Site banner
 
Menu arrow Home                    
 
 

0504
.
Simply typed lambda calculus
Nill

Simply typed lambda calculus - Terms - Encyclopedia II

Nill
To define the set of well typed lambda terms of a given type, we introduce typing contexts which are sequences of typing assumptions of the form x:σ where x is a variable. We introduce the judgment which means that t is a term of type σ in context Γ which is given by the following typing rules: Examples of closed terms are: (I), (K), and (S). These are the typed lambda calculus represen ...
Nill
Simply typed lambda calculus, Simply typed lambda calculus - Important results, Simply typed lambda calculus - Terms, Simply typed lambda calculus - Types
Nill
Nill
Nill

To define the set of well typed lambda terms of a given type, we introduce typing contexts which are sequences of typing assumptions of the form x where x is a variable. We introduce the judgment which means that t is a term of type σ in context Γ which is given by the following typing rules:

Examples of closed terms are:

  • (I),
  • (K), and
  • (S).

These are the typed lambda calculus representations of the basic combinators of combinatory logic.

The simply typed lambda calculus is closely related to propositional intuitionistic logic using only implication () as a connective (minimal logic) via the Curry-Howard isomorphism: the types inhabited by closed terms are precisely the tautologies of minimal logic.

Terms of the same type are identified via βη-equivalence, which is generated by the equations , where t[x: = u] stands for t with all free occurrences of x replaced by u, and , if x does not appear free in t. The simply typed lambda calculus (with βη-equivalence) is the internal language of Cartesian Closed Categories (CCCs), this was first observed by Lambek.




Wikipedia

Adapted from the Wikipedia article "Terms", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki/Main_Page

Nill
More material related to Simply Typed Lambda Calculus can be found here:
Nill
Main Page
for
Simply Typed Lambda Calcu...



Videos - Simply typed lambda calculus
EEP100 - Lecture 6EEP100 - Lecture 6

Markets, missing markets, no markets; elasticity; inverse demand; dead weight loss; indifference curves; constrained optimizatio...

Lecture 10B | MIT 6.001 Structure and Interpretation, 1986Lecture 10B | MIT 6.001 Structure and Interpretation, 1986

Storage Allocation and Garbage Collection Despite the copyright notice on the screen, this course is now offered under a Creativ...

Newspeak: A Principled Dynamic LanguageNewspeak: A Principled Dynamic Language

Google Tech Talk May 4, 2010 ABSTRACT In this talk, we present the main features of Newspeak, a dynamic programming language foc...

Lec 25 | MIT 18.085 Computational Science and Engineering I, Fall 2008Lec 25 | MIT 18.085 Computational Science and Engineering I, Fall 2008

Lecture 25: Fast Poisson solver (part 1) License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw...




.nill


  » Home » » Home »  


P