Glossary of Ψ Formalism - v0.1

Version: 0.1 Date: 2025-11-14

Key Terms

Definition: Binds a variable in an expression, creating a function. (e.g., λx.x)
Context: A fundamental operator in the Ψ formalism, enabling the creation of higher-order functions and the encapsulation of logic.

Definition: Captures the current evaluation context (a continuation) and makes it available as a value.
Context: A core operator in the Ψ formalism, complementary to abstraction. It models control, context switching, and non-local flow.
Minimal semantics: μk.M binds k to “the rest of the computation”, then evaluates M with access to k.
Canonical use-cases:
- Early exit / abort with a value.
- Backtracking or “rewind to a checkpoint”.
- Reifying “what I was doing” as an explicit object.
Examples (informal):
- μk. k v behaves like “return v immediately”.
- μk. M allows M to invoke k later as a jump back to the captured context.
Where the full spec lives: This is the glossary-level definition. The full formal rules (typing, reduction, and allowed compositions) belong in the OPERATORS canon (e.g., Lambda_Core_v0.2 / operator grammar).

This document does not cover:

The full algebraic properties or commutation rules of operators (handled in "Operator Grammar").
The foundational definitions of Ψ or its semantics (handled in "Foundations").
The dynamic update equations of the system (handled in "Core Equations").
Philosophical or cognitive interpretations (handled in "Interpretations").