare-cross-module-class-ref.

Types

Four shapes, all parenthesised except a bare type variable:

TYVAR-NAME                              ; type variable (e.g. `a`, `T`)
(con NAME TYPE-ARG*)                    ; type-constructor application
(fn-type (params PARAM*)
         (ret RETURN-PARAM)
         (effects EFFECT-NAME*)?)       ; function type
(forall (vars TYVAR+)
        (constraints (constraint CLASS-REF TYPE)+)?
        BODY-TYPE)                      ; polymorphic schema with optional constraints

PARAM and RETURN-PARAM are types, optionally wrapped in a mode annotation:

TYPE                ; no mode — REQUIRED for scalars (Int/Bool/Unit/Str), rejected for heap-shaped
(own TYPE)          ; caller transfers ownership; callee consumes
(borrow TYPE)       ; caller retains ownership; callee must not consume

EFFECT-NAME is a bare identifier. The only effect with a built-in op today is IO (op io/print_str); Diverge is a reserved name (no op, unimplemented). Effects are a set; order is irrelevant.

Built-in type-constructors: Int, Bool, Str, Unit. User ADTs use the name from the (data ...) def.

A (forall ...) may carry an optional (constraints ...) clause whose inner items are (constraint CLASS-REF TYPE) pairs. Each constraint requires the named class to have an instance at the given type; TYPE is typically a type variable bound by the same forall. CLASS-REF follows the canonical-form rule (bare for same-module, MODULE.CLASS for cross-module). At a call site, every constraint must discharge — by a matching instance in the workspace or by another constraint in the caller's own schema. An undischargeable constraint fires no-instance at ail check.

Examples:

(con Int)
(con List (con Int))
(fn-type (params (own (con List)) (borrow (con Int))) (ret (con Int)))
(forall (vars a) (fn-type (params (con List a)) (ret (con Int))))
(forall (vars a) (constraints (constraint prelude.Ord a))
                 (fn-type (params a a) (ret a)))

Terms

Atom forms (no parens):

• INT — integer literal
• STRING — string literal
• true, false — bool literals
• FLOAT — IEEE-754 binary64 literal: e.g. 1.5, 1.5e3, 1e10.
• NAME — variable reference (parameter, local, top-level def, or import alias)

Parenthesised forms:

(lit-unit)                              ; the unit value ()
(app FN ARG+)                           ; function application (≥1 arg)
(tail-app FN ARG+)                      ; tail-position application
(do OP-NAME ARG*)                       ; effect operation
(tail-do OP-NAME ARG*)                  ; tail-position effect
(let NAME VALUE-TERM BODY-TERM)         ; binding
(let-rec NAME (params NAME*) (type FN-TYPE) (body TERM)
         (in BODY-TERM))                ; recursive let (fn-shaped)
(if COND-TERM THEN-TERM ELSE-TERM)      ; conditional
(match SCRUTINEE-TERM (case PAT BODY)+) ; pattern match (≥1 arm)
(term-ctor TYPE-NAME CTOR-NAME ARG*)    ; constructor application
(lam (params (typed NAME TYPE)*)
     (ret RETURN-TYPE)
     (effects EFFECT-NAME*)?
     (body TERM))                       ; anonymous function
(seq EFFECTFUL-TERM RESULT-TERM)        ; sequence; lhs evaluated for effect
(clone TERM)                            ; explicit RC clone
(reuse-as SOURCE-TERM BODY-TERM)        ; explicit reuse hint
(loop (NAME TYPE INIT)* BODY-TERM+)     ; strict iteration block (loop-recur)
(recur ARG*)                            ; re-enter enclosing loop (loop-recur)
(new TYPE-NAME ARG+)                    ; functional construction (kernel-extension prep.2)

Notes:

