AILang/design/contracts/0013-typeclasses.md

Typeclasses

The schema, registry, and diagnostic contract for the typeclass layer. The resolution/monomorphisation whitepaper lives at models/typeclasses; the call-site lookup rule at method dispatch; the built-in classes the prelude ships at prelude classes.

Form-A schema (the JSON authoring surface)

Three additive schema extensions; no existing module becomes invalid. The canonical schema for ClassDef, InstanceDef, and the FnDef.type constraints field lives in Data model; this section is the typeclass-layer narrative.

ClassDef — top-level definition kind, declares a class:

{ "kind": "class",
  "name": "Show",
  "param": "a",
  "superclass": null,
  "methods": [
    { "name": "show",
      "type": { /* full FnSig over `a`, with mode annotations */ },
      "default": null
    }
  ]
}

superclass is either null or { "class": <name>, "type": "a" } where "a" MUST be the same identifier as the class's own param. default is either null (method is abstract-required at instance sites) or an AST body (method is optional with the body as fallback).

InstanceDef — top-level definition kind, declares an instance:

{ "kind": "instance",
  "class": "Show",
  "type": "Int",
  "methods": [
    { "name": "show", "body": <AST> }
  ]
}

type is a concrete type expression, never the class param. methods contains the bodies for every required method plus optional overrides of default-bearing methods.

FnDef.type extension — the existing FnSig schema gains a constraints sibling field next to forall:

"type": {
  "forall": ["a"],
  "constraints": [{ "class": "Show", "type": "a" }],
  "type": ["Fn", [...], "String"]
}

When forall is empty, constraints is also empty (and may be omitted for hash stability of older definitions). Each constraint's type field MUST reference a type variable bound by the surrounding forall.

Method invocation sites do NOT get a new node. A call to a class method is a normal Call node; resolution against a class is the typechecker's job, not the parser's. The LLM author writes show x exactly as for any free function.

Cross-module references in synthesised bodies

The unified mono pass (see models/typeclasses for the resolution/monomorphisation algorithm) synthesises mono symbols for polymorphic free fns and class-method instances in the symbol's owner module — e.g. print__Int lives in prelude (because print is defined in the prelude), but a user-ADT call site print (MkIntBox 7) causes synthesis of prelude.print__IntBox whose body references show_user_adt.show__IntBox (the user instance lives in the user-defining module per the orphan-free-coherence rule documented in models/typeclasses). The synthesised body crosses a module boundary the source template did not.

Three invariants make this work:

1. MonoTarget::FreeFn::type_args carries canonical types post-collection. At every site where subst.apply(m) produces a concrete substitution that enters MonoTarget::FreeFn::type_args (crates/ailang-check/src/mono.rs::collect_mono_targets and ::collect_residuals_ordered), the resolved Type must be passed through Registry::normalize_type_for_lookup(caller_module, &t) before being pushed. The downstream synthesised body's Phase 3 rewrite cursor (which runs in the OWNER module's context, not the caller's) keys lookups in Registry::entries by the canonical qualified form; a bare type-con reference at the type_args layer silently drops the cross-module mono-symbol synthesis and leaves a bare Var "show" post-mono that codegen later rejects with unknown variable.

2. Post-mono synthesised body cross-module references are resolved once, in lower_to_mir. prelude does not import user modules (the auto-injection runs one-way: user workspaces import prelude, never the inverse). But a synthesised body for prelude.print__<UserType> references <user_module>.show__<UserType>, created by mono — not by the prelude source — so the call crosses a module boundary the source template did not. This reference is resolved at lowering time: crates/ailang-check/src/lower_to_mir.rs::classify_callee resolves the callee against the workspace and emits Callee::Static { module, fn_name, .. } carrying the resolved owner. Codegen consumes that identity off the MIR App node and does not re-resolve it, per the check→codegen boundary. Both ends were independently typechecked under their own module contexts before mono ran; the cross-module reference is a post-mono construct, not a source-language one.

3. FreeFnCall synth pushes one residual per declared forall- constraint. At crates/ailang-check/src/lib.rs's synth Var arm for the prefix.suffix free-fn path, when the type is a Type::Forall { vars, constraints, body }, instantiation produces fresh metavars for the vars AND pushes one ResidualConstraint per entry in constraints (with rigid vars substituted by the freshly-generated metavars). The downstream discharge loop at check_fn's post-synth phase resolves each residual against the workspace registry; if no instance satisfies the residual at the unified concrete type, the NoInstance diagnostic fires at typecheck (correctly), not at codegen (confusingly). Without the residual push, polymorphic-helper negative cases (e.g. print f where f : Int -> Int) silently typecheck and surface as unknown variable: show from codegen instead of the right typecheck-phase NoInstance Show.

