SML (Stack-Map-Loglang) 📐

English | 中文

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SML (English)

An experimental formal semantic deduction engine and logical language (Loglang) based on an 8-stack, 5-mapping, 1-counter concatenative state machine.

Note

STATUS: SPECIFICATION & WORKING PROTOTYPE (v0.99)
SML eliminates the rigid fixed-place structures (x₁, x₂, ...) and scope-leakage issues common in loglangs like Lojban. It natively supports First-Order Restricted Quantification, Universal Event Reification (e ∈ Ω), Linear Relative Clauses, Clausal Event Nominalization, Higher-Order Modifier Distribution, and Dynamic Donkey-Sentence Anaphora purely via linear stack reductions and associative maps—completely free of syntactic tree overhead.

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🚀 Overview

Traditional formal semantics (e.g., Montague Grammar) relies heavily on compositional syntax trees and higher-order lambda-calculus λ-reductions. Similarly, classical loglangs (such as Lojban) encode predicate argument places as rigid, predetermined tuple slots (x₁, x₂, ..., xₙ), requiring elidable terminators, conversion particles, or awkward relative clauses for local modifications.

SML (Stack-Map-Loglang) replaces syntactic trees and fixed place structures with an 8-Stack + 5-Mapping + 1-Counter linear automaton.

By unifying all nominal concepts into unary sets (:S), reifying all actions into first-class events (e ∈ Ω), and decomposing all predicates into Neo-Davidsonian binary relations (:R), SML establishes a strict algebraic conservation law: every relational modifier R consumes exactly one entity S (ΔR = ΔS). Combined with an integrated Relation Stack (RL), a dedicated Clause Stack (CL), and an automatic Debt Counter (Count), SML enables seamless attachment of arbitrary adjuncts, nested relative clauses, and nominalized propositions without closing delimiters or cross-clause scope leakage.

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✨ Key Features & Concepts (v0.99)

• 8-Stack + 5-Mapping + 1-Counter State Machine:
  Decouples variable generation, active polarity cursors, quantifier scopes, modifier delays, relational frames, relative clause traces, nominal domain constraints, and syntactic debts into specialized linear stacks and key-value maps.
• Universal Event Reification (e ∈ Ω) & Zero Fixed Places:
  Actions are unified as first-class entities in the universe of events (Ω). Thematic roles (Subject:R, Object:R, Theme:R, etc.) are attached as universal binary relations, freeing users from memorizing predicate-specific argument indices.
• Linear Relative Clauses without Syntax Trees (CL & That):
  Relative clauses (定语从句) are resolved linearly using the Clause Stack (CL) and the That / Clause operators. Host entity variables are safely passed across scope boundaries and substituted into relative clauses without syntactic tree traversals or variable capture.
• Clausal Event Nominalization (Noun Operator):
  Complete propositions and complex event descriptions can be dynamically reified into first-class entity variables typed as Ω in Smap, allowing entire clauses to serve directly as subjects, objects, or hosts for adjectival modification.
• Terminator-Free Modifiers via ΔR = ΔS Conservation:
  Every relational link (Add) increments Count (logging open syntactic debt); core entities (Deter) decrement Count. This arithmetic balancing allows ad-hoc prepositional and adjectival attachments without closing delimiters (ku, vau, etc.).
• Dual-Track Negation (Propositional vs. Constituent):
  • Whole-Proposition Negation (Negation): Inverts entire closed relational propositions at the outer matrix level.
  • Constituent / Thematic Negation (Not + Judge): Flips truth polarity on the active variable cursor (CM), negating specific relational edges without scope drift.
• Higher-Order Modifier Calculus & Distributive Exchange (Exchange):
  • Adjectives (Modify): Dynamically restrict nominal domains in Fmap.
  • Adverbs (For / Modify): Recursively scale degree dimensions and event properties.
  • Composition & Combinators (Combine / Cancel): Merges modifiers via higher-order λ-abstractions.
  • Distributive Law (Exchange): Realizes A → (B ∧ C) ≡ (A → B) ∧ (A → C), distributing a single adverb across coordinate adjectives.
• In-Situ Morphological Derivation (:F Transform Words):
  Directly transforms base set categories at the map level (e.g., "Old$" applied to Person:S yields Old_Person), providing native morphological derivation without external preprocessors.
• Restricted Quantifier Construction (build Primitive):
  Quantifiers are constructed on demand via: $$\text{build}(Q, a, b, S, F, D) \triangleq Q a \in {b \in S \mid F} (D)$$ This cleanly isolates quantifier force (Qmap), base domain (Smap), and dynamic filter restrictions (Fmap).
• Dynamic Anaphora & Donkey Sentences:
  Registers Upload and Download interact with the environment map (Emap), allowing multi-clause pronouns and donkey-sentence coreferences to resolve cleanly.
• Emergent Surface Syntax (Chunking):
  While the underlying engine executes right-to-left via LIFO stacks, the surface grammar follows a natural VSO Head-Initial + Incremental Post-Modification template: $$\mathbf{Chunk} = [\text{Entity:S}] \ + \ [\text{Not}] \ + \ [\text{Quantifier:Q}] \ + \ [\text{Modifiers}\dots]$$

