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<blockquote data-quote="deaf_judger" data-source="post: 66419" data-attributes="member: 390">[PLAIN]Introduction[/PLAIN]&nbsp; [PLAIN]MiniKanren is an embedded constraint logic programming language designed for writing programs as [/PLAIN][PLAIN]relations[/PLAIN][PLAIN], rather than as functions or procedures. Unlike a function, a miniKanren relation makes no distinction between its inputs and outputs, leading to a variety of fascinating behaviors. For example, an interpreter written as a relation can also perform code synthesis, symbolic execution, and many other tasks. Core miniKanren has only 3 operators:&nbsp; [/PLAIN]&nbsp;
<ol>
<li data-xf-list-type="ol">[PLAIN]Unification: a two-way pattern matcher. It can be thought of as a type of equality operator. It matches variables on both sides. 
&nbsp; [/PLAIN] 
 
&nbsp; [CODE] 
&nbsp; &nbsp; [== 5 5] 
&nbsp; [/CODE] 
&nbsp; [PLAIN]This asserts that 5 is equal to 5, and will return [/PLAIN]`False&#039; [PLAIN]if it isnt. However, if a variable we dont know like `(== x&nbsp; 5)` is put in, x is also 5. This is an assertion. Just like the lisp I am building, each line is seperate.&nbsp; `(eq x 5) and (eq x 6)` is not&nbsp; &nbsp; inconsistent, because they are different branches. 
&nbsp; [/PLAIN] 
&nbsp;</li>
<li data-xf-list-type="ol">`fresh&#039;[PLAIN]: fresh introduces scoped logic variables; goals inside a fresh form are implicitly conjoined. 
&nbsp; [/PLAIN] 
&nbsp;</li>
<li data-xf-list-type="ol">`conde&#039;[PLAIN]: Disjunction. This is similar to lisps [/PLAIN]`cond&#039; [PLAIN]operator.&nbsp; It allows us to get multiple answers.&nbsp;&nbsp; We can see the result of each clause independently. Each clause represents an alternative logical branch; results are interleaved fairly during search. 
&nbsp; [/PLAIN] 
 
&nbsp; [CODE] 
&nbsp; &nbsp; (fresh (y) 
&nbsp; &nbsp; (conde 
&nbsp; &nbsp; ((== x 5)) 
&nbsp; &nbsp; ((== x 6)) 
&nbsp; &nbsp; ) 
&nbsp; [/CODE] 
&nbsp; [PLAIN]Will give [/PLAIN]`True&#039;[PLAIN], and [/PLAIN]`True&#039;[PLAIN]. Although the information appears inconsistent. 
&nbsp; [/PLAIN] 
&nbsp;</li>
</ol>[PLAIN]Representing Syntax[/PLAIN]&nbsp; [PLAIN]To move beyond simple scalars (like 5 or 6), we use recursive relations to define grammars. A Lambda Calculus term consists of three parts: Variables, Abstractions (Lambdas), and Applications.&nbsp; [/PLAIN]&nbsp; [CODE]&nbsp; x #variable. . We use the symbolo constraint to ensure a logic variable represents a scheme symbol.&nbsp; \lambda x. y #abstraction&nbsp; (f arg) # application&nbsp; [/CODE][PLAIN]Divergent Search[/PLAIN]&nbsp; [PLAIN]Because these are relations, we can use the same code for three distinct purposes by changing which parts of the call are &quot;logic variables&quot; (unknowns).&nbsp; [/PLAIN]&nbsp;
<ul>
<li data-xf-list-type="ul">`(LC-syn &#039;(lambda (x) x))&#039; [PLAIN]Returns Success. 
&nbsp; [/PLAIN] 
&nbsp;</li>
<li data-xf-list-type="ul">`(LC-syn q)&#039;&nbsp; [PLAIN]Returns an infinite stream of all possible valid Lambda Calculus terms. 
&nbsp; [/PLAIN] 
&nbsp;</li>
<li data-xf-list-type="ul">`(LC-syn &#039;(lambda (x) ,q))&#039; [PLAIN]and this fills the hole with valid bodies. 
&nbsp; [/PLAIN] 
&nbsp;</li>
</ul>[PLAIN]Type Inference and the Turnstile[/PLAIN]&nbsp; [PLAIN]([/PLAIN]$\Gamma \vdash e : \tau$[PLAIN]) The &quot;Vision&quot; concludes by showing that an interpreter/type-checker written relationally can perform type synthesis.&nbsp; [/PLAIN]&nbsp;
<ul>
<li data-xf-list-type="ul">[PLAIN]Environment ([/PLAIN]$\Gamma$[PLAIN]): A mapping of variables to types. 
&nbsp; [/PLAIN] 
&nbsp;</li>
<li data-xf-list-type="ul">[PLAIN]Expression ([/PLAIN]$e$[PLAIN]): The program code. 
&nbsp; [/PLAIN] 
&nbsp;</li>
<li data-xf-list-type="ul">[PLAIN]Type ([/PLAIN]$\tau$[PLAIN]): The resulting type (e.g., Int, Bool, or a function type). 
&nbsp; [/PLAIN] 
&nbsp;</li>
</ul>&nbsp; [PLAIN]Now, if you provide&nbsp; an expresion, it returns the type. If you provide a type, it generates all expressions that inhabit that type. This is achieved through the turnstile relation which recursively matches the structure of the expression against the typing rules of the language.&nbsp; [/PLAIN][PLAIN]References[/PLAIN]&nbsp; Erlang Solutions, ed. 2015. /A Vision for Relational Programming in&nbsp; miniKanren - William E. Byrd/. Directed by Erlang&nbsp; Solutions. &lt;[MEDIA=youtube]8gh4Ald4yZQ[/MEDIA]&gt;.</blockquote>

