en.wikipedia.org website review
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en.wikipedia.org is 57% geoptimaliseerd!
SEO Keyword summary for en.wikipedia.org/wiki/hindley%e2%80%93milner_type_system
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle type tau |
long Tail Keywords (2 words) type variables forall alpha type system gamma vdash rightarrow alpha |
long Tail Keywords (3 words) alpha rightarrow alpha forall alpha alpha alpha alpha rightarrow sdisplaystyle vdash s displaystyle forall alpha ddisplaystyle vdash d free type variables |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/hindley%e2%80%93milner_type_system page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
hindleyndashmilner type system wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
wikipedia free encyclopedia displaystyle trightarrow beginarraylrllextextrm variablevert textrm applicationvert lambda etextrm abstractionvert mathtt let endarray beginarrayllrlltextrm monotau alpha tau dots applicationtextrm polysigma vert forall sigma quantifierendarray beginarrayllrltextcontextgamma epsilon emptyvert gamma xsigma texttypinggamma vdash esigma beginarraylltextfree leftalpha righttextfree bigcup limits ntextfree textfree int string map set rightarrow intrightarrow ntau ngeq xlambda beta mathbf klambda xmathbf flambda texttt stringrightarrow sleft aimapsto right stau frac imapsto irighttau quad inot freeforall sqsubseteq mtau sleftalpha mapsto stringright longrightarrow sgamma essigma beginarraylrltextpredicatesigma not freegamma xalpha textjudgmenttexttypingtextpremisetextjudgment textpredicatetextconclusiontextjudgmenttextruledisplaystyle premise conclusionquad nameendarray name beginarraycldisplaystyle dxsigma vardisplaystyle appdisplaystyle xtau detau dlambda etau absdisplaystyle dmathtt letdisplaystyle desigma instdisplaystyle notin textfreegamma deforall genendarray var app abs inst gen didnint idforall nint beginarrayllll didforall varidforall didintrightarrow intmathtt dnintmathtt varnintin didnintmathtt textbf letidlambda dxalpha varxalpha leftxalpha xxalpha xxforall freeepsilon leftidforall dtextbf fftextrm trueftextrm xxtextbf inftextrm boolint sxtau setau slambda xbar smathtt letendarray bar hat freetau leftrightarrow leftarrow wedge unionab mathit instsigma jxtau newvarquad unifytau jetau jlambda jmathtt newvar unifyalpha sestau wxtau emptyset beginarrayllgamma newvars mathsf mgus endarraygamma wetau wlambda estau xoverline wmathtt textit union textsf mgu falpha beginarrayllltextcorrectnessgamma squad textcompletenessgamma textforall textwhere overline fixforall rec vmathit fixlambda entau nquad vnen vntau vnbar leq wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/hindley%e2%80%93milner_type_system
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for en.wikipedia.org/wiki/hindley%e2%80%93milner_type_system
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
system found in path !