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🏗️ The 8-Stack 5-Map 1-Counter Model

$$\text{State} = \langle \mathbf{IP}, \mathbf{VR}, \mathbf{CM}, \mathbf{QN}, \mathbf{MD}, \mathbf{RL}, \mathbf{CL}, \mathbf{OP}, \text{Count}, \mathbf{Emap}, \mathbf{Qmap}, \mathbf{Smap}, \mathbf{Fmap}, \mathbf{Amap} \rangle$$

1. The 8 Stacks (Right end is Top)

Stack	Identifier	Preset / Initial Top	Description
Input Stack	IP	(User tokens)	Instruction queue holding tokens, macros, and operators awaiting reduction.
Var Stack	VR	v1 v2 v3 ... (Infinite)	Infinite stream of fresh, mutually distinct variables.
Component Stack	CM	Empty	Active component cursor stack for truth polarities and active variables (True, False, v_i).
Quant Stack	QN	None	Active entity queue awaiting quantifier closure (Build/End). Supports arbitrary permutation (i_n, ..., i_1).
Modifier Stack	MD	Stop	Specialized stack for higher-order modifiers, adjectival/adverbial scopes, and delayed composition.
Relation Stack	RL	Deter	Manages open thematic roles and predicate barriers (Deter, Absorb, Join).
Clause Stack	CL	Empty	Trace memory storing host entity variables for relative clause binding (That/Clause).
Output Stack	OP	Empty	Working memory accumulating derived logical propositions, relations, and AST subtrees.

2. The Syntactic Debt Counter

• Count (Integer, initial 0): Tracks unfulfilled relational obligations. Relation macros invoke Add (Count++), while entity macros invoke Deter (Count-- if active, else push Deter barrier to RL). This eliminates the need for closing brackets around modifiers.

3. The 5 Associative Mappings (Keys are Variables)

Mapping	Name	Default / Miss Behavior	Purpose
Emap	Environment Map	Throws Error	Stores dynamic variable registers for coreference (Upload/Download).
Qmap	Quantifier Map	Returns ∃ (Exist)	Maps bound variables to quantifier force (∀, ∃).
Smap	Set Map	Throws Error	Maps domain variables to base set categories (e.g., Farmer, Book, Ω).
Fmap	Formula/Filter Map	Throws Error	Accumulates domain restrictions, relative clause formulas, and degree filters.
Amap	Association Map	Throws Error	Pairs quantified instance variables (a) with domain restriction variables (b).

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💡 Showcase Examples (v0.99 Verified)

1. Relative Clauses & Multi-Constraint Nominal Restriction

"The old cat that was not given to the child by the farmer and does not like catnip eats fish."

