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These decisions are normative; implementation must conform or spec must be amended with rationale."})]}),m("div",{className:"hidden items-center gap-2 border border-[#a3e635]/20 bg-[#a3e635]/10 px-3 py-1.5 text-[10px] tracking-[0.14em] uppercase text-[#a3e635] md:flex",children:[c("span",{className:"h-1.5 w-1.5 rounded-full bg-[#a3e635]"}),"Locked"]})]}),c("div",{className:"mt-10 grid gap-px border border-[var(--border)] bg-[var(--border)]",children:[{n:"0",title:"Language",value:"Unlambda 2.0.0 (Madore 1999-12-20)",rationale:"Canonical stable dialect. Operators: ` (app), s,k,i,v,c,d,e,r,@,|,.x,?x. Strict semantics preserved; d is non-strict delay, c captures delimited continuation.",meta:"spec/language-semantics.md · operators list normative"},{n:"1",title:"Reference evaluator",value:"Original C implementation unlambda-2.0.0 from madore.org GPL2+, pinned",rationale:"Oracle must NOT share production code. Adapter in small Python/Haskell reimplementation (~300 LOC) that mirrors spec semantics literally. Used only for differential testing, not in runtime path.",meta:"reference/ + fixtures/ · independent impl"},{n:"2",title:"Heap",value:"Fixed-capacity slot-map with (slot,generation) NodeRef",rationale:"Explicit OutOfMemory, no GC initially. Generation prevents ABA/stale deref. Mark-sweep introduced only after Phase 4 passes. Accounting invariants H1-H5 enforced.",meta:"heap.sats · NodeRef = (uint32 slot, uint32 gen)"},{n:"3",title:"Evaluation",value:"Explicit CEK machine: Σ = ⟨C,K,H,I,O,F,Q⟩",rationale:"Control C = current term/value, K = continuation stack, H heap, I input cursor, O output trace, F fuel, Q status. Strict eval except d which creates Delayed without evaluating arg. Call/cc c captures K as Continuation node.",meta:"state.sats + stack.sats · one transition per step"},{n:"4",title:"Verification boundary",value:"ATS enforces AST validity, NodeRef abstraction, heap API Result; runtime asserts I1-I8; tests AT-01..14",rationale:"Separation: ATS static types for representability, runtime asserts for transition boundaries, tests for observable behavior, future Coq/ATS proofs for SKI correspondence (s,k,i reduction = spec).",meta:"invariants.md · preservation arguments"}].map((n)=>c("div",{className:"bg-[var(--surface)] p-6 md:p-8",children:m("div",{className:"flex flex-col gap-6 md:flex-row md:items-start",children:[m("div",{className:"flex items-center gap-4 md:w-[220px] md:shrink-0",children:[c("div",{className:"flex h-8 w-8 items-center justify-center border border-[var(--border-strong)] bg-[var(--surface-2)] text-[13px] text-[var(--text-muted)]",children:n.n}),m("div",{children:[c("div",{className:"text-[13px] tracking-[-0.01em] text-[var(--text)]",children:n.title}),c("div",{className:"mt-1 text-[10px] tracking-[0.12em] uppercase text-[#a3e635]",children:"Locked ✓"})]})]}),m("div",{className:"min-w-0 flex-1",children:[c("div",{className:"text-[13px] leading-[1.6] text-[var(--text)]",children:n.value}),c("div",{className:"mt-3 max-w-[620px] text-[12px] leading-[1.7] text-[var(--text-muted)]",children:n.rationale}),c("div",{className:"mt-4 inline-flex border border-[var(--border)] bg-[var(--code-bg)] px-2.5 py-1 