Realm
Principles
Formal and modeling disciplines that keep distinctions precise across the graph.
Entries
Adjunctions
Adjunctions describe paired constructions that translate between domains in the best available way, even when the translations are not inverses.
Algebras and Coalgebras
Algebras and coalgebras provide complementary ways to model construction and behavior.
Asynchronous Computability Theorem
The asynchronous computability theorem characterizes which distributed tasks can be solved wait-free in an asynchronous read/write system.
CALM Theorem
The CALM theorem, "Consistency as Logical Monotonicity", states that a program has a consistent, coordination-free distributed implementation if and only if it can be expressed in monotonic logic.
Categorical Principles
Categorical principles provide modeling discipline for the Cohesive System Model. They are not the entry point for ordinary readers, but they help keep distinctions precise when relating domain semantics, system graph, operational concerns, and realization substrate.
Compositionality
Compositionality is the principle that complex systems should be understood from parts and the rules by which those parts compose.
Concurrency
Concurrency is the boundary-relative absence of an established ordering between occurrences or enabled work.
Control Flow
Control flow describes how one possible action, operation, step, or continuation becomes enabled, selected, and followed by another at a declared boundary.
Control Theory
Control theory is the discipline of regulating the behavior of a dynamical system through observation, decision, actuation, and feedback over time.
Curry–Howard Correspondence
The Curry–Howard correspondence relates formal proofs to typed programs: propositions correspond to types, proofs correspond to terms inhabiting those types, and proof normalization corresponds to program evaluation.
Database Sheaf Semantics
Database Sheaf Semantics views a database schema as a category, a database instance as a structure-preserving functor into sets, and local database views as sections that can be restricted, compared on overlaps, and sometimes glued into a coherent larger instance.
Duality and Symmetry
Duality and symmetry are principles for recognizing paired concepts that explain one another through reversal, complementarity, or mirrored structure.
Enrichment and Order
Enrichment adds structure to relationships. Instead of merely asking whether a relationship exists, an enriched view asks what kind of value the relationship has: order, distance, cost, probability, time, authority, confidence, or information.
Equivalence vs Equality
Equivalence and equality should not be confused.
Event-State Duality
Event-state duality is a modeling principle and an instance of duality and symmetry: the relationship between two views of behavior:
Execution Kernel
An execution kernel is a shared semantic and interpretation boundary through which portable transition and process descriptions become executable without making one runtime, storage engine, workflow product, actor system, or host-language program the source of meaning.
Fibrations and Indexed Structure
Fibrations and indexed structure describe situations where each object in a base domain has a category of things lying over it.
Fixed Points
A fixed point is a value, structure, or behavior that a specified transformation leaves unchanged:
Functional Programming
Functional programming describes computation primarily through values, functions, composition, and evaluation rather than through a distinguished sequence of commands that mutate shared state.
Functoriality
Functoriality is the principle that a mapping between domains should preserve the structure that matters: identities, relationships, composition, and change.
Glitch Principle
The glitch principle states that a non-trivial device making a discrete decision among finitely many outcomes from a continuous range of possible inputs cannot guarantee a uniform finite decision time for every input.
Happened-Before
Happened-before is a strict partial order over occurrences that preserves potential causal influence without requiring one global clock or one total execution order.
Judgement
A judgement is a context-indexed assertion that a specified relation holds. It makes explicit what is being claimed, under which assumptions and rules, at which boundary, and with what evidence or authority the claim is accepted.
Lambda Calculus
The lambda calculus is a formal calculus of variables, function abstraction, application, and substitution. It supplies a foundational language for functions and evaluation, and underlies large parts of functional programming, type theory, proof theory, and categorical semantics.
Law of Excluded Middle
The law of excluded middle is the logical schema:
Linear Logic
Linear logic is a resource-sensitive logic in which assumptions cannot ordinarily be duplicated or discarded implicitly. It makes the use of hypotheses part of proof structure, separating connectives that combine independent resources from connectives that offer alternatives and modalities that explicitly permit reuse.
Logic
Logic studies formal languages, interpretations, and valid inference. It separates the expressions a language permits, the structures in which those expressions have meaning, and the rules by which conclusions follow from assumptions.
Monads Monoids and Duals
Monads, monoids, and their duals provide recurring patterns for sequencing, accumulation, context, observation, and composition.
Naturality
Naturality is the principle that a transformation should be independent of arbitrary representation choices. It should commute with the structure-preserving maps between representations.
Nondeterminism and Choice
Nondeterminism describes a model in which one context admits more than one possible continuation. Choice describes how, where, or by whom that multiplicity is resolved.