Input:
End Eat_Macro Binary_Identity_Perm_Clause_Closing_Macro Negation Like_Macro That Ternary_Identity_Perm_Clause_Closing_Macro Negation Give_Macro Farmer_Macro Child_Macro That Cat_Macro Old_Macro Catnip_Macro Fish_Macro

Evaluated Logical Output:
v26∈Ω ∧ (Exist v1∈Fish (Exist v6∈{v7∈Cat |
    v13∈Ω ∧ (Exist v5∈Large_Age (Exist v11∈Age_Is Subject(v11,v7) ∧ Object(v11,v5) ∧ Predicate(v13,v11))) ∧
    v20∈Ω ∧ (Exist v14∈Child (Exist v16∈Farmer (Exist v18∈Give Not(Subject(v18,v16) ∧ Object(v18,v14) ∧ Theme(v18,v7) ∧ Predicate(v20,v18))))) ∧
    v23∈Ω ∧ (Exist v3∈Catnip (Exist v21∈Like Not(Subject(v21,v7) ∧ Object(v21,v3) ∧ Predicate(v23,v21))))}
    (Exist v24∈Eat Subject(v24,v6) ∧ Object(v24,v1) ∧ Predicate(v26,v24)))) v26

Note: That pushes the cat variable v7 onto CL, allowing multiple independent relative clauses to safely capture it as their theme/subject.

2. Clausal Event Nominalization & Propositional Objects

"There exists an event where the predicate is not discover, the subject is not the child, and the object is not the interesting event of the cat not liking catnip."

Input:
End Discover_Macro Not Child_Macro Not Ternary_Identity_Perm_Nominalization_Closing_Macro Not Interesting_Macro Negation Like_Macro Cat_Macro Catnip_Macro

Evaluated Logical Output:
v20∈Ω ∧ (Exist v7∈{v9∈Ω |
    (Exist v1∈Catnip (Exist v3∈Cat (Exist v5∈Like Not(Subject(v5,v3) ∧ Object(v5,v1) ∧ Predicate(v9,v5))))) ∧
    v15∈Ω ∧ (Exist v8∈Large_Interest (Exist v13∈Interest_Is Subject(v13,v9) ∧ Object(v13,v8) ∧ Predicate(v15,v13)))}
    (Exist v16∈Child (Exist v18∈Discover Not Subject(v18,v16) ∧ Not Object(v18,v7) ∧ Not Predicate(v20,v18)))) v20

Note: The clausal proposition "the cat does not like catnip" is nominalized into an entity v7 of type Ω, modified by the adjective "interesting", and consumed as the object of "discover".

3. Higher-Order Adverb Distribution across Coordinate Adjectives

"An A-and-very-ly heavy, B-and-very-ly tall person."

Input:
Person:S Exchange Very_Macro Tall_Macro Adv_B_Macro Heavy_Macro Adv_A_Macro

Evaluated Domain Filter (Fmap for v26):
And_consequent(v39,v38) ∧ And_antecedent(v39,v32) ∧
v38∈Ω ∧ (Exist v2∈Large_Weight (Exist v36∈Weight_Is Subject(v36,v26) ∧ Object(v36,v2) ∧ Predicate(v38,v36))) ∧
v32∈Ω ∧ (Exist v10∈Large_Height (Exist v30∈Height_Is Subject(v30,v26) ∧ Object(v30,v10) ∧ Predicate(v32,v30)))

4. Localized Spatiotemporal Scoping & Fine-Grained Role Negation

"The red team that was not in the west yesterday attacks the blue team that is not in the east today."

Input:
End Attack_Macro RedTeam_Macro Yesterday_Macro Not At_Macro West_Macro Not At_Macro BlueTeam_Macro Today_Macro Not At_Macro East_Macro Not At_Macro

Evaluated Logical Output:
v15∈Ω ∧ (Exist v1∈East (Exist v3∈Today (Exist v5∈BlueTeam (Exist v7∈West (Exist v9∈Yesterday (Exist v11∈RedTeam (Exist v13∈Attack
    Not At(v5,v3) ∧ Not At(v5,v1) ∧
    Not At(v11,v9) ∧ Not At(v11,v7) ∧
    Subject(v13,v11) ∧ Object(v13,v5) ∧ Predicate(v15,v13)))))))) v15

5. Dynamic Anaphora & Donkey Sentence with Negation

"If a farmer does not give a child a book, the child will not read it."