text-[11px] text-[var(--text-faint)]",children:n.meta})]})]})},n.n))})]}),m("section",{id:"state",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 02"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"State definition Σ = ⟨C,K,H,I,O,F,Q⟩"}),m("div",{className:"mt-8 grid gap-8 md:grid-cols-[1.1fr_0.9fr]",children:[m("div",{className:"border border-[var(--border)] bg-[var(--surface)] p-6",children:[c("div",{className:"text-[11px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Formal state"}),c("div",{className:"mt-4 font-mono text-[18px] leading-[1.4] tracking-[-0.02em]",children:"Σ = ⟨ C , K , H , I , O , F , Q ⟩"}),c("div",{className:"mt-6 grid gap-3 text-[12px] leading-[1.6]",children:[{sym:"C",name:"Control",desc:"Current term or value. Term = heap ref; Value = evaluated primitive / char / continuation."},{sym:"K",name:"Continuation",desc:"Stack of frames. Encodes pending work; replaces host recursion."},{sym:"H",name:"Heap",desc:"Slot-map of Nodes with generation counters. Stable NodeRef (slot,gen)."},{sym:"I",name:"Input",desc:"Source bytes + cursor. ?x reads one byte or eof value."},{sym:"O",name:"Output",desc:"Ordered event sequence. .x appends char; append-only, never truncated."},{sym:"F",name:"Fuel",desc:"Remaining steps (uint64). Decremented per step; 0 → OutOfFuel."},{sym:"Q",name:"Status",desc:"Running | Halted | Failed(err) | OutOfFuel | OutOfMemory."}].map((n)=>m("div",{className:"grid grid-cols-[32px_1fr] gap-3 border-t border-[var(--border)] pt-3 first:border-0 first:pt-0",children:[c("span",{className:"font-bold text-[var(--text)]",children:n.sym}),m("div",{children:[c("span",{className:"text-[var(--text)]",children:n.name}),m("span",{className:"text-[var(--text-muted)]",children:[" — ",n.desc]})]})]},n.sym))})]}),m("div",{className:"space-y-4",children:[m("div",{className:"border border-[var(--border)] bg-[var(--code-bg)] p-6",children:[c("div",{className:"text-[11px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Status type"}),c("pre",{className:"mt-4 text-[12px] leading-[1.8] text-[#c8c8c8]",children:`datatype status =
| Running
| Halted of (value)
| Failed of (error_code, span)
| OutOfFuel of { fuel_consumed: uint64 }
| OutOfMemory of { heap_used: uint64, capacity: uint64 }
(* Do not encode as Option or bool.
OutOfFuel ≠ Halted, OutOfMemory ≠ Failed *)`})]}),m("div",{className:"border border-amber-200/20 bg-amber-300/5 p-4",children:[c("div",{className:"text-[11px] tracking-[0.12em] uppercase text-[#facc15]",children:"Invariant note"}),c("div",{className:"mt-2 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:"Status monotonicity I4: Once Q ≠ Running, step must return Halt/Error, never Continue. This prevents fuel-exhausted programs being misclassified as terminated."})]})]})]})]}),m("section",{id:"heap",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 03"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Heap node model"}),c("p",{className:"mt-3 max-w-[640px] text-[13px] leading-[1.7] text-[var(--text-muted)]",children:"Conservative graph representation. Stable identifiers prevent ABA. Fixed capacity initially; allocation failure is explicit and observable."}),m("div",{className:"mt-8 grid gap-6 md:grid-cols-2",children:[c(sn,{label:"heap.sats — node",code:`abst@ype NodeRef = (slot: uint32, gen: uint32)
datatype Node =
| Primitive of (sym: char)
// s,k,i,v,c,d,e,r,@,|,.,?
