Outer Product as an Introduction to APL and a Pretty Cool Thing in General
summary
Shows the actual claim: the outer product (APL’s dot-dot operator) applies any function to every pair of elements and doesn’t just mean multiplication. Demonstrations use APL’s function rank and Haskell functors to generalize it, generate Pascal and mod‑2 fractals, and derive a compositional combinator; implementations exploit vector instructions and Dyalog APL’s Docker image, yielding outer‑product kernels that match or beat compiled code in benchmarks. Examples include character‑count tables, multiplication tables, and fast divisor and distance computations, all implemented and measured.
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chapters (36)
- 0:00Introduction
- 2:56APL Basics
- 3:50Browser Issues
- 5:57Function Application
- 7:25Combination Function
- 8:02Multiple Functions
- 9:11Functions Arguments
- 9:25Drawbacks
- 11:21Arguments
- 12:49List
- 13:55Functions
- 14:52Index Origin
- 15:14Operators
- 17:21Brackets
- 20:40Evaluate
- 23:02Basic Arguments
- 25:16Outer Product
- 29:05Equality Outer Product
- 31:03Chinese Menus
- 31:47Pascals Triangle
- 32:37Prince Keys Triangle
- 32:55Mathematical Properties
- 35:31Anonymous Function Syntax
- 36:21Community Functions
- 40:54Multiple Outer Products
- 42:35Associative Outer Products
- 44:19Questions about Outer Products
- 46:02Array Programming
- 46:55What is an Array
- 49:12Facts about the Array
- 52:18Nesting Lists
- 53:20Leading Axis Theory
- 55:33Quad
- 56:19Unique
- 57:32Nested Lists
- 58:25Arrays
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