Input:
End Then:C Negation Read_Macro Exist Download child Download book Negation Give_Macro Exist Farmer_Macro All Upload child Child_Macro All Upload book Book_Macro All

Evaluated Logical Output:
v13∈Ω ∧ (All v1∈Book (All v3∈Child (All v5∈Farmer (Exist v7∈Give (Exist v10∈Read
    Then_consequent(v13,v12) ∧ Then_antecedent(v13,v9) ∧
    Not(Subject(v10,v3) ∧ Object(v10,v1) ∧ Predicate(v12,v10)) ∧
    Not(Subject(v7,v5) ∧ Object(v7,v3) ∧ Theme(v7,v1) ∧ Predicate(v9,v7))))))) v13

6. In-Situ Lexical Derivation

"Old person (Elder)."

Input:
"Old$" Person:S

Evaluated State:
Smap (Sets): [("v2", "Old_Person")]

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💻 REPL Commands

• :r — Reset automaton state, stacks, and maps (macro definitions are preserved).
• :q — Exit the deduction engine.
• // <expr> — Step-by-step trace mode (prints state transitions across all 8 stacks and 5 maps).
• define <Name> := <Expr> — Define a reusable macro expansion.

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📝 Design & Architecture Notes

The theoretical foundations, formal semantic rules, 8-Stack 5-Map 1-Counter automaton architecture, event reification algebra, and relational reduction calculus of SML were conceived and mathematically designed entirely by the author.

The reference implementation was generated with AI assistance based strictly on the author's formal reduction rules, serving as an executable proof of the deduction rules and empirical verification of zero-leakage scoping.

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SML (中文)

基于“八栈五映射一计数器”（8-Stack 5-Map 1-Counter）串接式状态机的形式语义推导引擎与逻辑语言（Loglang）原型。

Note

当前状态：形式规范与可用原型 (v0.99)
SML 彻底攻克了传统逻辑语（如 Lojban）饱受诟病的固定位点结构（x₁, x₂, ... 位点记忆负担）与修饰语作用域全局泄漏难题。系统无需句法树，仅依靠线性多栈状态转移、代数计数平衡与关联映射，即可完备支持一阶受限量词、全事件集合本体化（e ∈ Ω）、定语从句（关系从句）线性绑定、主宾语从句（事件名词化）、高阶修饰分配递归、词法派生与动态驴子句照应。

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🚀 简介

经典形式语义学（如蒙太格语法）高度依赖复杂的句法语义树递归与高阶 λ 规约；而传统逻辑语（如 Lojban）则将多元谓词绑定为固定的位点结构（如 x₁ 到 x₅），导致实词记忆负担极重，且为单个论元添加局部时空修饰或嵌套定语从句时语法繁琐。

SML (Stack-Map-Loglang) 提出了全新的八栈五映射一计数器（8-Stack + 5-Map + 1-Counter）自动机模型。

系统将全语言的概念统一为单目集合（:S），将所有动作统一实体化为事件集合（Ω）中的一阶个体（e ∈ Ω），并将所有多元谓词拆解为新大卫森二元关系（:R）。由此建立了一条严密的数学守恒律：每一个二元修饰关系 R 在拓扑上必然且唯一地要求消费一个实体集合 S（ΔR = ΔS）。配合关系栈（RL）、从句栈（CL）与债务计数器（Count），SML 允许自由挂载任意时空修饰、定语从句与主宾语从句，既无需手动书写闭合括号/终止子（Terminator-Free），也彻底杜绝了跨层级作用域污染。

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✨ 核心概念与特性 (v0.99)