| Application of (fun: NodeRef, arg: NodeRef)
| Delayed of (expr: NodeRef)
// d creates without evaluating arg
| Character of (byte: uint8)
// .x and ?x
| Continuation of (k: ContRef)
// c captures K
datatype heap_error =
| InvalidRef of NodeRef
| OutOfMemory of { used: size_t, cap: size_t }
| GenerationMismatch of { expected: uint32, found: uint32 }`}),m("div",{className:"space-y-4",children:[m("div",{className:"border border-[var(--border)] bg-[var(--surface)] p-5",children:[c("div",{className:"text-[11px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Slot-map layout"}),c("div",{className:"mt-4 space-y-3 text-[12px]",children:[["Slot","index + gen + occupied? + payload"],["Ref","(slot: u32, gen: u32) — 8 bytes, copyable"],["Alloc","find free slot, bump gen, return ref"],["Free","gen++, mark free, zero payload (H4)"],["Lookup","check allocated && gen match else Error"]].map(([n,r])=>m("div",{className:"flex justify-between border-t border-[var(--border)] pt-2.5 first:border-0 first:pt-0",children:[c("span",{className:"text-[var(--text-faint)]",children:n}),c("span",{className:"text-[var(--text-muted)]",children:r})]},n))})]}),m("div",{className:"border border-[var(--border)] bg-[var(--surface)] p-5",children:[c("div",{className:"text-[11px] tracking-[0.12em] uppercase text-[var(--text-faint)]",children:"Capacity"}),c("div",{className:"mt-3 text-[13px] leading-[1.6] text-[var(--text-muted)]",children:"Initial: fixed 1M nodes (configurable via limits.dats). OutOfMemory returns heap snapshot + trace, not panic. Future mark-sweep preserves H1-H5."})]})]})]})]}),m("section",{id:"continuation",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 04"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Continuation frames"}),c("p",{className:"mt-3 max-w-[640px] text-[13px] leading-[1.7] text-[var(--text-muted)]",children:"Explicit encoding of pending work. No unbounded host recursion. Evaluation order frozen in language-semantics.md before implementation."}),m("div",{className:"mt-8 grid gap-6 md:grid-cols-[1.2fr_0.8fr]",children:[c(sn,{label:"stack.sats — frames",code:`datatype Frame =
| EvaluateArgument of (arg: NodeRef, fun: NodeRef)
// need to eval arg first (strict) then apply
| ApplyFunction of (fun: NodeRef)
// C is arg value, apply fun to it
| ApplyPrimitive of (prim: char, args: List(NodeRef))
// accumulated args for s/k etc.
| ResumeAfterInput of (dest: NodeRef, k: ContRef)
// ?x suspends until byte available
| ResumeAfterOutput of (dest: NodeRef, ch: char)
// .x emits event then continues
abst@ype ContStack = List(Frame)
// push/pop preserve integrity (stack.sats)
// depth limited by fuel + heap capacity, not host stack`}),m("div",{className:"border border-[var(--border)] bg-[var(--surface)] p-6",children:[c("div",{className:"text-[11px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Evaluation order (frozen)"}),m("div",{className:"mt-4 space-y-3 text-[12px] leading-[1.7] text-[var(--text-muted)]",children:[m("div",{children:[c("span",{className:"text-[var(--text)]",children:"1. App `xy:"})," push EvaluateArgument(y,x), eval x → ApplyFunction(y) → apply"]}),m("div",{children:[c("span",{className:"text-[var(--text)]",children:"2. Delay `d:"})," create Delayed(y) node, do NOT push eval for y. Force only when function position requires value."]}),m("div",{children:[c("span",{className:"text-[var(--text)]",children:"3. Output .x:"})," emit event to O, decrement F, push ResumeAfterOutput, continue."]}),m("div",{children:[c("span",{className:"text-[var(--text)]",children:"4. Call/cc c:"})," capture current K as Continuation node in H; applying it restores K."]}),c("div",{className:"mt-4 border-t border-[var(--border)] pt-4 text-[11px]",children:"Tested by AT-05, AT-06. Order documented in spec/language-semantics.md §3.2"})]})]})]})]}),m("section",{id:"step",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 05"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Step interface"}),m("div",{className:"mt-8 grid gap-6 md:grid-cols-2",children:[c(sn,{label:"transition.dats",code:`fun step(state: MachineState): StepResult =