type found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
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en.m.wikipedia.org |
en.wikipedia.org wikimedia foundation inc
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w page information
printable version
syntaxdirected
httpsenwikipediaorgwindexphptitlehindleymilnertypesystemoldid1221871317
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wiki type system
lambda calculus
parametric polymorphism
hindley j roger
milner robin
completeness
most general type
type annotations
type inference
complexity
functional languages
type class higherkinded polymorphism
haskell
functional programming
simply typed lambda calculus
haskell curry
robert feys
lists
c
overloading
objectoriented programming
polymorphic lambda calculus
syntax rules
surface grammar
depth grammar
typing rules
trees
identity function
cardinality
assignments
bindings
prolog
constant function
unification
partial order
inference rules
formal system
judgments
collapses
fresh
robinsons
unification
unionfind
equivalence classes
procedure
side effect
nphard
undecidable
occurs check
programming practical
fixed point combinator
type theory
strong normalisation property
inhabited
ad hoc overloading
lattice
kind
second order lambda calculus
dependent type system
subtyping
fbounded polymorphism
cardelli
system
row polymorphism
dexptime
pathological
jstor
citeseerx
s2cid
isbn
mairson harry g
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Links to external pages
Outloing links
ru.wikipedia.org
vi.wikipedia.org
www.wikidata.org
en.wiktionary.org
www.doi.org
www.jstor.org
citeseerx.ist.psu.edu
www.doi.org
api.semanticscholar.org
hdl.handle.net
web.cs.wpi.edu
hdl.handle.net
api.semanticscholar.org
hal.inria.fr
www.doi.org
web.archive.org
www.microsoft.com
hal.inria.fr
www.doi.org
www.doi.org
www.microsoft.com
api.semanticscholar.org
www.doi.org
www.github.com
eli.thegreenplace.net
foundation.wikimedia.org
foundation.wikimedia.org
www.wikimediafoundation.org
SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 65% | A title should reflect the contents of a site. This site has a 50 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 45 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 50% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 172 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 35% | Headers should reflect the contents of a site. This site has a 15 % match | |
Links | 12% | Link anchors should to some degree reflect the contents of a site. This site has a 6 % match | |
Image alt tags | 22% | Image alt tags should to some degree reflect the contents of a site. This site has a 8 % match | |
Bold and italic | 33% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 11 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 99% | 98.529411764706 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 9205 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 81.31% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 430 inline style declarations ( <a style="color:green">) with a size of 14615 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
en.wikipedia.org images and descriptions
130 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ac3ccda10ec411c24d89a87b7e1b8dcfcabcef65 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{lrl}{\text{predicate}}&=&\sigma \sqsubseteq \sigma '\\&\vert \ &\alpha \not \in free(\gamma )\\&\vert \ &x:\alpha \in \gamma \\\\{\text{judgment}}&=&{\text{typing}}\\{\text{premise}}&=&{\text{judgment}}\ \vert \ {\text{predicate}}\\{\text{conclusion}}&=&{\text{judgment}}\\\\{\text{rule}}&=&\displaystyle {\frac {{\textrm {premise}}\ \dots }{\textrm {conclusion}}}\quad [{\mathtt {name}}]\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24a4d0545a7e59d4d062510afb55181eb3c047f7 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {name}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/10d6e781d61259108db5fbfcfd84cb47daac33a6 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{cl}\displaystyle {\frac {x:\sigma \in \gamma }{\gamma \vdash _{d}x:\sigma }}&[{\mathtt {var}}]\\\\\displaystyle {\frac {\gamma \vdash _{d}e_{0}:\tau \rightarrow \tau '\quad \quad \gamma \vdash _{d}e_{1}:\tau }{\gamma \vdash _{d}e_{0}\ e_{1}:\tau '}}&[{\mathtt {app}}]\\\\\displaystyle {\frac {\gamma ,\;x:\tau \vdash _{d}e:\tau '}{\gamma \vdash _{d}\lambda \ x\ .