• 八栈五映射一计数器（8-Stack 5-Map 1-Counter）架构:
  将变量源、极性游标、量词闭包、输出命题、修饰语计算、关系格框、从句穿透记忆以及修饰债务完全解耦。
• 全事件集合本体化（e ∈ Ω）与消灭固定位点:
  事件作为基底集合 Ω 中的一阶个体，与普通实体具有同等数学地位。题元角色（主语:R, 宾语:R, 传递物:R 等）作为全局通用的二元关系自由挂载，使用者无需记忆谓词特有的位点列表。
• 无需句法树的定语从句线性求解（CL 与 That）:
  通过从句栈 CL 与 That / Clause 算子，被修饰名词的变量可在栈间穿透，并在从句推导完成后通过 Substitute 精准代入从句的“空缺位（Trace）”，实现零 AST 开销的定语从句绑定。
• 事件名词化与从句充当论元（Noun 算子）:
  完整命题（如“猫不喜欢猫薄荷”）可通过 Noun 算子直接降维打包为类型为 Ω 的一阶实体变量，直接充当主句的主语、宾语，或接受形容词修饰。
• 零终止子的修饰吸收律（ΔR = ΔS 计数平衡）:
  任何关系修饰（Add）都会让 Count++（登记语法债务）；而核心实体宏的 Deter 会在有债务时代替压栈执行 Count--（结清债务），彻底杜绝 Lojban 式的冗余闭合词（如 ku, vau）。
• 双轨否定系统（命题全局否定 vs. 题元成分否定）:
  • 命题全局否定（Negation）: 直接对已闭合的关系命题外层取反。
  • 题元成分否定（Not + Judge）: 通过 CM 游标翻转局部极性，精准实现具体关系边（如 ¬在(x, y)）的否定，作用域绝不漂移。
• 高阶修饰语演算与分配律（Exchange）:
  • 形容词（Modify）: 动态收缩名词在 Fmap 中的受限集合内涵。
  • 副词（For / Modify）: 对程度标尺与事件属性进行高阶函数抽象与连续修饰。
  • 合并与组合子（Combine / Cancel）: 借助高阶 λ-演算合并多个修饰语。
  • 分配律（Exchange）: 完美实现 A → (B ∧ C) ≡ (A → B) ∧ (A → C)，让单个副词自动向并列形容词分支分配。
• 原位词法派生（:F 变换词）:
  支持直接在映射层变换基底集合（如 "老$" 作用于 人:S 得到 老人），使语言原生具备词根派生能力。
• 受限量词构建原语 (build Primitive):
  统一使用受限量词模板进行语义闭包： $$\text{build}(Q, a, b, S, F, D) \triangleq Q a \in {b \in S \mid F} (D)$$ 解耦量词力量（Qmap）、基底集合（Smap）与修饰过滤式（Fmap）。
• 跨从句动态指代与代词照应:
  通过 Upload 与 Download 指令存取环境映射（Emap），以图（DAG）的形式优雅解决跨子句论元复用与经典驴子句照应。
• 高度模块化的人性表层语法（Chunking）:
  虽然底层是逆向消费的 LIFO 栈式抽象机，但表层语言呈现出极其自然的 VSO 动词前置 + 后置渐进限定 模式： $$\mathbf{Chunk} = [\text{实体宏:S}] \ + \ [\text{Not}] \ + \ [\text{量词:Q}] \ + \ [\text{修饰语/从句}\dots]$$

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🏗️ 八栈五映射一计数器自动机模型

$$\text{State} = \langle \mathbf{IP}, \mathbf{VR}, \mathbf{CM}, \mathbf{QN}, \mathbf{MD}, \mathbf{RL}, \mathbf{CL}, \mathbf{OP}, \text{Count}, \mathbf{Emap}, \mathbf{Qmap}, \mathbf{Smap}, \mathbf{Fmap}, \mathbf{Amap} \rangle$$

