Merge branch 'fix-pnf' into dev

Cargo.toml

@@ -4,3 +4,8 @@ edition = "2018"
 name = "laddertypes"
 version = "0.1.0"
 
+[dependencies]
+tiny-ansi = { version = "0.1.0", optional = true }
+
+[features]
+pretty = ["dep:tiny-ansi"]

README.md

@@ -5,6 +5,8 @@ Rust Implementation of Ladder-Types (parsing, unification, rewriting, etc)
 
 ## Ladder Types
 
+### Motivation
+
 In order to implement complex datastructures and algorithms, usually
 many layers of abstraction are built ontop of each other.
 Consequently higher-level data types are encoded into lower-level data
@@ -57,6 +59,48 @@ this:
 1696093021:1696093039:1528324679:1539892301:1638141920:1688010253
 ```
 
+### Syntax
+
+In their core form, type-terms can be one of the following:
+- (**Atomic Type**)        |   `SomeTypeName`
+- (**Literal Integer**)    |   `0` | `1` | `2` | ...
+- (**Literal Character**)  |   `'a'` | `'b'` | `'c'` | ...
+- (**Literal String**)     |   `"abc"`
+- (**Parameter Application**) | `<T1 T2>` given `T1` and `T2` are type-terms
+- (**Ladder**)                | `T1 ~ T2` given `T1` and `T2` are type-terms
+
+Ontop of that, the following syntax-sugar is defined:
+
+#### Complex Types
+- `[ T ]` <===> `<Seq T>`
+- `{ a:A b:B }` <===> `<Struct <"a" A> <"b" B>>`
+- `a:A | b:B` <===> `<Enum <"a" A> <"b" B>>`
+
+#### Function Types
+- `A -> B` <===> `<Fn A B>`
+
+#### Reference Types
+- `*A`  <===> `<Ptr A>`
+- `&A`  <===> `<ConstRef A>`
+- `&!A` <===> `<MutRef A>`
+
+
+### Equivalences
+
+#### Currying
+`<<A B> C>` <===> `<A B C>`
+
+#### Ladder-Normal-Form
+exhaustively apply `<A B~C>` ===> `<A B>~<A C>`
+
+e.g. `[<Digit 10>]~[Char]~[Ascii]` is in **LNF**
+
+#### Parameter-Normal-Form
+exhaustively apply `<A B>~<A C>` ===> `<A B~C>`
+
+e.g. `[<Digit 10>~Char~Ascii]` is in **PNF**
+
+
 ## How to use this crate
 
 ```rust
@@ -73,6 +117,19 @@ fn main() {
 }
 ```
 
+## Roadmap
+
+- [x] (Un-)Parsing
+- [x] (De-)Currying
+- [x] Unification
+- [x] Ladder-Normal-Form
+- [x] Parameter-Normal-Form
+- [ ] (De)-Sugaring
+  - [ ] Seq
+  - [ ] Enum
+  - [ ] Struct
+  - [ ] References
+  - [ ] Function
 
 ## License
 [GPLv3](COPYING)

src/dict.rs

@@ -2,7 +2,7 @@ use crate::bimap::Bimap;
 
 //<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
 
-#[derive(Eq, PartialEq, Hash, Clone, Debug)]
+#[derive(Eq, PartialEq, Hash, Clone, Copy, Debug)]
 pub enum TypeID {
     Fun(u64),
     Var(u64)
@@ -54,6 +54,10 @@ impl TypeDict {
     pub fn get_typeid(&self, tn: &String) -> Option<TypeID> {
         self.typenames.mλ.get(tn).cloned()
     }
+
+    pub fn get_varname(&self, var_id: u64) -> Option<String> {
+        self.typenames.my.get(&TypeID::Var(var_id)).cloned()
+    }
 }
 
 //<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>

src/lib.rs

@@ -5,17 +5,22 @@ pub mod term;
 pub mod lexer;
 pub mod parser;
 pub mod unparser;
+pub mod sugar;
 pub mod curry;
 pub mod lnf;
+pub mod pnf;
 pub mod subtype;
 pub mod unification;
 
 #[cfg(test)]
 mod test;
 
+#[cfg(feature = "pretty")]
+mod pretty;
+
 pub use {
     dict::*,
     term::*,
-    unification::*
+    sugar::*,
+    unification::*,
 };
-

src/pnf.rs

@@ -0,0 +1,138 @@
+use crate::term::TypeTerm;
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
+
+pub fn splice_ladders( mut upper: Vec< TypeTerm >, mut lower: Vec< TypeTerm >  ) -> Vec< TypeTerm > {
+    for i in 0 .. upper.len() {
+        if upper[i] == lower[0] {
+            let mut result_ladder = Vec::<TypeTerm>::new();
+            result_ladder.append(&mut upper[0..i].iter().cloned().collect());
+            result_ladder.append(&mut lower);
+            return result_ladder;
+        }
+    }
+
+    upper.append(&mut lower);
+    upper
+}
+
+impl TypeTerm {
+    /// transmute type into Parameter-Normal-Form (PNF)
+    ///
+    /// Example:
+    /// ```ignore
+    /// <Seq <Digit 10>>~<Seq Char>
+    /// ⇒ <Seq <Digit 10>~Char>
+    /// ```
+    pub fn param_normalize(mut self) -> Self {
+        match self {
+            TypeTerm::Ladder(mut rungs) => {
+                if rungs.len() > 0 {
+                    let mut new_rungs = Vec::new();
+                    while let Some(bottom) = rungs.pop() {
+                        if let Some(last_but) = rungs.last_mut() {
+                            match (bottom, last_but) {
+                                (TypeTerm::App(bot_args), TypeTerm::App(last_args)) => {