\ e:\tau \rightarrow \tau '}}&[{\mathtt {abs}}]\\\\\displaystyle {\frac {\gamma \vdash _{d}e_{0}:\sigma \quad \quad \gamma ,\,x:\sigma \vdash _{d}e_{1}:\tau }{\gamma \vdash _{d}{\mathtt {let}}\ x=e_{0}\ {\mathtt {in}}\ e_{1}:\tau }}&[{\mathtt {let}}]\\\\\\\displaystyle {\frac {\gamma \vdash _{d}e:\sigma '\quad \sigma '\sqsubseteq \sigma }{\gamma \vdash _{d}e:\sigma }}&[{\mathtt {inst}}]\\\\\displaystyle {\frac {\gamma \vdash _{d}e:\sigma \quad \alpha \notin {\text{free}}(\gamma )}{\gamma \vdash _{d}e:\forall \ \alpha \ .\ \sigma }}&[{\mathtt {gen}}]\\\\\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/628d2784ad2b052345194319297d3c584de91587 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {var}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/deb1cf4ec74d9df5e57b0040f2c60fc3846762c6 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {app}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/71bc6d1d849781626931e41c6d2fce47d324adf8 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {abs}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/49c4b2e6d201032726e709bbc3d76e3c6ff0cc84 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {let}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ee42296fd58b5cb88b23b83a009f8275384c5c5 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {inst}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dd1e72f9437e047dd4f407d6d52fa265f8f13419 height: height attribute not set width: width attribute not set description: {\displaystyle [{\mathtt {gen}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8b0c1ee0ab142ebd2e1d54c94170077aa8ffbe2 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{d}id(n):int} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/66d1f668844423bdbd9defae6bed33f8a24ef397 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma =id:\forall \alpha .\alpha \rightarrow \alpha ,\ n:int} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/34ed34426c0a380e1e7fc7a3ea9dd4ec38dba70b height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{llll}1:&\gamma \vdash _{d}id:\forall \alpha .\alpha \rightarrow \alpha &[{\mathtt {var}}]&(id:\forall \alpha .\alpha \rightarrow \alpha \in \gamma )\\2:&\gamma \vdash _{d}id:int\rightarrow int&[{\mathtt {inst}}]&(1),\ (\forall \alpha .\alpha \rightarrow \alpha \sqsubseteq int\rightarrow int)\\3:&\gamma \vdash _{d}n:int&[{\mathtt {var}}]&(n:int\in \gamma )\\4:&\gamma \vdash _{d}id(n):int&[{\mathtt {app}}]&(2),\ (3)\\\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eb95ddd33164c653984a3a3e349318ed309b2f8f height: height attribute not set width: width attribute not set description: {\displaystyle \vdash _{d}\ {\textbf {let}}\,id=\lambda x.x\ {\textbf {in}}\ id\,:\,\forall \alpha .\alpha \rightarrow \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0f49451f87a28e6a54c772cdd46f882fb77f2d5c height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{llll}1:&x:\alpha \vdash _{d}x:\alpha &[{\mathtt {var}}]&(x:\alpha \in \left\{x:\alpha \right\})\\2:&\vdash _{d}\lambda x.x:\alpha \rightarrow \alpha &[{\mathtt {abs}}]&(1)\\3:&\vdash _{d}\lambda x.x:\forall \alpha .\alpha \rightarrow \alpha &[{\mathtt {gen}}]&(2),\ (\alpha \not \in free(\epsilon ))\\4:&id:\forall \alpha .\alpha \rightarrow \alpha \vdash _{d}id:\forall \alpha .\alpha \rightarrow \alpha &[{\mathtt {var}}]&(id:\forall \alpha .\alpha \rightarrow \alpha \in \left\{id:\forall \alpha .\alpha \rightarrow \alpha \right\})\\5:&\vdash _{d}{\textbf {let}}\,id=\lambda x.x\ {\textbf {in}}\ id\,:\,\forall \alpha .\alpha \rightarrow \alpha &[{\mathtt {let}}]&(3),\ (4)\\\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6846501ab44a6bca4f3571e69694d3955747c0a0 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda x.e} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fcb5f3a8a1039d03c539764cef14eb9a03192fdf height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ,\ x:\tau \vdash _{d}e:\tau '} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5e2c347b0d16b819ddb1ee61f4b599c5f592e20 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ,\ x:\sigma \vdash _{d}e_{1}:\tau } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a height: height attribute not set width: width attribute not set description: {\displaystyle \lambda } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/12307fcbdcb8001d520c8633dd2019648ec65c6b height: height attribute not set width: width attribute not set description: {\displaystyle \lambda f.