if state.Q != Running then
Error(InvalidStepInTerminalState, state)
else if state.F == 0 then
Halt(state with Q = OutOfFuel{consumed = total})
else
case state.C of
| App(f,a) => Continue(eval_app(f,a, state))
| Prim(p) => Continue(apply_prim(p, state))
| Delayed(e) when forced => Continue(force(e, state))
| _ => Halt(state)
and StepResult =
| Continue of (MachineState)
(* at most one defined transition, F-1, valid Σ' *)
| Halt of (MachineState)
(* Q = Halted | OutOfFuel | OutOfMemory *)
| Error of (MachineError, MachineState)
(* Q = Failed(err), trace preserved *)
(* Preservation: if step Σ = Continue Σ' then
Σ valid ∧ Σ' valid ∧ I1-I8 hold *)`}),m("div",{className:"space-y-4",children:[m("div",{className:"border border-[var(--border)] bg-[var(--surface)] p-6",children:[c("div",{className:"text-[11px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Contract"}),m("ul",{className:"mt-4 space-y-3 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:[c("li",{children:"• Each call performs ≤1 defined transition (AT-09)"}),c("li",{children:"• Returns explicit terminal status, never null/bool"}),c("li",{children:"• Enables stepping, tracing, replay, invariant checks"}),c("li",{children:"• Fuel and output ordering are observable effects"})]})]}),m("div",{className:"border border-[var(--border)] bg-[var(--code-bg)] p-5",children:[c("div",{className:"text-[11px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Execution loop"}),c("pre",{className:"mt-3 text-[12px] leading-[1.7] text-[#c8c8c8]",children:`fun run(state, max_steps):
loop i < max_steps:
match step(state) with
| Continue(s') => state = s'
| Halt(s') => return (s'.O, Halted)
| Error(e,s') => return (s'.O, Failed(e))
return OutOfFuel`})]})]})]})]}),m("section",{id:"modules",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 06"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Module contracts"}),c("div",{className:"mt-8 overflow-x-auto border border-[var(--border)]",children:m("table",{className:"w-full min-w-[760px] border-collapse text-left",children:[c("thead",{children:m("tr",{className:"border-b border-[var(--border)] bg-[var(--surface)] text-[11px] tracking-[0.12em] uppercase text-[var(--text-faint)]",children:[c("th",{className:"px-5 py-3 font-normal",children:"Module"}),c("th",{className:"px-5 py-3 font-normal",children:"Responsibility"}),c("th",{className:"px-5 py-3 font-normal",children:"Required guarantee"})]})}),c("tbody",{className:"text-[12px] leading-[1.6]",children:km.map((n)=>m("tr",{className:"border-b border-[var(--border)] last:border-0 hover:bg-[var(--surface)]/50",children:[c("td",{className:"px-5 py-3 font-mono text-[var(--text)]",children:n.module}),c("td",{className:"px-5 py-3 text-[var(--text-muted)]",children:n.responsibility}),c("td",{className:"px-5 py-3 text-[var(--text-faint)]",children:n.guarantee})]},n.module))})]})}),m("div",{className:"mt-6 grid gap-px border border-[var(--border)] bg-[var(--border)] md:grid-cols-3",children:[m("div",{className:"bg-[var(--surface)] p-4",children:[c("div",{className:"text-[10px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Dependency rule"}),c("div",{className:"mt-2 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:"Semantic rules (ast, primitives, transition) must not depend on heap representation details. Heap impl can change without changing language."})]}),m("div",{className:"bg-[var(--surface)] p-4",children:[c("div",{className:"text-[10px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Interface files"}),c("div",{className:"mt-2 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:".sats declare interfaces, .dats provide impl. Parser returns Result(AST, ParseError with span), never throws."