1. 八个线性栈（均以右端为栈顶）

栈名称	缩写	预置栈顶	功能说明
输入栈	IP	(用户输入)	待处理的 Token 流、宏指令与操作符队列。
变量栈	VR	v1 v2 v3 ... (无穷)	预置的无穷新鲜变量源。
成分栈	CM	空	当前活跃成分的真值极性与变量游标栈（True, False, v_i）。
量化栈	QN	None	论元变量排队栈，暂存等待参与量词闭包（Build/End）的变量。支持任意置换 (i_n, ..., i_1)。
修饰栈	MD	Stop	专用的修饰语暂存区，维护形容词、副词的作用域与延迟合成。
关系栈	RL	Deter	维护当前未闭合的题元角色与关系定界屏障（Deter, Absorb, Join）。
从句栈	CL	空	专用于关系从句（定语从句）的宿主实体变量追踪栈（That/Clause）。
输出栈	OP	空	逻辑命题工作区，累加推导中的中间关系项与最终逻辑公式。

2. 语法债务计数器

• Count (整数，初值 0): 实时追踪当前悬挂的二元修饰关系债务。遇到关系宏执行 Add（Count++）；遇到实体宏执行 Deter（若 Count > 0 则消费债务 Count--，否则正常压入 Deter 隔离屏障）。

3. 五个关联映射（键均为变量名）

映射表	对应全称	缺省行为 (Lookup Miss)	用途说明
Emap	环境映射 (Environment)	报错 (Error)	记录动态变量别名，用于代词照应（Upload/Download）。
Qmap	量化映射 (Quantifier)	缺省为 ∃ (Exist)	绑定量化变量的量词属性（∀, ∃）。
Smap	集合映射 (Set)	报错 (Error)	记录变量所属的基底类别（如 农夫, 书, Ω）。
Fmap	表达式映射 (Filter)	报错 (Error)	累积形容词收缩条件、定语从句约束与程度过滤器。
Amap	关联变量映射 (Association)	报错 (Error)	将量化实体变量 (a) 与其定义域限制变量 (b) 关联。

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💡 典型例句推导展示 (v0.99 核实)

1. 多重定语从句与复合名词内涵收缩

“不是农夫给小孩的、不喜欢猫薄荷的老猫吃鱼”

输入 (Input):
End 吃宏 二元恒等排列从句结语宏 Negation 喜欢宏 That 三元恒等排列从句结语宏 Negation 给宏 农夫宏 小孩宏 That 猫宏 老的宏 猫薄荷宏 鱼宏

推导逻辑输出 (Output):
v26∈Ω ∧ (Exist v1∈鱼 (Exist v6∈{v7∈猫 |
    v13∈Ω ∧ (Exist v5∈较大的年龄 (Exist v11∈年龄为 主语(v11,v7) ∧ 宾语(v11,v5) ∧ 谓语(v13,v11))) ∧
    v20∈Ω ∧ (Exist v14∈小孩 (Exist v16∈农夫 (Exist v18∈给 Not(主语(v18,v16) ∧ 宾语(v18,v14) ∧ 传递物(v18,v7) ∧ 谓语(v20,v18))))) ∧
    v23∈Ω ∧ (Exist v3∈猫薄荷 (Exist v21∈喜欢 Not(主语(v21,v7) ∧ 宾语(v21,v3) ∧ 谓语(v23,v21))))}
    (Exist v24∈吃 主语(v24,v6) ∧ 宾语(v24,v1) ∧ 谓语(v26,v24)))) v26

注：That 算子将被修饰词“猫”的变量 v7 压入 CL 栈，使两个独立的否定定语从句能够精准将其捕获为传递物与主语。

2. 完整事件名词化（主/宾语从句具象化）

“存在事件，谓语不是发现，主语不是小孩，宾语不是‘猫不喜欢猫薄荷’这件有趣的事”

