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# Dusa Language | ||
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[![Coverage Status](https://coveralls.io/repos/github/robsimmons/dusa/badge.svg?branch=main)](https://coveralls.io/github/robsimmons/dusa?branch=main) | ||
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Dusa is a logic programming language that shares properties of Datalog (as implemented in systems like | ||
[Soufflé](https://souffle-lang.github.io/program)) and Answer Set Programming (as implemented in systems | ||
like [Potassco](https://potassco.org/)). | ||
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Dusa lives online at [dusa.rocks](https://dusa.rocks/). | ||
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# Quick start | ||
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## Introduction to Datalog | ||
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Datalog-like languages try to use logical implication to express the sorts of problems that, in a | ||
language like SQL, you would solve with database joins. The simplest declarations in Dusa are just | ||
declaring facts, like who a character's parent is. | ||
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parent "Arya" "Catelyn". | ||
parent "Arya" "Eddard". | ||
parent "Brandon" "Rickard". | ||
parent "Eddard" "Lyarra". | ||
parent "Eddard" "Rickard". | ||
parent "Rickard" "Edwyle". | ||
parent "Rickard" "Marna". | ||
parent "Sansa" "Catelyn". | ||
parent "Sansa" "Eddard". | ||
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You can use these facts and logical implication to derive more facts, like "if X's parent is Y, and Y's | ||
parent is Z, then the grandparent of X is Z." That looks like this: | ||
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grandparent X Z :- parent X Y, parent Y Z. | ||
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It's also easy to have inferences that build on each other: an ancestor is either your parent or an | ||
ancestor of your parent. In Dusa, that looks like this: | ||
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ancestor X Y :- parent X Y. | ||
ancestor X Z :- parent X Y, ancestor Y Z. | ||
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Using these rules, Dusa will calculate all of Arya's ancestors: Catelyn, Eddard, Edwyle, Marna, and | ||
Rickard. | ||
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## Propositions: relations and functions | ||
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The propositions in the previous section were all _relations_. Each of `parent`, `grandparent`, | ||
and `ancestor` were relations between two characters. | ||
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It's also possible to have propositions that are functions. | ||
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- Relations look like this: `prop t1 t2 ... tn-1 tn` | ||
- Functions look like this: `prop t1 t2 ... tn-1 is tn` | ||
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A function describes a unique key-value relationship. Familiar relationships don't work like that: Arya | ||
has multiple parents and Eddard has multiple children. But we could use `weapon Char is W` as a | ||
functional proposition to describe a character's favorite weapon. | ||
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weapon "Arya" is "smallsword". | ||
weapon "Eddard" is "greatsword". | ||
weapon "Sansa" is "bow". | ||
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## Integrity constraints | ||
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Functional propositions create integrity constraints on the database of facts that Dusa maintains. | ||
If these constraints are violated by saying that multiple keys map to the same value, then the database | ||
is thrown out completely. | ||
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Consider trying to make `sibling` a functional proposition instead of a relational proposition in our | ||
example, like this: | ||
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sibling A is B :- parent A P, parent B P, A != B. | ||
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This will work initially, deriving that Arya and Sansa are siblings, as are Brandon and Eddard. But if | ||
we then add a seemingly innoccuous additional fact... | ||
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parent "Bran" "Eddard". | ||
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...then Dusa will report that there are no solutions. By trying to derive both `sibling "Arya" is | ||
"Sansa"` and `sibling "Arya" is "Bran"`, the database failed an integrity constraint. The right solution | ||
here is to make the `sibling` relationship a relation, not a function. | ||
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Integrity constraints can also be added with the `#forbid` and `#demand` directives. If we want to | ||
insist that no two characters have the same weapon, we can write. | ||
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#forbid weapon Char1 is W, weapon Char2 is W, Char1 != Char2. | ||
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Note that it's necessary to say `Char1 != Char2`. If we left that out, Dusa could match both `Char1` | ||
and `Char2` to `"Arya"` and therefore invalidate the database for violating an integrity constraint. | ||
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A `#demand` predicate expresses something that must be true in order for the database to be valid. This | ||
can be used like an assertion in programming, invalidating the database if an expected fact doesn't | ||
hold. If we want to make sure we derive Marna as an ancestor of Arya, we can write this: | ||