(f\,{\textrm {true}},f\,{\textrm {0}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ac009cabcabe3ab29e9aae919072a7b2b6fe3b1a height: height attribute not set width: width attribute not set description: {\displaystyle {\textbf {let}}\ f=\lambda x.x\,{\textbf {in}}\,(f\,{\textrm {true}},f\,{\textrm {0}})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc9183a52040ee9115fcac55896a46f7ea4c0412 height: height attribute not set width: width attribute not set description: {\displaystyle (bool,int)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4fad2bce626384c0e0f02c65941e8ae5048050af height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{d}e:\sigma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f651717191876215501149b018707753412d91a5 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{cl}\displaystyle {\frac {x:\sigma \in \gamma \quad \sigma \sqsubseteq \tau }{\gamma \vdash _{s}x:\tau }}&[{\mathtt {var}}]\\\\\displaystyle {\frac {\gamma \vdash _{s}e_{0}:\tau \rightarrow \tau '\quad \quad \gamma \vdash _{s}e_{1}:\tau }{\gamma \vdash _{s}e_{0}\ e_{1}:\tau '}}&[{\mathtt {app}}]\\\\\displaystyle {\frac {\gamma ,\;x:\tau \vdash _{s}e:\tau '}{\gamma \vdash _{s}\lambda \ x\ .\ e:\tau \rightarrow \tau '}}&[{\mathtt {abs}}]\\\\\displaystyle {\frac {\gamma \vdash _{s}e_{0}:\tau \quad \quad \gamma ,\,x:{\bar {\gamma }}(\tau )\vdash _{s}e_{1}:\tau '}{\gamma \vdash _{s}{\mathtt {let}}\ x=e_{0}\ {\mathtt {in}}\ e_{1}:\tau '}}&[{\mathtt {let}}]\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1065f21ceb3bee19a6ab62b85ad5638d288dbecd height: height attribute not set width: width attribute not set description: {\displaystyle {\bar {\gamma }}(\tau )=\forall \ {\hat {\alpha }}\ .\ \tau \quad \quad {\hat {\alpha }}={\textrm {free}}(\tau )-{\textrm {free}}(\gamma )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa1cd1c630e80ca50281a1622ec418f7f6bc3b6d height: height attribute not set width: width attribute not set description: {\displaystyle {\bar {\gamma }}(\tau )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2e468b05943f8f7a12ba93fdf5bc8919486045cf height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{d}\ e:\sigma \leftrightarrow \gamma \vdash _{s}\ e:\sigma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ae29eefbd82b20bb9ccf77024f55f1f10e69b655 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{d}\ e:\sigma \leftarrow \gamma \vdash _{s}\ e:\sigma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa49c82d2fbdf1b7eb367a0769815c09b8f127ab height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{d}\ e:\sigma \rightarrow \gamma \vdash _{s}\ e:\sigma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c9afdb3180b40e769771228151e7df259d5e8863 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda \ x.x:\forall \alpha .\alpha \rightarrow \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eb4d9a95574935d5623c01ff6723690ea1f47db1 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda \ x.x:\alpha \rightarrow \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d07254cfc5b7f63648c8e5c89bbd8cd3406ab81a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{d}\ e:\sigma \rightarrow \gamma \vdash _{s}\ e:\tau \wedge {\bar {\gamma }}(\tau )\sqsubseteq \sigma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3cdba2d16a861158dec68f9572b80b37a849dfc5 height: height attribute not set width: width attribute not set description: {\displaystyle \tau \rightarrow \tau '} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7f0de0e9a1a02b9be081008594ef621d06c60809 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathtt {union}}(a,b)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe94a01f9724acb484213b8d45d3fd6cb29999f7 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{cl}\displaystyle {\frac {x:\sigma \in \gamma \quad \tau ={\mathit {inst}}(\sigma )}{\gamma \vdash _{j}x:\tau }}&[{\mathtt {var}}]\\\\\displaystyle {\frac {\gamma \vdash _{j}e_{0}:\tau _{0}\quad \gamma \vdash _{j}e_{1}:\tau _{1}\quad \tau '={\mathit {newvar}}\quad {\mathit {unify}}(\tau _{0},\ \tau _{1}\rightarrow \tau ')}{\gamma \vdash _{j}e_{0}\ e_{1}:\tau '}}&[{\mathtt {app}}]\\\\\displaystyle {\frac {\tau ={\mathit {newvar}}\quad \gamma ,\;x:\tau \vdash _{j}e:\tau '}{\gamma \vdash _{j}\lambda \ x\ .