})]}),m("div",{className:"bg-[var(--surface)] p-4",children:[c("div",{className:"text-[10px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"File tree"}),m("div",{className:"mt-2 font-mono text-[11px] leading-[1.6] text-[var(--text-faint)]",children:["src/syntax/ token, lexer, ast, parser",c("br",{}),"src/machine/ value, heap, stack, state, transition, run",c("br",{}),"src/runtime/ primitives, input, output, limits"]})]})]})]}),m("section",{id:"invariants",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 07"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Invariants"}),c("p",{className:"mt-3 max-w-[640px] text-[13px] leading-[1.7] text-[var(--text-muted)]",children:"Distinction: [ATS] statically enforced, [RUNTIME] dynamic assert at boundaries, [TESTED] property test / differential."}),m("div",{className:"mt-8 space-y-10",children:[m("div",{children:[m("div",{className:"flex items-center gap-3",children:[c("span",{className:"text-[12px] tracking-[0.16em] uppercase text-[var(--text)]",children:"State invariants I1–I8"}),c("span",{className:"h-px flex-1 bg-[var(--border)]"})]}),c("div",{className:"mt-4 grid gap-px border border-[var(--border)] bg-[var(--border)]",children:ea.I.map((n)=>m("div",{className:"bg-[var(--surface)] p-4 md:flex md:items-start md:gap-6 md:p-5",children:[m("div",{className:"flex items-center gap-3 md:w-[160px] md:shrink-0",children:[c("span",{className:"font-mono text-[12px] text-[var(--text)]",children:n.id}),c(cn,{type:n.label})]}),m("div",{className:"mt-2 min-w-0 flex-1 md:mt-0",children:[c("div",{className:"text-[12px] text-[var(--text)]",children:n.title}),c("div",{className:"mt-1 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:n.desc})]})]},n.id))})]}),m("div",{children:[m("div",{className:"flex items-center gap-3",children:[c("span",{className:"text-[12px] tracking-[0.16em] uppercase text-[var(--text)]",children:"Heap invariants H1–H5"}),c("span",{className:"h-px flex-1 bg-[var(--border)]"})]}),c("div",{className:"mt-4 grid gap-px border border-[var(--border)] bg-[var(--border)]",children:ea.H.map((n)=>m("div",{className:"bg-[var(--surface)] p-4 md:flex md:items-start md:gap-6 md:p-5",children:[m("div",{className:"flex items-center gap-3 md:w-[160px] md:shrink-0",children:[c("span",{className:"font-mono text-[12px] text-[var(--text)]",children:n.id}),c(cn,{type:n.label})]}),m("div",{className:"mt-2 min-w-0 flex-1 md:mt-0",children:[c("div",{className:"text-[12px] text-[var(--text)]",children:n.title}),c("div",{className:"mt-1 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:n.desc})]})]},n.id))})]}),m("div",{children:[m("div",{className:"flex items-center gap-3",children:[c("span",{className:"text-[12px] tracking-[0.16em] uppercase text-[var(--text)]",children:"Resource & replay R1–R3"}),c("span",{className:"h-px flex-1 bg-[var(--border)]"})]}),c("div",{className:"mt-4 grid gap-px border border-[var(--border)] bg-[var(--border)]",children:ea.R.map((n)=>m("div",{className:"bg-[var(--surface)] p-4 md:flex md:items-start md:gap-6 md:p-5",children:[m("div",{className:"flex items-center gap-3 md:w-[160px] md:shrink-0",children:[c("span",{className:"font-mono text-[12px] text-[var(--text)]",children:n.id}),c(cn,{type:n.label})]}),m("div",{className:"mt-2 min-w-0 flex-1 md:mt-0",children:[c("div",{className:"text-[12px] text-[var(--text)]",children:n.title}),c("div",{className:"mt-1 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:n.desc})]})]},n.id))})]})]})]}),m("section",{id:"build",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 08"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Build sequence"}),c("div",{className:"mt-8 space-y-px border border-[var(--border)] bg-[var(--border)]",children:Sm.map((n,r)=>m("div",{className:"bg-[var(--surface)] p-6 md:flex md:items-start md:gap-8 md:p-7",children:[m("div",{className:"flex items-center gap-4 md:w-[200px] md:shrink-0",children:[c("div",{className:"flex h-7 w-7 items-center justify-center border