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#demand ancestor "Arya" "Marna". | ||
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## Introduction to answer set programming | ||
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Answer set programming is a way of writing Datalog-like programs to compute acceptable models (answer | ||
sets) that meet certain contraints. Whereas traditional Datalog aims to compute just one database (or | ||
zero databases, if an integrity constraint fails), answer set programming allows different choices to | ||
be made that let multiple possible databases diverge. | ||
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Dusa allows this kind of programming by supporting mutually exclusive assignments to a functional | ||
predicate. Any assignment which satisfies all integrity constraints is a valid solution. (Answer set | ||
programming calls them "answer sets" or "models," Dusa calls them "solutions," but they're the same | ||
concept.) | ||
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If we have three suspects, Amy, Harry, and Sally, we can assign each of them guilt or | ||
innocence with the following program: | ||
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suspect amy. | ||
suspect harry. | ||
suspect sally. | ||
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guilt Susp is { innocent, guilty } :- suspect Susp. | ||
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Dusa will, in no particular order, generate eight different solutions, corresponding to the two | ||
different guilt assignments for the three suspects. | ||
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If we then add a constraint that only one suspect may be guilty... | ||
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#forbid guilt Susp1 is guilty, guilt Susp2 is guilty, Susp1 != Susp2. | ||
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...Dusa will only be able to generate four solutions, one where each suspect is guilty and one where all | ||
suspects are innocent. If we want someone to be guilty, which would limit us to three models, we can specify | ||
that too: | ||
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#demand guilt _ is guilty. | ||
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# Syntax | ||
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## Lexical tokens | ||
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- A `<variable>` matches `/[A-Z][a-zA-Z0-9_]*/` | ||
- A `<wildcard>` matches `/_[a-zA-Z0-9_]*/` and represents variable names that you wish to be ignored. | ||
- An `<identifier>` matches `/[a-z][a-zA-Z0-9_]` | ||
- A `<string-literal>` is a regular string constant with no escape characters: two double quotes `"` | ||
surrounding any ASCII character in the range 32-126 except for `"` and `\`. | ||
- An `<int-literal>` matches `/0|-?[1-9][0-9]*/` | ||
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## Grammar | ||
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<program> ::= <declaration> <program> | "" | ||
<declaration> ::= "#builtin" <builtin> <identifier> [ "." ] | ||
| "#demand" <premises> "." | ||
| "#forbid" <premises> "." | ||
| <conclusion> ":-" <premises> "." | ||
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<premises> ::= <premise> | <premise> "," <premises> | ||
<premise> ::= <term> "!=" <term> | ||
| <term> "==" <term> | ||
| <attribute> | ||
| <attribute> "is" <term> | ||
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<conclusion> ::= <attribute> | ||
| <attribute> "is" <term> | ||
| <attribute> "is" "{" <options> "}" | ||
<conc-options> ::= <term> | <term> "?" | <conc-option> "," <conc-options> | ||
<conc-option> ::- <term> | "?" | ||
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<attribute> ::= <identifier> | <identifier> <arguments> | ||
<arguments> ::= <atomic-term> | <atomic-term> <arguments> | ||
<atomic-term> ::= <wildcard> | <variable> | ||
| <string-literal> | <int-literal> | ||
| <identifier> | <builtin-identifier> | ||
| "(" <term> ")" | ||
<term> ::= <atomic-term> | ||
| <identifier> <arguments> | ||
| <builtin-identifier> <arguments> | ||
<builtin> ::= "INT_PLUS" | "INT_MINUS" | ||
| "NAT_ZERO" | "NAT_SUCC" | ||
| "STRING_CONCAT" | ||
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## Built-in values and constructors | ||
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On their own, built-in numbers and strings act no different than random uninterpreted constants, | ||
but they can be manipualted with special constructors added by `#builtin` declarations. | ||
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A `#builtin` declarations change the lexer to represent certain identifiers as operations on built-in | ||
types. If you write | ||
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#builtin INT_PLUS plus | ||
#builtin NAT_SUCC s | ||
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then the identifiers `plus` and `s` will be parsed as `<builtin-identifiers>` instead of as regular | ||
identifiers until those built-ins are redefined. | ||
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- The `NAT_ZERO` builtin takes no arguments and represents the natural number zero. | ||
- The `NAT_SUCC` builtin takes one natural number argument, and adds one to it. If `NAT_SUCC` is `s`, | ||
then the premise `s X == 0` will always fail, since `X` would have to be negative for that solution | ||
to work. | ||
- The `INT_PLUS` builtin takes two or more integer arguments and adds them all. | ||
- The `INT_MINUS` builtin takes two integer arguments and returns an integer, subtracting the second | ||
from the first. | ||
- The `STRING_CONCAT` builtin takes two or more string arguments and concatenates them. |
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