[QUOTE="deaf_judger, post: 66419, member: 390"] [B][SIZE=6][PLAIN]Introduction[/PLAIN][/SIZE][/B] [PLAIN]MiniKanren is an embedded constraint logic programming language designed for writing programs as [/PLAIN][B][PLAIN]relations[/PLAIN][/B][PLAIN], rather than as functions or procedures. Unlike a function, a miniKanren relation makes no distinction between its inputs and outputs, leading to a variety of fascinating behaviors. For example, an interpreter written as a relation can also perform code synthesis, symbolic execution, and many other tasks. Core miniKanren has only 3 operators: [/PLAIN] [LIST=1] [*][PLAIN]Unification: a two-way pattern matcher. It can be thought of as a type of equality operator. It matches variables on both sides. [/PLAIN] [CODE] [== 5 5] [/CODE] [PLAIN]This asserts that 5 is equal to 5, and will return [/PLAIN]`False' [PLAIN]if it isnt. However, if a variable we dont know like `(== x 5)` is put in, x is also 5. This is an assertion. Just like the lisp I am building, each line is seperate. `(eq x 5) and (eq x 6)` is not inconsistent, because they are different branches. [/PLAIN] [*]`fresh'[PLAIN]: fresh introduces scoped logic variables; goals inside a fresh form are implicitly conjoined. [/PLAIN] [*]`conde'[PLAIN]: Disjunction. This is similar to lisps [/PLAIN]`cond' [PLAIN]operator. It allows us to get multiple answers. We can see the result of each clause independently. Each clause represents an alternative logical branch; results are interleaved fairly during search. [/PLAIN] [CODE] (fresh (y) (conde ((== x 5)) ((== x 6)) ) [/CODE] [PLAIN]Will give [/PLAIN]`True'[PLAIN], and [/PLAIN]`True'[PLAIN]. Although the information appears inconsistent. [/PLAIN] [/LIST] [B][SIZE=6][PLAIN]Representing Syntax[/PLAIN][/SIZE][/B] [PLAIN]To move beyond simple scalars (like 5 or 6), we use recursive relations to define grammars. A Lambda Calculus term consists of three parts: Variables, Abstractions (Lambdas), and Applications. [/PLAIN] [CODE] x #variable. . We use the symbolo constraint to ensure a logic variable represents a scheme symbol. \lambda x. y #abstraction (f arg) # application [/CODE] [B][SIZE=6][PLAIN]Divergent Search[/PLAIN][/SIZE][/B] [PLAIN]Because these are relations, we can use the same code for three distinct purposes by changing which parts of the call are "logic variables" (unknowns). [/PLAIN] [LIST] [*]`(LC-syn '(lambda (x) x))' [PLAIN]Returns Success. [/PLAIN] [*]`(LC-syn q)' [PLAIN]Returns an infinite stream of all possible valid Lambda Calculus terms. [/PLAIN] [*]`(LC-syn '(lambda (x) ,q))' [PLAIN]and this fills the hole with valid bodies. [/PLAIN] [/LIST] [B][SIZE=6][PLAIN]Type Inference and the Turnstile[/PLAIN][/SIZE][/B] [PLAIN]([/PLAIN]$\Gamma \vdash e : \tau$[PLAIN]) The "Vision" concludes by showing that an interpreter/type-checker written relationally can perform type synthesis. [/PLAIN] [LIST] [*][PLAIN]Environment ([/PLAIN]$\Gamma$[PLAIN]): A mapping of variables to types. [/PLAIN] [*][PLAIN]Expression ([/PLAIN]$e$[PLAIN]): The program code. [/PLAIN] [*][PLAIN]Type ([/PLAIN]$\tau$[PLAIN]): The resulting type (e.g., Int, Bool, or a function type). [/PLAIN] [/LIST] [PLAIN]Now, if you provide an expresion, it returns the type. If you provide a type, it generates all expressions that inhabit that type. This is achieved through the turnstile relation which recursively matches the structure of the expression against the typing rules of the language. [/PLAIN] [B][SIZE=6][PLAIN]References[/PLAIN][/SIZE][/B] Erlang Solutions, ed. 2015. /A Vision for Relational Programming in miniKanren - William E. Byrd/. Directed by Erlang Solutions. <[MEDIA=youtube]8gh4Ald4yZQ[/MEDIA]>. [/QUOTE]

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