\ e:\tau \rightarrow \tau '}}&[{\mathtt {abs}}]\\\\\displaystyle {\frac {\gamma \vdash _{j}e_{0}:\tau \quad \quad \gamma ,\,x:{\bar {\gamma }}(\tau )\vdash _{j}e_{1}:\tau '}{\gamma \vdash _{j}{\mathtt {let}}\ x=e_{0}\ {\mathtt {in}}\ e_{1}:\tau '}}&[{\mathtt {let}}]\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ff656f71ab2c8ac66c90253a20f03e71e42c4ed4 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ,e} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf725360386838057b3e502dfddce41dccb0dca3 height: height attribute not set width: width attribute not set description: {\displaystyle inst(\sigma )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/67bd3334e9fce99663a37676bf600b21110632da height: height attribute not set width: width attribute not set description: {\displaystyle newvar} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5fdcdd56318cce7bbfc9aaa8afd4c2ae42f071aa height: height attribute not set width: width attribute not set description: {\displaystyle {\mathit {unify}}(\alpha ,\tau )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4513de75971656d0dfed037102378a78744e016c height: height attribute not set width: width attribute not set description: {\displaystyle \lambda \ x.(x\ x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc5288af03959cb7a5c0ee54a5619f6fb88fbfc3 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda f.(f\ 1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a08dc2862dc3b6c387c1c67376a7af05d2c434d8 height: height attribute not set width: width attribute not set description: {\displaystyle int\rightarrow \beta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1154c05f1fc18a4ef70af846f7f3cc5188c88b4e height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash _{s}e:\tau \quad \longrightarrow \quad s\gamma \vdash _{s}e:s\tau } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/431b94815103ac9dc77d0e92739456c3c2c90803 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{cl}\displaystyle {\frac {x:\sigma \in \gamma \quad \tau ={\mathit {inst}}(\sigma )}{\gamma \vdash _{w}x:\tau ,\emptyset }}&[{\mathtt {var}}]\\\\\displaystyle {\frac {\begin{array}{ll}\gamma \vdash _{w}e_{0}:\tau _{0},s_{0}&s_{0}\gamma \vdash _{w}e_{1}:\tau _{1},s_{1}\\\tau '={\mathit {newvar}}&s_{2}={\mathsf {mgu}}(s_{1}\tau _{0},\ \tau _{1}\rightarrow \tau ')\end{array}}{\gamma \vdash _{w}e_{0}\ e_{1}:s_{2}\tau ',s_{2}s_{1}s_{0}}}&[{\mathtt {app}}]\\\\\displaystyle {\frac {\tau ={\mathit {newvar}}\quad \gamma ,\;x:\tau \vdash _{w}e:\tau ',s}{\gamma \vdash _{w}\lambda \ x\ .\ e:s\tau \rightarrow \tau ',s}}&[{\mathtt {abs}}]\\\\\displaystyle {\frac {\gamma \vdash _{w}e_{0}:\tau ,s_{0}\quad s_{0}\gamma ,\,x:{\overline {s_{0}\gamma }}(\tau )\vdash _{w}e_{1}:\tau ',s_{1}}{\gamma \vdash _{w}{\mathtt {let}}\ x=e_{0}\ {\mathtt {in}}\ e_{1}:\tau ',s_{1}s_{0}}}&[{\mathtt {let}}]\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8792f019258d1fdba8c903fdda01acac90c44596 height: height attribute not set width: width attribute not set description: {\displaystyle {\textit {union}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de6e810a93f67802ecb603ee0e3324005c6e583e height: height attribute not set width: width attribute not set description: {\displaystyle s_{i}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8156fe6d62a8255800e7bbd35a95c97945b24685 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma \vdash e:\tau ,s} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2c340d15e9b48dcf938db89bbfb426ee850809 height: height attribute not set width: width attribute not set description: {\displaystyle {\textsf {mgu}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c4fcefd1443ca4dcaee505dc2e2fe822427e9b1 height: height attribute not set width: width attribute not set description: {\displaystyle 1:int,\ f:\alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/57faa5323feecd210c841bb92cfdfea70cdd667a height: height attribute not set width: width attribute not set description: {\displaystyle f\ 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8 height: height attribute not set width: width attribute not set description: {\displaystyle \beta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3ed4cf396a53bc917bed1db9ba1485ac4c2d1c59 height: height attribute not