+                                    if bot_args.len() == last_args.len() {
+                                        let mut new_rung_params = Vec::new();
+                                        let mut require_break = false;
+
+                                        if bot_args.len() > 0 {
+                                            if let Ok(_idx) =  last_args[0].is_syntactic_subtype_of(&bot_args[0]) {
+                                                for i in 0 .. bot_args.len() {
+
+                                                    let spliced_type_ladder = splice_ladders(
+                                                        last_args[i].clone().get_lnf_vec(),
+                                                        bot_args[i].clone().get_lnf_vec()
+                                                    );
+                                                    let spliced_type =
+                                                        if spliced_type_ladder.len() == 1 {
+                                                            spliced_type_ladder[0].clone()
+                                                        } else if spliced_type_ladder.len() > 1 {
+                                                            TypeTerm::Ladder(spliced_type_ladder)
+                                                        } else {
+                                                            TypeTerm::unit()
+                                                        };
+
+                                                    new_rung_params.push( spliced_type.param_normalize() );
+                                                }
+
+                                            } else {
+                                                new_rung_params.push(
+                                                    TypeTerm::Ladder(vec![
+                                                        last_args[0].clone(),
+                                                        bot_args[0].clone()
+                                                    ]).normalize()
+                                                );
+
+                                                for i in 1 .. bot_args.len() {
+                                                    if let Ok(_idx) = last_args[i].is_syntactic_subtype_of(&bot_args[i]) {
+                                                        let spliced_type_ladder = splice_ladders(
+                                                            last_args[i].clone().get_lnf_vec(),
+                                                            bot_args[i].clone().get_lnf_vec()
+                                                        );
+                                                        let spliced_type =
+                                                            if spliced_type_ladder.len() == 1 {
+                                                                spliced_type_ladder[0].clone()
+                                                            } else if spliced_type_ladder.len() > 1 {
+                                                                TypeTerm::Ladder(spliced_type_ladder)
+                                                            } else {
+                                                                TypeTerm::unit()
+                                                            };
+
+                                                        new_rung_params.push( spliced_type.param_normalize() );
+                                                    } else {
+                                                        new_rung_params.push( bot_args[i].clone() );
+                                                        require_break = true;
+                                                    }
+                                                }
+                                            }
+                                        }
+
+                                        if require_break {
+                                            new_rungs.push( TypeTerm::App(new_rung_params) );
+                                        } else {
+                                            rungs.pop();
+                                            rungs.push(TypeTerm::App(new_rung_params));
+                                        }
+
+                                    } else {
