(uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject.
calculi
Definitions, parts of speech, synonyms, and sentence examples for calculi.
Editorial note
If one does a deep embedding then powerful calculi can be embedded in much weaker calculi.
Quick take
(uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject.
Meaning at a glance
The clearest senses and uses of calculi gathered in one view.
(countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.
(dated, countable) Calculation; computation.
Definitions
Core meanings and parts of speech for calculi.
noun
(uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject.
noun
(countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.
noun
(dated, countable) Calculation; computation.
noun
(countable, medicine) A stony concretion that forms in a bodily organ.
Example sentences
If one does a deep embedding then powerful calculi can be embedded in much weaker calculi.
The problem is bad enough when dealing with core calculi---as this post demonstrates, being precise is doubly important when dealing with feature-rich languages, like C#.
Graphical calculi for monoidal categories date back to Kelly and Laplaza (1980), with later refinements by Joyal-Street and Yetter.
Any suggestions for resources that could help get me more comfortable with reading and understanding type calculi?
Strong normalization theorems are used for typed lambda calculi like the Calculus of Inductive Constructions to show consistency, as well.
Functional programming languages, at their core, are just lambda calculi with some syntactic sugar.
In particular, linguists use typed λ-calculi to construct formal semantics for sentences.
It's good to learn about applying types to process calculi.
Summary for the layperson: The Curry-Howard Isomorphism is an exact syntactic correspondence between types for lambda calculi, propositions in intuitionistic logics, and objects in closed Cartesian categories.
Point-free reasoning is a good way to avoid some of these complications, which contributes to the popularity of combinator calculi like SKI when teaching untyped lambda calculus.
Linear-session-typed process calculi are guaranteed deadlock-free and race-free.
How many process calculi are you familiar with?
Quote examples
A slow-paced textbook like Hankin's "An Introduction to Lambda Calculi for Computer Scientists", and doing the exercises in the first few chapters should do the job.
The problem then becomes a matter of learning various types of "lambda calculi", or similar formalism, usually in 10 minutes, and you don't have to waste a life-time learning the indentation and semi-colon termination rules of yet another procedural language thrown out at you from the blogosphere.
Proper noun examples
Communicating Sequential Processes (CSP) also came out of the Process Calculi.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use calculi in a sentence?
If one does a deep embedding then powerful calculi can be embedded in much weaker calculi.
What does calculi mean?
(uncountable, often definite, the calculus) Differential calculus and integral calculus considered as a single subject.
What part of speech is calculi?
calculi is commonly used as noun.