set width: width attribute not set description: {\displaystyle \left\{\alpha \mapsto int\rightarrow \beta \right\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bccb78581742dc2911b9e6bdcf8cb73adcecce94 height: height attribute not set width: width attribute not set description: {\displaystyle free(\gamma )=\emptyset } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/45993f47d07a4ad31afd97a39e839422177b7473 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{lll}{\text{(correctness)}}&\gamma \vdash _{w}e:\tau ,s&\quad \longrightarrow \quad \gamma \vdash _{s}e:\tau \\{\text{(completeness)}}&\gamma \vdash _{s}e:\tau &\quad \longrightarrow \quad \gamma \vdash _{w}e:\tau ',s\quad \quad {\text{forall}}\ \tau \ {\text{where}}\ {\overline {\emptyset }}(\tau ')\sqsubseteq \tau \end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2 height: height attribute not set width: width attribute not set description: {\displaystyle s} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb886cf09eaf9c22665e9265872dd570aa9c3fe5 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathit {fix}}:\forall \alpha .(\alpha \rightarrow \alpha )\rightarrow \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/96fcd9232dd58973b7c483bcf403d3e09d8f5d18 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathtt {rec}}\ v=e_{1}\ {\mathtt {in}}\ e_{2}\ ::={\mathtt {let}}\ v={\mathit {fix}}(\lambda v.e_{1})\ {\mathtt {in}}\ e_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/60420139b5a66ee5266a37bf8e5d64d2d481c973 height: height attribute not set width: width attribute not set description: {\displaystyle \displaystyle {\frac {\gamma ,\gamma '\vdash e_{1}:\tau _{1}\quad \dots \quad \gamma ,\gamma '\vdash e_{n}:\tau _{n}\quad \gamma ,\gamma ''\vdash e:\tau }{\gamma \ \vdash \ {\mathtt {rec}}\ v_{1}=e_{1}\ {\mathtt {and}}\ \dots \ {\mathtt {and}}\ v_{n}=e_{n}\ {\mathtt {in}}\ e:\tau }}\quad [{\mathtt {rec}}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d551ec676acf7fa3c1a440075c06e3b1f2ded8 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma '=v_{1}:\tau _{1},\ \dots ,\ v_{n}:\tau _{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ff80de1ed823194a74cd80cf9a83b792166ad579 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ''=v_{1}:{\bar {\gamma }}(\ \tau _{1}\ ),\ \dots ,\ v_{n}:{\bar {\gamma }}(\ \tau _{n}\ )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d05c89f1e91c5b58141222fd17f76e6922d7f40c height: height attribute not set width: width attribute not set description: {\displaystyle {\mathtt {in}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ce6c9508fcaf9efc73c105a2577fb0901b0d70ad height: height attribute not set width: width attribute not set description: {\displaystyle \forall a.a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7e427a55bc001434e2a87abf838cce38cfbece66 height: height attribute not set width: width attribute not set description: {\displaystyle *\to *} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1e07a72ce124f90f49f1116fb06547c8864d7f47 height: height attribute not set width: width attribute not set description: {\displaystyle \forall \alpha .\ (\alpha \leq t)\rightarrow \alpha \rightarrow \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81201e11b7e57d61b0edd41ae2778bdd22a8396e height: height attribute not set width: width attribute not set description: {\displaystyle \alpha \leq t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e7f2513ad12a638bd485fd3a582c7115e0cffa0 height: height attribute not set width: width attribute not set description: {\displaystyle f_{<:}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b03dc6c76cbfc66f8f82c5d97f46b3f8ef39ae01 height: height attribute not set width: width attribute not set description: {\displaystyle c\ \tau \dots \tau } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ddd5f03e663651b7cb450dd5a9dfa662e19992b6 height: height attribute not set width: width attribute not set description: {\displaystyle \tau \rightarrow \tau } |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.png height: 31 width: 88 description: wikimedia foundation |
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http://en.wikipedia.org/static/images/footer/poweredby_mediawiki_88x31.png height: 31 width: 88 description: powered by mediawiki |
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