+                                        new_rungs.push( TypeTerm::App(bot_args) );
+                                    }
+                                }
+                                (bottom, last_buf) => {
+                                    new_rungs.push( bottom );
+                                }
+                            }
+                        } else {
+                            new_rungs.push( bottom );
+                        }
+                    }
+
+                    new_rungs.reverse();
+
+                    if new_rungs.len() > 1 {
+                        TypeTerm::Ladder(new_rungs)
+                    } else if new_rungs.len() == 1 {
+                        new_rungs[0].clone()
+                    } else {
+                        TypeTerm::unit()
+                    }
+                } else {
+                    TypeTerm::unit()
+                }
+            }
+
+            TypeTerm::App(params) => {
+                TypeTerm::App(
+                    params.into_iter()
+                        .map(|p| p.param_normalize())
+                        .collect())
+            }
+
+            atomic => atomic
+        }
+    }
+}
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\

src/pretty.rs

@@ -0,0 +1,148 @@
+use {
+    crate::TypeDict,
+    crate::sugar::SugaredTypeTerm,
+    tiny_ansi::TinyAnsi
+};
+
+impl SugaredTypeTerm {
+    pub fn pretty(&self, dict: &TypeDict, indent: u64) -> String {
+        let indent_width = 4;
+        match self {
+            SugaredTypeTerm::TypeID(id) => {
+                format!("{}", dict.get_typename(id).unwrap_or("??".bright_red())).bright_blue()
+            },
+
+            SugaredTypeTerm::Num(n) => {
+                format!("{}", n).bright_cyan()
+            }
+
+            SugaredTypeTerm::Char(c) => {
+                format!("'{}'", c)
+            }
+
+            SugaredTypeTerm::Univ(t) => {
+                format!("{} {} . {}",
+                    "∀".yellow().bold(),
+                    dict.get_varname(0).unwrap_or("??".into()).bright_blue(),
+                    t.pretty(dict,indent)
+                )
+            }
+
+            SugaredTypeTerm::Spec(args) => {
+                let mut s = String::new();
+                s.push_str(&"<".yellow().bold());
+                for i in 0..args.len() {
+                    let arg = &args[i];
+                    if i > 0 {
+                        s.push(' ');
+                    }
+                    s.push_str( &arg.pretty(dict,indent+1) );
+                }
+                s.push_str(&">".yellow().bold());
+                s
+            }
+
+            SugaredTypeTerm::Struct(args) => {
+                let mut s = String::new();
+                s.push_str(&"{".yellow().bold());
+                for arg in args {
+                    s.push('\n');
+                    for x in 0..(indent+1)*indent_width {
+                        s.push(' ');
+                    }
+                    s.push_str(&arg.pretty(dict, indent + 1));
+                    s.push_str(&";\n".bright_yellow());
+                }
+
+                s.push('\n');
+                for x in 0..indent*indent_width {
+                    s.push(' ');
+                }
+                s.push_str(&"}".yellow().bold());
+                s
+            }
+
+            SugaredTypeTerm::Enum(args) => {
+                let mut s = String::new();
+                s.push_str(&"(".yellow().bold());
+                for i in 0..args.len() {
+                    let arg = &args[i];
+                    s.push('\n');
+                    for x in 0..(indent+1)*indent_width {
+                        s.push(' ');
+                    }
+                    if i > 0 {
+                        s.push_str(&"| ".yellow().bold());
+                    }
+                    s.push_str(&arg.pretty(dict, indent + 1));
+                }
+
+                s.push('\n');
+                for x in 0..indent*indent_width {
+                    s.push(' ');
+                }
+                s.push_str(&")".yellow().bold());
+                s
+            }
+
+            SugaredTypeTerm::Seq(args) => {
+                let mut s = String::new();
+                s.push_str(&"[ ".yellow().bold());
+                for i in 0..args.len() {
+                    let arg = &args[i];
