SICP Skill

"Programs must be written for people to read, and only incidentally for machines to execute." — Abelson & Sussman

Geometric morphism translation from sicp.info preserving the hierarchical node structure as an ACSet with GF(3) coloring for trifurcated processing.

Overview

Structure and Interpretation of Computer Programs (Second Edition)
by Harold Abelson and Gerald Jay Sussman, with Julie Sussman
Foreword by Alan J. Perlis
© 1996 Massachusetts Institute of Technology

The wizard book for computational thinking—procedures as abstractions, data as abstractions, and the interpreter as the ultimate abstraction.

Chapters

Chapter 1: Building Abstractions with Procedures [PLUS]

• 1-1: The Elements of Programming (expressions, naming, evaluation)
• 1-2: Procedures and the Processes They Generate (recursion, iteration, orders of growth)
• 1-3: Formulating Abstractions with Higher-Order Procedures (λ, returned values)

Key concepts: Substitution model, lexical scoping, fixed points, Newton's method

Chapter 2: Building Abstractions with Data [ERGODIC]

• 2-1: Introduction to Data Abstraction (rational numbers, barriers)
• 2-2: Hierarchical Data and the Closure Property (sequences, trees, picture language)
• 2-3: Symbolic Data (quotation, differentiation, sets, Huffman encoding)
• 2-4: Multiple Representations for Abstract Data (tagged data, data-directed programming)
• 2-5: Systems with Generic Operations (type coercion, symbolic algebra)

Key concepts: Pairs, cons/car/cdr, closure property, abstraction barriers, message passing

Chapter 3: Modularity, Objects, and State [PLUS]

• 3-1: Assignment and Local State (set!, costs of assignment)
• 3-2: The Environment Model of Evaluation (frames, procedure objects)
• 3-3: Modeling with Mutable Data (queues, tables, digital circuits, constraints)
• 3-4: Concurrency: Time Is of the Essence (serializers, deadlock)
• 3-5: Streams (delayed evaluation, infinite streams, signal processing)

Key concepts: State, identity, time, streams vs objects duality

Chapter 4: Metalinguistic Abstraction [PLUS]

• 4-1: The Metacircular Evaluator (eval/apply, syntax procedures, environments)
• 4-2: Variations on a Scheme (lazy evaluation, normal vs applicative order)
• 4-3: Variations on a Scheme: Nondeterministic Computing (amb, backtracking)
• 4-4: Logic Programming (unification, pattern matching, query systems)

Key concepts: eval/apply loop, special forms, thunks, amb evaluator, Prolog-style logic

Chapter 5: Computing with Register Machines [ERGODIC]

• 5-1: Designing Register Machines (data paths, controllers, subroutines)
• 5-2: A Register-Machine Simulator (the machine model, assembler)
• 5-3: Storage Allocation and Garbage Collection (vectors, stop-and-copy)
• 5-4: The Explicit-Control Evaluator (machine code for Scheme)
• 5-5: Compilation (structure of compiler, lexical addressing, interfacing)

Key concepts: Register allocation, continuation-passing, tail recursion, compilation

GF(3) Conservation

The Info file nodes distribute perfectly across GF(3) trits:

Total nodes: 138
MINUS (-1):  46  ████████████████
ERGODIC (0): 46  ████████████████
PLUS (+1):   46  ████████████████
Sum mod 3:   0
Conserved:   ✓ BALANCED

This perfect 46/46/46 distribution enables optimal trifurcated parallel processing.

ACSet Schema (Geometric Morphism)

The translation from Info to Skill uses a geometric morphism f: InfoTopos → SkillTopos:

Objects (Ob):
  Node      - Info nodes (sections, subsections)
  Edge      - Navigation and reference links
  Content   - Extracted text and code blocks

Morphisms (Hom):
  next: Node → Node     - Sequential navigation
  prev: Node → Node     - Backward navigation  
  up:   Node → Node     - Hierarchical parent
  menu: Node → Node     - Chapter/section containment
  xref: Node → Node     - Cross-references (*Note)

Attributes:
  trit: Node → GF(3)    - Deterministic color assignment
  text: Node → String   - Node content

Integration with Gay.jl

The GF(3) coloring uses the same SplitMix64 hash as Gay.jl:

using Gay

# Color SICP nodes deterministically
for node in sicp_nodes
    seed = hash(node.id)
    color = gay_color(seed)  # Returns palette with GF(3) trit
    node.trit = color.trit
end

# Verify conservation
@assert sum(n.trit for n in sicp_nodes) % 3 == 0

Commands

# Read in Emacs
info sicp

# Re-translate with geometric morphism
bb info_to_skill_morphism.bb translate sicp.info

# Verify grammar and GF(3) conservation
bb info_to_skill_morphism.bb verify sicp.info

# Parse to CRDT-style sexp
bb info_to_skill_morphism.bb parse sicp.info > sicp.sexp

References

• Full text online
• MIT OCW 6.001
• SICP Distilled (Clojure version)