• app and do REQUIRE the right tag for the right thing. Constructors are NEVER called with app; always use term-ctor.
• tail-app / tail-do mark the call as occurring in tail position; the tag is explicit rather than inferred. Codegen lowers them to musttail call. Use the tail variant whenever a recursive call is the final action of an arm — it converts unbounded recursion into iteration. Non-tail variants are otherwise indistinguishable in semantics.
• seq is (seq A B) — A is evaluated for its effects and result discarded; B is the value of the whole expression. For pure A, prefer (let _ A B) or just drop A.
• reuse-as requires SOURCE-TERM to be a bare variable reference (a NAME in the term grammar). Anything else fails the linearity check with reuse-as-source-not-bare-var.
• loop opens a strict iteration block. (NAME TYPE INIT) binder triples (zero or more) are followed by a body of zero or more Unit-typed statements and exactly one final expression (right- folded into Term::Seq). recur re-enters the lexically innermost enclosing loop, rebinding its binders positionally; (recur ARG*)'s arg count must equal the binder count and recur must be in tail position of the loop body — both enforced at typecheck (recur-arity-mismatch, recur-not-in-tail-position). loop/recur make no termination claim: a loop with no non-recur exit runs forever. See docs/specs/0034-loop-recur.md.
• new is functional construction: (new TYPE-NAME ARG+) calls the new def in TYPE-NAME's home module with the supplied args. Each arg is positional and disambiguated by syntactic form: a parenthesised form whose head ident is one of con, fn-type, borrow, own parses as a Type-positional arg (instantiating one of new's outer Forall vars); anything else parses as a Value-positional arg (a Term checked against the corresponding param type). Zero args is rejected at parse-time. Diagnostics: new-type-not-constructible (T's home module has no new def), new-arg-kind-mismatch (arg's kind disagrees with the sig at that position). Codegen lands in the raw-buf milestone.

Patterns

_                              ; wildcard; matches anything, binds nothing
NAME                           ; variable; binds the value to NAME
(pat-lit LIT-FORM)             ; literal match: integer, true/false, string
(pat-ctor CTOR-NAME FIELD*)    ; constructor; FIELD is itself a pattern

LIT-FORM is INT, true, false, or STRING — the same atoms used as terms.

A pattern variable may bind at most once per arm. Pattern-binders are in scope inside the arm body.

Schema invariants enforced by ail check

The parser will accept syntactically valid Form-A that violates these; the typechecker will not. Producing Form-A that obeys them yields checked code on the first try.

1. Mode annotations on every heap-shaped (fn ...) parameter. A parameter type in the (params ...) clause of a (fn ...) definition's (fn-type ...), and the return type, MUST be wrapped in (own T) or (borrow T) whenever the type is heap-shaped (i.e. anything other than (con Int), (con Bool), (con Unit), (con Str)). A scalar (non-heap-shaped) parameter or return takes no mode: write it bare, e.g. (con Int). Scalars are primitive value types, not linear resources; putting a mode on a scalar makes the checker hold the primitive to linear discipline (single use under own, no use while a borrow is live), so an ordinary scalar reused in the body (sample * sample) trips a body-pointing use-after-consume / consume-while-borrowed rather than a mode error. Implicit (omitted) mode on a heap-shaped (fn ...) parameter or return is rejected.
2. Constructors via term-ctor. Cons(1, Nil) becomes (term-ctor List Cons 1 (term-ctor List Nil)), never (app Cons 1 (app Nil)).
3. Effects on side-effecting fns. A function whose body uses (do ...) MUST list every effect operation's effect in its (effects ...) clause. The only built-in effect op is io/print_str, whose effect is IO.
4. Tail correctness. (tail-app f x) MUST appear in tail position — i.e. as the body of a fn, the last expression of a (seq ...), the chosen arm of an (if ...) or (match ...), or the body of a (let ...). A tail-app outside a tail position is rejected.
5. Linearity for own/borrow. A parameter declared (own T) must be consumed exactly once on every reachable path; a (borrow T) must never be consumed. The diagnostic catalog has named codes for the typical violations.

Pitfalls

LLMs without prior AILang exposure tend to make the following errors. Reading these once before generating Form-A reduces re-roll cost significantly.