+                    if i > 0 {
+                        s.push(' ');
+                    }
+                    s.push_str(&arg.pretty(dict, indent+1));
+                }
+                s.push_str(&" ]".yellow().bold());
+                s
+            }
+
+            SugaredTypeTerm::Morph(args) => {
+                let mut s = String::new();
+                for arg in args {
+                    s.push_str(&"  ~~morph~~>  ".bright_yellow());
+                    s.push_str(&arg.pretty(dict, indent));
+                }
+                s
+            }
+
+            SugaredTypeTerm::Func(args) => {
+                let mut s = String::new();
+                for i in 0..args.len() {
+                    let arg = &args[i];
+                    if i > 0{
+                        s.push('\n');
+                        for x in 0..(indent*indent_width) {
+                            s.push(' ');
+                        }                
+                        s.push_str(&"-->  ".bright_yellow());
+                    } else {
+//                        s.push_str("   ");
+                    }
+                    s.push_str(&arg.pretty(dict, indent));
+                }
+                s
+            }
+
+            SugaredTypeTerm::Ladder(rungs) => {
+                let mut s = String::new();
+                for i in 0..rungs.len() {
+                    let rung = &rungs[i];
+                    if i > 0{
+                        s.push('\n');
+                        for x in 0..(indent*indent_width) {
+                            s.push(' ');
+                        }
+                        s.push_str(&"~ ".yellow());
+                    }
+                    s.push_str(&rung.pretty(dict, indent));
+                }
+                s
+            }
+        }
+    }
+}
+
+

src/sugar.rs

@@ -0,0 +1,95 @@
+use {
+    crate::{TypeTerm, TypeID}
+};
+
+pub enum SugaredTypeTerm {
+    TypeID(TypeID),
+    Num(i64),
+    Char(char),
+    Univ(Box< SugaredTypeTerm >),
+    Spec(Vec< SugaredTypeTerm >),
+    Func(Vec< SugaredTypeTerm >),
+    Morph(Vec< SugaredTypeTerm >),
+    Ladder(Vec< SugaredTypeTerm >),
+    Struct(Vec< SugaredTypeTerm >),
+    Enum(Vec< SugaredTypeTerm >),
+    Seq(Vec< SugaredTypeTerm >)
+}
+
+impl TypeTerm {
+    pub fn sugar(self: TypeTerm, dict: &mut crate::TypeDict) -> SugaredTypeTerm {
+        match self {
+            TypeTerm::TypeID(id) => SugaredTypeTerm::TypeID(id),
+            TypeTerm::Num(n) => SugaredTypeTerm::Num(n),
+            TypeTerm::Char(c) => SugaredTypeTerm::Char(c),
+            TypeTerm::App(args) => if let Some(first) = args.first() {
+                if first == &dict.parse("Func").unwrap() {
+                    SugaredTypeTerm::Func( args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect() )
+                }
+                else if first == &dict.parse("Morph").unwrap() {
+                    SugaredTypeTerm::Morph( args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect() )
+                }
+                else if first == &dict.parse("Struct").unwrap() {
+                    SugaredTypeTerm::Struct( args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect() )
+                }
+                else if first == &dict.parse("Enum").unwrap() {
+                    SugaredTypeTerm::Enum( args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect() )
+                }
+                else if first == &dict.parse("Seq").unwrap() {
+                    SugaredTypeTerm::Seq( args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect() )
+                }
+                else if first == &dict.parse("Spec").unwrap() {
+                    SugaredTypeTerm::Spec( args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect() )
+                }
+                else if first == &dict.parse("Univ").unwrap() {
+                    SugaredTypeTerm::Univ(Box::new(
+                        SugaredTypeTerm::Spec(
+                            args[1..].into_iter().map(|t| t.clone().sugar(dict)).collect()
+                        )
+                    ))
+                }
+                else {
+                    SugaredTypeTerm::Spec(args.into_iter().map(|t| t.sugar(dict)).collect())
+                }
+            } else {
+                SugaredTypeTerm::Spec(args.into_iter().map(|t| t.sugar(dict)).collect())