Optics and Lenses
Optics are structured ways to focus on, observe, transform, or update part of a larger structure.
Pattern Languages and Correspondence
Pattern languages and catalogs preserve experience about recurring problems, forces, arrangements, and consequences. Cohesive reconciles them by placing each imported pattern into the realms where its claims belong and recording the correspondences among those claims.
Process Calculi
Process calculi are formal languages for describing and reasoning about interacting, concurrent, and mobile processes. They provide syntax for composing process descriptions, operational rules for how interactions advance, and equivalences for deciding when different descriptions exhibit the same relevant behavior.
Process Theories
Process theories are modeling disciplines for work, interaction, change, and behavior that unfold over time.
Programming Paradigms
Programming paradigms are recurring ways of interpreting and organizing computation. They select which structures are primary, which composition laws matter, and which operational details are left to a language, compiler, runtime, or other realization.
Queueing Theory
Queueing theory is the mathematical and operational discipline for reasoning about work that arrives, waits, receives finite-capacity service, moves among resources, and completes.
Quorum Intersection
Quorum intersection is the principle that selected participant sets overlap so that later decisions or observations encounter evidence constraining earlier incompatible choices.
Recursion
Recursion defines a value, structure, or behavior in terms of other instances of the same form. The recursive reference may point to a smaller component, a prior step, a nested process, or another derivation of the same relation.
Reduction, Evaluation, and Confluence
Reduction, evaluation, and confluence describe how a computation advances through possible intermediate expressions or states, how an execution strategy selects a path, and when divergent paths remain semantically coherent.
Relational and Logic Programming
Relational and logic programming are approaches in which programs state which combinations of values, facts, or terms hold or are admissible, rather than prescribing only a function from distinguished inputs to distinguished outputs.
Service
A service is a boundary-relative role in which a provider makes a capability available to a consumer through a contract, including declared semantic and operational guarantees. The role says what can be requested, observed, or relied upon at that boundary; it does not by itself determine where the behavior is implemented, whether it runs in another process, how it is deployed, or which team owns it.
Session Types
Session types are behavioral types for structured communication. They describe how a participant may use a channel or protocol endpoint over the course of a conversation: which values or labels it sends and receives, which choices it makes or offers, how the interaction recurs, and when it completes.
Sheaves and Gluing
Sheaves and gluing provide a local-to-global principle for systems of observations: many observers, contexts, processors, time intervals, schemas, views, or execution cuts may each see part of a system, and the model needs to say when those partial views agree enough to form a coherent larger view.
State Machines
State machines are a modeling principle for behavior described by current state, admissible transitions, inputs, and outputs.
Stuff Structure Property
Stuff, structure, and property are a modeling distinction for separating what a model contains, how it is organized, and what constraints it satisfies.
Substitution
Substitution replaces variables with terms while preserving the binding, scope, sorting, typing, and contextual relationships that make an expression meaningful. It is a foundational operation in logic, type theory, the lambda calculus, rewriting, proof theory, and compiler semantics.
Synchrony and Asynchrony
Synchrony and Asynchrony describe whether events, observations, transitions, or participants are coupled into one boundary-relative unit.
System Language and Realization
Cohesive aims to provide a standard language for describing systems and a family of compiler-like realizations that project that language into working infrastructure.
Systems Sheaf Semantics
Systems Sheaf Semantics uses sheaf-theoretic local-to-global structure to model how observations, state, versions, histories, process state, and knowledge vary over contexts such as observers, boundaries, and causally valid cuts of execution.
Temporal Logic
Temporal logic is a family of logics for stating how propositions hold across behaviors, runs, traces, or branching transition structures. It adds modalities for time and succession without requiring every temporal claim to use wall-clock timestamps or metric durations.
Trace and Feedback
Trace and feedback describe systems where outputs are fed back as future inputs.
Type Theory
Type theory studies terms together with the types that classify them and the judgements that establish when those terms are well formed. It can serve as a foundation for mathematics, a formal system for proofs, and a semantic basis for programming-language type systems. Substitution transports terms and types across contexts, while typed lambda calculi provide foundational term languages for abstraction and application.
Ubiquitous Language
A ubiquitous language is a shared, model-grounded language used by domain practitioners and software practitioners within an explicitly bounded context. It gives the terms and statements used in conversation, scenarios, documentation, models, interfaces, tests, and code a common boundary-relative meaning.
Universal Constructions
Universal constructions are principles for naming "the" object determined by a diagram of related objects and morphisms.
Yoneda Lemma
The Yoneda lemma says, roughly, that an object is determined by how it relates to all other objects through maps into or out of it.