Data morphisms in Catecon contain information that can be used in a composite. For example, f(2) = 6. The domain for a data morphism is generally ℕ, but the codomain may have a complex form such as (𝔽×𝔽)×(ℤ×ℤ)×(ℕ×ℕ). The old data morphisms in Catecon were simply a mapping from an index to a value which…
Factor Morphisms In Catecon a factor morphism is derived from a product domain by listing indices giving factors in the the product hierarchy. This then forms various projections and deltas from the given domain to the codomain. For example, suppose you have a domain of AxBxC, and you want to make two copies of A,…
Some current details about the development status of Catecon: The Categorical Console. October 15, 2018 New Objects And Named Identities Created a new object panel to replace the old one with all the issues it provided. You could not create a decent named object, like Point say as defined as F*F, and have it act…
A screenshot from Catecon, the Categorical Console, showing basic string shots. Here we start to see the colored chalkings of coherence.
Let’s try to see the Fibonacci numbers. As you know, the Fibonacci number of n is the Fibonacci number of n-1 plus the Fibonacci number of n-2. Looks like a natural use of recursion so buckle up. Let’s start by having our own Fibonacci diagram. Drag the natural numbers onto the diagram. Control-drag to form…
Prior video Catecon: Introduction. My first machine to play on beyond some sticks to rub together (a slide rule) was an Olivetti Programma 101 with magnetic cards. My first program, well, one with loops, was to compute factorials. Let’s do that here, with recursion. Given a natural number n, the factorial of n is n…
Videos for the Categorical Console. Introduction Up to “Hello, world!” “Now, Bob,” I distinctly recall Saunders saying to me. “You have to have good names for your ideas.” I had gone in for our weekly meeting to complain about one of his names, namely that of “central morphisms”. I opined that the “centrality” should extend…
Vortex, A Categorical Database In the early 90’s I led a product team of three folks to create Vortex, a database for electronic design automation (EDA). This work at Intergraph Electronics/Dazix/Veribest was based on the categorical programming technique previously developed for the Clipper microprocessor. As it happens the product was never released. The one remaining…
Have You Shorts Or Opens? Categorical programming was applied to the building of the Clipper microprocessor. Read how part of it was done. Beginning work ’84 at Fairchild Semiconductor as a CAD engineer on the Clipper microprocessor, one of the early assignments was to look at a pen plotter. A pen plotter possesses a few…