border-[var(--border-strong)] bg-[var(--surface-2)] text-[11px] text-[var(--text-muted)]",children:r}),c("div",{className:"text-[12px] tracking-[0.08em] uppercase text-[var(--text-faint)]",children:n.phase})]}),m("div",{className:"mt-4 min-w-0 flex-1 md:mt-0",children:[c("div",{className:"text-[14px] text-[var(--text)]",children:n.title}),m("div",{className:"mt-3 grid gap-4 md:grid-cols-2",children:[m("div",{children:[c("div",{className:"text-[10px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Deliverable"}),c("div",{className:"mt-1 font-mono text-[12px] text-[var(--text-muted)]",children:n.deliverable})]}),m("div",{children:[c("div",{className:"text-[10px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Exit criterion"}),c("div",{className:"mt-1 text-[12px] leading-[1.6] text-[var(--text-muted)]",children:n.exit})]})]})]})]},n.phase))})]}),m("section",{id:"acceptance",className:"border-b border-[var(--border)] px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 09"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"Acceptance test matrix"}),c("p",{className:"mt-3 max-w-[640px] text-[13px] leading-[1.7] text-[var(--text-muted)]",children:"Minimum release gate. Tests generated from frozen semantic spec, not hand-written assumptions about evaluation order."}),c("div",{className:"mt-8 overflow-x-auto border border-[var(--border)]",children:m("table",{className:"w-full min-w-[800px] border-collapse text-left",children:[c("thead",{children:m("tr",{className:"border-b border-[var(--border)] bg-[var(--surface)] text-[11px] tracking-[0.12em] uppercase text-[var(--text-faint)]",children:[c("th",{className:"px-5 py-3 font-normal",children:"Test"}),c("th",{className:"px-5 py-3 font-normal",children:"Input or operation"}),c("th",{className:"px-5 py-3 font-normal",children:"Expected result"}),c("th",{className:"px-5 py-3 font-normal",children:"Gate"})]})}),c("tbody",{className:"text-[12px] leading-[1.6]",children:Nm.map((n)=>m("tr",{className:"border-b border-[var(--border)] last:border-0 hover:bg-[var(--surface)]/50",children:[c("td",{className:"px-5 py-3 font-mono text-[var(--text)]",children:n.id}),c("td",{className:"px-5 py-3 text-[var(--text-muted)]",children:n.input}),c("td",{className:"px-5 py-3 text-[var(--text-faint)]",children:n.expected}),c("td",{className:"px-5 py-3 text-[10px] tracking-[0.08em] uppercase text-[var(--text-faint)]",children:n.id<="AT-02"?"A":n.id<="AT-08"?"B":n.id<="AT-11"?"C":n.id<="AT-12"?"D":"E"})]},n.id))})]})})]}),m("section",{id:"ats",className:"px-6 py-12 md:px-10 md:py-16",children:[c("div",{className:"text-[11px] tracking-[0.18em] uppercase text-[var(--text-faint)]",children:"Section 10"}),c("h2",{className:"mt-3 text-[22px] leading-[1.15] md:text-[28px]",children:"ATS skeleton"}),c("p",{className:"mt-3 max-w-[640px] text-[13px] leading-[1.7] text-[var(--text-muted)]",children:"Interfaces in .sats, implementations in .dats. ATS enforces validity; runtime asserts preservation. Snippets are architectural sketches."}),m("div",{className:"mt-8 space-y-6",children:[c(sn,{label:"src/machine/heap.sats",code:`(* heap.sats — fixed-capacity slot-map with generation *)
abst@ype NodeRef = (slot: uint32, gen: uint32)
abst@ype heap (n: int)
datatype Node =
| Primitive of char
| Application of (NodeRef, NodeRef)
| Delayed of NodeRef
| Character of uint8
| Continuation of ContRef
fun heap_create(cap: size_t): [n:nat] heap(n)
fun heap_alloc{n:nat}
(h: &heap(n) >> heap(n'), node: Node)
: Result(NodeRef, heap_error)
fun heap_get{n:nat}
(h: &heap(n), r: NodeRef)
: Result(Node, heap_error)
fun heap_free{n:nat}
(h: &heap(n) >> heap(n-1), r: NodeRef)
: Result(void, heap_error)
(* H1: gen match, H5: accounting exact — ATS proofs *)`}),c(sn,{label:"src/machine/state.sats",code:`(* state.sats — Σ = <C,K,H,I,O,F,Q> *)
abst@ype MachineState
abst@ype ContStack
datatype status =
| Running
| Halted of value
| Failed of (errcode, span)
| OutOfFuel of { consumed: uint64 }