+            },
+            TypeTerm::Ladder(rungs) =>            
+               SugaredTypeTerm::Ladder(rungs.into_iter().map(|t| t.sugar(dict)).collect())
+        }
+    }
+}
+
+impl SugaredTypeTerm {
+    pub fn desugar(self, dict: &mut crate::TypeDict) -> TypeTerm {
+        match self {
+            SugaredTypeTerm::TypeID(id) => TypeTerm::TypeID(id),
+            SugaredTypeTerm::Num(n) => TypeTerm::Num(n),
+            SugaredTypeTerm::Char(c) => TypeTerm::Char(c),
+            SugaredTypeTerm::Univ(t) => t.desugar(dict),
+            SugaredTypeTerm::Spec(ts) => TypeTerm::App(ts.into_iter().map(|t| t.desugar(dict)).collect()),
+            SugaredTypeTerm::Ladder(ts) => TypeTerm::Ladder(ts.into_iter().map(|t|t.desugar(dict)).collect()),
+            SugaredTypeTerm::Func(ts) => TypeTerm::App(
+                std::iter::once( dict.parse("Func").unwrap() ).chain(
+                    ts.into_iter().map(|t| t.desugar(dict))
+                ).collect()),
+            SugaredTypeTerm::Morph(ts) => TypeTerm::App(
+                std::iter::once( dict.parse("Morph").unwrap() ).chain(
+                    ts.into_iter().map(|t| t.desugar(dict))
+                ).collect()),
+            SugaredTypeTerm::Struct(ts) => TypeTerm::App(
+                std::iter::once( dict.parse("Struct").unwrap() ).chain(
+                    ts.into_iter().map(|t| t.desugar(dict))
+                ).collect()),
+            SugaredTypeTerm::Enum(ts) => TypeTerm::App(
+                std::iter::once( dict.parse("Enum").unwrap() ).chain(
+                    ts.into_iter().map(|t| t.desugar(dict))
+                ).collect()),
+            SugaredTypeTerm::Seq(ts) => TypeTerm::App(
+                std::iter::once( dict.parse("Seq").unwrap() ).chain(
+                    ts.into_iter().map(|t| t.desugar(dict))
+                ).collect()),
+        }
+    }
+}
+

src/term.rs

@@ -57,7 +57,7 @@ impl TypeTerm {
     pub fn repr_as(&mut self, t: impl Into<TypeTerm>) -> &mut Self {
         match self {
             TypeTerm::Ladder(rungs) => {
-                rungs.push(t.into());                
+                rungs.push(t.into());
             }
 
             _ => {

src/test/mod.rs

@@ -3,6 +3,7 @@ pub mod lexer;
 pub mod parser;
 pub mod curry;
 pub mod lnf;
+pub mod pnf;
 pub mod subtype;
 pub mod substitution;
 pub mod unification;

src/test/pnf.rs

@@ -0,0 +1,59 @@
+use crate::dict::TypeDict;
+
+#[test]
+fn test_param_normalize() {
+    let mut dict = TypeDict::new();
+
+    assert_eq!(
+        dict.parse("A~B~C").expect("parse error"),
+        dict.parse("A~B~C").expect("parse error").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<A B>~C").expect("parse error"),
+        dict.parse("<A B>~C").expect("parse error").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<A B~C>").expect("parse error"),
+        dict.parse("<A B>~<A C>").expect("parse error").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<A~Y B>").expect("parse error"),
+        dict.parse("<A B>~<Y B>").expect("parse error").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<A B~C D~E>").expect("parse error"),
+        dict.parse("<A B D>~<A C D>~<A C E>").expect("parse errror").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<A~X B~C D~E>").expect("parse error"),
+        dict.parse("<A B D>~<A B~C E>~<X C E>").expect("parse errror").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<Seq <Digit 10>~Char>").expect("parse error"),
+        dict.parse("<Seq <Digit 10>>~<Seq Char>").expect("parse errror").param_normalize(),
+    );
+
+    assert_eq!(
+        dict.parse("<Seq Char> ~ <<ValueDelim '\\0'> Char> ~ <<ValueDelim '\\0'> Ascii~x86.UInt8>").expect("parse error").param_normalize(),
+        dict.parse("<Seq~<ValueDelim '\\0'> Char~Ascii~x86.UInt8>").expect("parse error")
+    );
+    assert_eq!(
+        dict.parse("<Seq Char~Ascii> ~ <<ValueDelim '\\0'> Char~Ascii> ~ <<ValueDelim '\\0'> x86.UInt8>").expect("parse error").param_normalize(),
+        dict.parse("<Seq~<ValueDelim '\\0'> Char~Ascii~x86.UInt8>").expect("parse error")
+    );
+
+    assert_eq!(
+        dict.parse("<A~Y <B C~D~E> F H H>").expect("parse error"),
+        dict.parse("<A <B C> F H H>
+                   ~<A <B D> F H H>
+                   ~<A~Y <B E> F H H>").expect("parse errror")
+               .param_normalize(),
+    );
+}
+