4. Bare-prelude-fn calls resolve via implicit-prelude-import at typecheck AND at codegen. A user-module source-level call (app float_eq 1.5 1.5) writes the bare name float_eq, not the qualified form prelude.float_eq. The typechecker resolves this via the auto-injected prelude import (see invariant (2) for the one-way auto-injection rule); codegen's lower_app::resolve_callee + is_static_callee + resolve_top_level_fn each carry a parallel prelude-fallback: when the bare name does not resolve in the caller-module's symbol table, fall back to prelude.<name>. This is the source-level counterpart to invariant (2)'s post-mono fallback — both make the implicit- prelude-import a workspace invariant rather than a typechecker- only feature. The fallback is load-bearing for the surface (app float_eq …) / (app float_lt …) / etc. of the operator-routing-eq-ord milestone; without it the LLM-author must write prelude.float_eq explicitly, which is exactly the syntactic noise the implicit import exists to eliminate.

The four invariants are lockstep partners: invariant (1) creates the cross-module reference, invariant (2) makes codegen able to resolve post-mono references, invariant (3) makes the typecheck-time discharge fire correctly when no instance exists, invariant (4) makes bare prelude-fn names resolve from user modules at the source level. Loosening any one breaks the user-ADT trajectory or the Float-named-fn surface, so each is pinned: crates/ail/tests/codegen_import_map_fallback_pin.rs (invariant 2), crates/ail/tests/polyfn_dot_qualified_branch_pin.rs (invariant 3

• lockstep), crates/ail/tests/float_compare_smoke_e2e.rs (invariant 4 — drives (app float_eq …) end-to-end across the implicit-prelude-import boundary), and the existing crates/ail/tests/show_user_adt fixture (full trajectory) collectively protect the contract.

Defaults and superclasses

Defaults. A ClassDef.methods[i].default is either null (the method is required at instance level) or an AST body. When an InstanceDef does not specify a method that has a default, the typechecker uses the default body for that instance, with the class param substituted to the instance type. Default bodies may call other methods of the same class (the canonical example is default ne x y = not (eq x y)); the called methods resolve at monomorphisation time against the same instance.

Superclasses. A ClassDef.superclass of { "class": "Eq", "type": "a" } declares that any instance C T requires a corresponding instance Eq T to exist. The check fires at workspace-load time: for each InstanceDef whose class declares a superclass, the registry is queried for the matching superclass instance. Missing → MissingSuperclassInstance.

Superclass auto-expansion in constraint contexts. When a function declares Ord a as a constraint, the typechecker treats the constraint context as { Ord a, Eq a } for the purposes of MissingConstraint checking. This is the one deviation from "alles sichtbar": the extension is anchored in the class's own superclass field, so the relation is schema-visible at the class declaration even when the constraint at the function site reads Ord a alone.

Superclass chains are linear (single-superclass relation per class) and auto-expansion closes transitively across the chain.

No deriving. AILang does not auto-derive instances. instance Eq MyType must be written by hand.

Diagnostic categories

The typeclass layer introduces three families of diagnostics. Exact wording is fixed; the categories and their triggers are:

Workspace-load (registry-build) diagnostics:

• OrphanInstance — instance is not in class's or type's module.
• DuplicateInstance — two instances match the same key.
• MissingSuperclassInstance — superclass instance absent.
• MissingMethod — instance omits a required method.
• OverridingNonExistentMethod — instance specifies a method not in the class.

Cross-class method sharing is structurally legal; ambiguity surfaces at the call site via AmbiguousMethodResolution or, for class-fn name overlap, via the class-method-shadowed-by-fn warning. See Method dispatch.

Class-schema diagnostics (validation of class declarations):

• InvalidSuperclassParam — superclass type differs from the class's own param.
• UnboundConstraintTypeVar — a class method's signature carries a constraint mentioning a type variable bound neither by the method's forall nor by the class param.

A class param appearing in applied position (e.g., f a where f is the class param) is rejected earlier by the canonical-form validator as BareCrossModuleTypeRef — f is a bare, non-primitive name not declared as a TypeDef in the owning module.

Typecheck diagnostics (per function body):

• MissingConstraint — body's residual constraint is not covered by declared (and superclass-expanded) constraints.
• NoInstance — fully concrete constraint has no registry entry. Carries an optional candidate_classes field surfacing the multi-candidate set when the bare-method dispatch path's filter collapses to zero registry survivors.
• AmbiguousMethodResolution — a monomorphic Term::Var call site survives both type-driven and constraint-driven filters with more than one candidate class. LLM-author writes the explicit qualifier form <module>.<Class>.<method> to disambiguate.
• UnknownClass — an explicit class qualifier in Term::Var.name names a qualified class that is not in the workspace's candidate-class index for the method.
• class-method-shadowed-by-fn (warning) — a Term::Var resolved via fn lookup precedence (locals → caller-module-fn → imported-fn) while a class method of the same name also exists in the workspace. Fn resolution proceeds; the warning surfaces the shadow so the LLM-author can disambiguate via explicit class-qualified call if the shadow was unintentional.

There is no AmbiguousInstance diagnostic at the registry level — coherence (DuplicateInstance at registry build, W2) makes per-(class, type) ambiguity structurally impossible. Cross-class method ambiguity is a separate concern resolved at the call site via AmbiguousMethodResolution (see Method dispatch).

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