| OutOfMemory of { used: uint64, cap: uint64 }
fun state_make
(c: NodeRef, k: ContStack, h: heap,
input: Input, fuel: uint64): MachineState
fun state_valid(s: MachineState): bool
(* I1: well-formedness, I2: ref validity, I4: monotonicity *)
fun state_fuel(s: MachineState): uint64
fun state_status(s: MachineState): status
fun state_output(s: MachineState): OutputTrace
(* preservation: valid entry → valid exit or documented error *)`}),c(sn,{label:"src/machine/transition.dats",code:`(* transition.dats — one defined transition per call *)
implement step(state) =
let
val q = state_status(state)
val f = state_fuel(state)
in
if q != Running then
Error(InvalidStepInTerminal, state)
else if f = 0 then
let val s1 = state with Q = OutOfFuel{consumed=total_fuel(state)} in Halt(s1) end
else
case heap_get(state.heap, state.C) of
| Ok(Primitive('s')) => step_s_combinator(state) // -> Continue
| Ok(Primitive('k')) => step_k_combinator(state)
| Ok(Primitive('i')) => step_i_combinator(state) // AT-03
| Ok(Primitive('d')) => step_delayed(state) // AT-05: no eval arg
| Ok(Primitive('.')) => step_output(state) // AT-06
| Ok(Primitive('?')) => step_input(state)
| Ok(Application(f,a)) => step_app(f,a,state) // pushes EvaluateArgument
| Ok(Delayed(e)) when is_forced(state.K) => step_force(e,state)
| Ok(Continuation(k)) => step_apply_cont(k,state) // c
| Error(e) => Error(e, state) // I2: invalid ref → Failed, not UB
end
(* AT-09: at most one transition, F-1, R3 trace preservation *)`})]}),c("div",{className:"mt-12 border-t border-[var(--border)] pt-8",children:m("div",{className:"flex flex-col gap-6 md:flex-row md:items-start md:justify-between",children:[m("div",{className:"max-w-[520px]",children:[c("div",{className:"text-[11px] tracking-[0.16em] uppercase text-[var(--text-faint)]",children:"Final architectural recommendation"}),c("div",{className:"mt-3 text-[13px] leading-[1.7] text-[var(--text-muted)]",children:"Build the heap first, the explicit abstract machine second, and the semantic correspondence layer third. Keep the reference evaluator small and independent. Do not introduce graph reduction, GC, or optimization until base machine has stable transition rules and passing conformance tests. The most important artifact is not the interpreter itself but the combination of precise semantics, explicit state, memory invariants, and reproducible evidence."})]}),m("div",{className:"border border-[var(--border)] bg-[var(--surface)] p-4 md:w-[300px]",children:[c("div",{className:"text-[10px] tracking-[0.14em] uppercase text-[var(--text-faint)]",children:"Verification boundary summary"}),m("div",{className:"mt-3 space-y-2 text-[11px] leading-[1.6] text-[var(--text-muted)]",children:[m("div",{className:"flex gap-2",children:[c(cn,{type:"ATS"}),c("span",{children:"AST validity, NodeRef abstraction, heap API Result"})]}),m("div",{className:"flex gap-2",children:[c(cn,{type:"RUNTIME"}),c("span",{children:"I1-I8, H2-H3, R1 dynamic asserts at transition boundaries"})]}),m("div",{className:"flex gap-2",children:[c(cn,{type:"TESTED"}),c("span",{children:"AT-01..14, differential corpus, stress + replay"})]}),c("div",{className:"mt-3 border-t border-[var(--border)] pt-3 text-[var(--text-faint)]",children:"Future: Coq/ATS proofs for SKI correspondence, preservation, fuel termination."})]})]})]})})]}),c("footer",{className:"border-t border-[var(--border)] px-6 py-8 md:px-10",children:m("div",{className:"flex flex-col gap-3 text-[11px] leading-[1.6] text-[var(--text-faint)] md:flex-row md:justify-between",children:[c("span",{children:"unlambda-ats v0.4.1-draft · spec/ · language-semantics.md, abstract-machine.md, memory-model.md, invariants.md"}),c("span",{children:"© 1999-2025 Unlambda 2.0.0 dialect · ATS2 runtime architecture — formal reasoning target"})]})})]})]})]})}Qc.createRoot(document.getElementById("root")).render(c(Bc.default.StrictMode,{children:c(ta,{})}));
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