Homomorphism as Specification

Denotation acts as algebraic homomorphism, making implementations correct-by-construction when they satisfy this property

Source paper

extracted_from

(2015) · Elliott, Conal

community

Homomorphism-based program specification
members_of
Deriving laws and specifications algebraically from semantic homomorphisms in functional programming.

concept

Laws for Free
supports
Consequence of semantic type class morphism: type class laws hold automatically from denotational specification without manual proof.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

The specification for (⊸) is a category homomorphism (µ id = id, µ(g ∘ f) = µg ∘ µf), leading to a correct-by-construction implementation.claim0.800
Demonstration on linear transformations.
Applicative Homomorphismconcept0.788
semantic type class homomorphismconcept0.772
The property that the denotation function distributes over class operations, ensuring the semantics respects the algebraic structure.
Monoid Homomorphismconcept0.762
Functor Homomorphismconcept0.758
Representational Isomorphismconcept0.742
The desired property of a bidirectional, behavior-preserving mapping between model representations; the goal MAS pursues.
Laws for free from semantic homomorphism.claim0.738
If a semantic function is a homomorphism with respect to a type class, the implemented instance automatically satisfies the class laws.hypothesis0.728
Core hypothesis enabling 'laws for free': denotational semantics guarantee algebraic law satisfaction.