What is the type of 2 + 2 = 4?
All elementary functions from a single operator
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin\sin, cos\cos, \sqrt{\phantom{x}}, and log\log has always required multiple distinct operations. Here we show that a single binary operator,
Grade 3 » Operations & Algebraic Thinking » Represent and solve problems involving multiplication and division. » 1 | Common Core State Standards Initiative
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
A theory of type polymorphism in programming
The aim of this work is largely a practical one. A widely employed style of programming, particularly in structure-processing languages which impose n…
ignore the code: Toggles Considered Harmful
I just read this post from Marcin Wichary's Unsung, where he points out a peculiar macOS dialog box that shows boolean toggles in four different shades of grey:
4-Clause BSD Explained in Plain English - TLDRLegal
4-Clause BSD summarized/explained in plain English.
Syntax and Semantics of Linear Dependent Types
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax...
Variety (cybernetics)
In cybernetics, the term variety denotes the total number of distinguishable elements of a set, most often the set of states, inputs, or outputs of a finite-state machine or transformation, or the binary logarithm of the same quantity.[1] Variety is used in cybernetics as an information theory that is easily related to deterministic finite automata, and less formally as a conceptual tool for thinking about organization, regulation, and stability. It is an early theory of complexity in automata, complex systems,[1]: 6  and operations research.[2]
A modal analysis of staged computation | Journal of the ACM
We show that a type system based on the intuitionistic modal logic S4 provides an expressive framework for specifying and analyzing computation stages in the context of typed λ-calculi and functional languages. We directly demonstrate the sense in which ...
The Principal Type-Scheme of an Object in Combinatory Logic
R. Hindley, The Principal Type-Scheme of an Object in Combinatory Logic, Transactions of the American Mathematical Society, Vol. 146 (Dec., 1969), pp. 29-60
GHC/Typed holes - HaskellWiki
Typed holes are a powerful feature in GHC inspired by Agda. But what are typed holes, and how do they help us write code?
An invitation into Droste's Lair
A swords-and-sorcery programming environment for building and counting mathematical structures
Theorems for free! | Proceedings of the fourth international conference on Functional programming languages and computer architecture
The polymorphic blame calculus integrates static typing, including universal types, with dynamic typing. The primary challenge with this integration is preserving parametricity: even dynamically-typed code should satisfy it once it has been cast to a ...
An invitation into Droste's Lair
A swords-and-sorcery programming environment for building and counting mathematical structures
inanna-malick/jev-dsl
Agent-first Haskell DSL for TypeSafe's Jev judgment model: typed packets, inferred types, answers under the same labels