输入 (Input):
End 发现宏 Not 小孩宏 Not 三元恒等排列名词化结语宏 Not 有趣的宏 Negation 喜欢宏 猫宏 猫薄荷宏

推导逻辑输出 (Output):
v20∈Ω ∧ (Exist v7∈{v9∈Ω |
    (Exist v1∈猫薄荷 (Exist v3∈猫 (Exist v5∈喜欢 Not(主语(v5,v3) ∧ 宾语(v5,v1) ∧ 谓语(v9,v5))))) ∧
    v15∈Ω ∧ (Exist v8∈较大的趣味 (Exist v13∈趣味为 主语(v13,v9) ∧ 宾语(v13,v8) ∧ 谓语(v15,v13)))}
    (Exist v16∈小孩 (Exist v18∈发现 Not 主语(v18,v16) ∧ Not 宾语(v18,v7) ∧ Not 谓语(v20,v18)))) v20

注：命题“猫不喜欢猫薄荷”被 Noun 算子实体化为类型为 Ω 的变量 v7，进而接受形容词“有趣的”修饰，并作为“发现”的宾语。

3. 并列形容词的高阶副词分配律

“A且非常地重的、B且非常地高的人”

输入 (Input):
人:S Exchange 非常的宏 高的宏 B副词宏 重的宏 A副词宏

推导集合内涵输出 (Fmap 对应 v26):
And_consequent(v39,v38) ∧ And_antecedent(v39,v32) ∧
v38∈Ω ∧ (Exist v2∈较大的重量 (Exist v36∈重量为 主语(v36,v26) ∧ 宾语(v36,v2) ∧ 谓语(v38,v36))) ∧
v32∈Ω ∧ (Exist v10∈较大的高度 (Exist v30∈高度为 主语(v30,v26) ∧ 宾语(v30,v10) ∧ 谓语(v32,v30)))

4. 局部时空精准界定与细粒度题元否定

“不在昨天的不在西边的红队攻击不在今天的不在东边的蓝队”

输入 (Input):
End 攻击宏 红队宏 昨天宏 Not 在宏 西边宏 Not 在宏 蓝队宏 今天宏 Not 在宏 东边宏 Not 在宏

推导逻辑输出 (Output):
v15∈Ω ∧ (Exist v1∈东边 (Exist v3∈今天 (Exist v5∈蓝队 (Exist v7∈西边 (Exist v9∈昨天 (Exist v11∈红队 (Exist v13∈攻击
    Not 在(v5,v3) ∧ Not 在(v5,v1) ∧
    Not 在(v11,v9) ∧ Not 在(v11,v7) ∧
    主语(v13,v11) ∧ 宾语(v13,v5) ∧ 谓语(v15,v13)))))))) v15

5. 动态代词照应与带否定的经典驴子句

“农民不给小孩书，小孩就不会读它。”

输入 (Input):
End 就:C Negation 读宏 Exist Download child Download book Negation 给宏 Exist 农夫宏 All Upload child 小孩宏 All Upload book 书宏 All

推导逻辑输出 (Output):
v13∈Ω ∧ (All v1∈书 (All v3∈小孩 (All v5∈农夫 (Exist v7∈给 (Exist v10∈读
    就_consequent(v13,v12) ∧ 就_antecedent(v13,v9) ∧
    Not(主语(v10,v3) ∧ 宾语(v10,v1) ∧ 谓语(v12,v10)) ∧
    Not(主语(v7,v5) ∧ 宾语(v7,v3) ∧ 传递物(v7,v1) ∧ 谓语(v9,v7))))))) v13

6. 原位词法派生

“老人”

输入 (Input):
"老$" 人:S

推导状态输出 (Smap):
Smap (Sets): [("v2", "老人")]

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💻 交互式环境 (REPL)

• :r — 重置自动机状态、栈与映射（保留已加载的宏）。
• :q — 退出推导引擎。
• // <expr> — 单步跟踪模式（逐步打印全系统 8 栈 5 映射的状态流转）。
• define <名称> := <表达式> — 注册全局宏定义。

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📝 关于设计与实现

SML 的理论基石、形式语义规则体系、“八栈五映射一计数器”自动机架构、事件实体化代数以及关系消解演算均由作者本人独立构思并完成严格的数学化定义。

参考代码由作者提供精确的状态转移规范并借助 AI 辅助生成，作为可执行的语义虚拟机，验证了所有规约规则的自洽性与无泄漏修饰的工程可行性。