• Bare type names instead of (con T). Writing Int where a type is expected does NOT work — types live inside (con ...). Only TYVAR-NAME (a single ident) parses as a type without parens, and it is interpreted as a type variable. So (fn-type (params Int) ...) parses as "function with one type-variable parameter named Int", which is almost certainly not what was meant.
• Forgetting mode annotations on a heap-shaped parameter. (fn-type (params (con List)) ...) is accepted by the parser but rejected by the checker. Wrap every heap-shaped (fn ...) parameter in (own ...) or (borrow ...).
• Putting a mode on a scalar parameter. The inverse trap: (fn-type (params (own (con Int))) ...) is wrong — scalars (Int/Bool/Unit/Str) take no mode, write them bare (con Int). A mode on a scalar makes the checker treat the primitive as a linear resource, so an ordinary reuse trips a body-pointing use-after-consume / consume-while-borrowed instead of pointing at the signature.
• Using app for constructors. Constructors are NOT first-class functions. (app Cons 1 Nil) is interpreted as "apply variable Cons to ...", which then fails because Cons is not a fn.
• Forgetting tail-. A non-tail call in tail position works, but three million stack frames will overflow. For recursive fns where the recursive call is the final action, use tail-app.
• Wrong arity in (case (pat-ctor C f1 f2 ...) ...). The number of pattern fields must equal the constructor's declared arity. The checker catches this but the message is clearer if you do too.
• Strings inside (suppress (because ...)) must be non-empty. Empty is an error. Whitespace-only is an error. Write a real reason.

Few-shot corpus

These four modules are real examples/*.ail content. Each one is parseable and typechecks clean. Pattern-match against them when generating new code.

1 — hello.ail: minimal IO program

(module hello
  (fn main
    (type (fn-type (params) (ret (con Unit)) (effects IO)))
    (params)
    (body (do io/print_str "Hello, AILang."))))

2 — borrow_own_demo.ail: mode annotations on a recursive list

(module borrow_own_demo

  (data List
    (doc "Monomorphic singly-linked Int list — boxed, recursive.")
    (ctor Nil)
    (ctor Cons (con Int) (con List)))

  (fn list_length
    (doc "Borrow xs, count its elements.")
    (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 t)
          (app + 1 (app list_length t))))))

  (fn sum_list
    (doc "Consume xs, sum its elements.")
    (type
      (fn-type
        (params (own (con List)))
        (ret (con Int))))
    (params xs)
    (body
      (match xs
        (case (pat-ctor Nil) 0)
        (case (pat-ctor Cons h t)
          (app + h (app sum_list t))))))

  (fn main
    (type (fn-type (params) (ret (con Unit)) (effects IO)))
    (params)
    (body
      (let xs
        (term-ctor List Cons 1
          (term-ctor List Cons 2
            (term-ctor List Cons 3
              (term-ctor List Nil))))
        (seq
          (app print (app list_length xs))
          (app print (app sum_list xs)))))))

3 — lit_pat.ail: literal patterns and nested ctor patterns

(module lit_pat

  (data IntList
    (ctor Nil)
    (ctor Cons (con Int) (con IntList)))

  (fn classify
    (type (fn-type (params (con Int)) (ret (con Int))))
    (params n)
    (body
      (match n
        (case (pat-lit 0) 100)
        (case (pat-lit 1) 200)
        (case _ 999))))

  (fn categorize_first
    (type (fn-type (params (own (con IntList))) (ret (con Int))))
    (params xs)
    (body
      (match xs
        (case (pat-ctor Nil) -1)
        (case (pat-ctor Cons (pat-lit 0) _) 0)
        (case (pat-ctor Cons h _) h)))))

4 — Tail-recursive sum (the canonical big-N pattern)

(module sum_demo
  (data IntList
    (ctor INil)
    (ctor ICons (con Int) (con IntList)))

  (fn sum_acc
    (doc "Tail-recursive accumulator.")
    (type
      (fn-type
        (params (own (con IntList)) (con Int))
        (ret (con Int))))
    (params xs acc)
    (body
      (match xs
        (case (pat-ctor INil) acc)
        (case (pat-ctor ICons h t)
          (tail-app sum_acc t (app + acc h))))))

  (fn sum_list
    (type
      (fn-type
        (params (own (con IntList)))
        (ret (con Int))))
    (params xs)
    (body
      (app sum_acc xs 0))))

Notice in (4): the recursive sum_acc call is tail-app, the addition is plain app. The accumulator parameter is (con Int) (no mode — Int is a primitive value type, not heap-shaped, so modes do not apply to it).