Graph reduction

Evaluation of a functional program by rewriting a shared expression graph so lazy subexpressions are computed at most once.

Version

v1 · 2026-09-08 · History

Domain-specific #

4771

Origin domain

functional programming

Subdomain

functional programming

Core Idea

The graph represents applications and values with shared nodes, non-strict evaluation selects a reducible expression only when demanded and updates the node with its result for all references. A reduction machine follows demand to an outer redex, rewrites it in place and preserves sharing through indirection or update nodes, avoiding duplicated evaluation that tree substitution would cause. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application

Graph reduction belongs to functional programming and is useful where the analyst can specify the typed functional programming carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the source calculus and evaluation semantics, expression graph and sharing, redex-selection rule, rewrite and update operation, treatment of recursion and garbage, normal form and observational-equivalence argument are explicit. The scope is broad within that domain but bounded by the need for the source calculus and evaluation semantics, expression graph and sharing, redex-selection rule, rewrite and update operation, treatment of recursion and garbage, normal form and observational-equivalence argument are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making the source calculus and evaluation semantics, expression graph and sharing, redex-selection rule, rewrite and update operation, treatment of recursion and garbage, normal form and observational-equivalence argument are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Graph reduction. Graph reduction compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: the typed functional programming carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the source calculus and evaluation semantics, expression graph and sharing, redex-selection rule, rewrite and update operation, treatment of recursion and garbage, normal form and observational-equivalence argument are explicit independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of functional programming because they reuse the typed functional programming carrier, including its objects, relations, parameters, conventions, evidence, boundary cases, and comparison targets, A reduction machine follows demand to an outer redex, rewrites it in place and preserves sharing through indirection or update nodes, avoiding duplicated evaluation that tree substitution would cause., and type the carrier, state every parameter and convention in the definition, test that the source calculus and evaluation semantics, expression graph and sharing, redex-selection rule, rewrite and update operation, treatment of recursion and garbage, normal form and observational-equivalence argument are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction Graph reduction Domain-specific

Parents (1) — more general patterns this builds on

• Graph reduction is a kind of Equivalence-Preserving Rewriting Prime

  The proposed strict upward parent is prime:equivalence_preserving_rewriting.

Hierarchy paths (2) — routes to 2 parentless roots

• Graph reduction → Equivalence-Preserving Rewriting → Transformation → Function (Mapping)

Show alternative path (1)

Neighborhood in Abstraction Space

Graph reduction sits in a crowded region of the domain-specific corpus (35^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Graph Structure & Width (12 abstractions)

Nearest neighbors

• Transitive reduction — 0.91
• Graph rewriting — 0.90
• Abstract semantic graph — 0.90
• Anamorphism — 0.90
• Mutual recursion — 0.90

Computed from structural-signature embeddings · 2026-09-08