Victor Taelin VictorTaelin

HOC - Thesis and Future Direction

At HOC, we believe Interaction Nets technology can lead to valuable market products. Two years ago, we raised $4 million to explore and validate this idea. During this period, we developed HVM and Bend—tools that significantly speed up functional and symbolic programs.

As we wrap up this research phase, we've identified the Symbolic AI market as our best opportunity. This market is rapidly growing, highly values computational efficiency, and aligns perfectly with HVM's strengths in

The Interaction Calculus

The Interaction Calculus (IC) is term rewriting system inspired by the Lambda Calculus (λC), but with some major differences:

Vars are affine: they can only occur up to one time.
Vars are global: they can occur anywhere in the program.
There is a new core primitive: the superposition.

An IC term is defined by the following grammar:

The Interaction Calculus

The Interaction Calculus (IC) is term rewriting system inspired by the Lambda Calculus (λC), but with some major differences:

Vars are affine: they can only occur up to one time.
Vars are global: they can occur anywhere in the program.
There is a new core primitive: the superposition.

An IC term is defined by the following grammar:

Prompt

Create a λ-Term fold that, when applied to a Church nat N, a function F, an initial value X, and a Church N-Tuple, performs a right-fold over the N-tuple. In other words, create a generic fold<N,F,X,t> function for N-tuples. Example:

(fold λf.λx.(f x) F X λt(t 1)) == (F 1 X)
(fold λf.λx.(f (f x)) F X λt(t 1 2)) == (F 1 (F 2 X))
(fold λf.λx.(f (f (f x))) F X λt(t 1 2 3)) == (F 1 (F 2 (F 3 X)))

Your final answer must be a λ-Term that implements fold correctly, as follows:

	import Control.Monad (when)
	import Data.Char (chr, ord)
	import Data.IORef
	import Data.Word
	import Debug.Trace
	import System.IO.Unsafe (unsafePerformIO)
	import Text.Parsec hiding (State)
	import qualified Data.IntMap.Strict as IntMap
	import qualified Data.Map as Map
	import qualified Text.Parsec as Parsec


	╭────────────────────────────────────────────╮
	│ ✻ Welcome to Claude Code research preview! │
	│ │
	│ /help for help │
	│ │
	│ cwd: /Users/v/vic/dev/IC │
	╰────────────────────────────────────────────╯

	! cat InteractionCalculus.md

	the current dir has the following files:

	bench_cnots.hvml
	bench_count.hs
	bench_count.hvml
	bench_sum_range.hs
	bench_sum_range.hvml
	bench_sum_range.js
	bug_tmp
	docs

	This is a debugging challenge.
	Read the document below, and identify the bug.

	---

	# The Interaction Calculus

	The Interaction Calculus (IC) is term rewriting system inspired by the Lambda
	Calculus (λC), but with some major differences:
	1. Vars are affine: they can only occur up to one time.

	//./runtime.c//
	//./reduce.hs//

	# The Interaction Calculus

	The Interaction Calculus (IC) is term rewritting system inspired by the Lambda
	Calculus (λC), but with some major differences:
	1. Vars are affine: they can only occur up to one time.
	2. Vars are global: they can occur anywhere in the program.
	3. There is a new core primitive: the superposition.