add test for find_morphism_path()

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)

src/lib.rs

@@ -9,6 +9,7 @@ pub mod curry;
 pub mod lnf;
 pub mod subtype;
 pub mod unification;
+pub mod morphism;
 
 #[cfg(test)]
 mod test;

src/morphism.rs

@@ -0,0 +1,202 @@
+use {
+    crate::{
+        TypeTerm, TypeID,
+        unification::UnificationProblem,
+    },
+    std::collections::HashMap
+};
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
+
+pub struct MorphismType {
+    pub src_type: TypeTerm,
+    pub dst_type: TypeTerm,
+}
+
+pub struct MorphismBase<Morphism: Clone> {
+    morphisms: Vec< (MorphismType, Morphism) >,
+    list_typeid: TypeID
+}
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
+
+impl MorphismType {
+    fn normalize(self) -> Self {
+        MorphismType {
+            src_type: self.src_type.normalize(),
+            dst_type: self.dst_type.normalize()
+        }
+    }
+}
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
+
+impl<Morphism: Clone> MorphismBase<Morphism> {
+    pub fn new(list_typeid: TypeID) -> Self {
+        MorphismBase {
+            morphisms: Vec::new(),
+            list_typeid
+        }
+    }
+
+    pub fn add_morphism(&mut self, morph_type: MorphismType, morphism: Morphism) {
+        self.morphisms.push( (morph_type.normalize(), morphism) );
+    }
+
+    pub fn enum_morphisms(&self, src_type: &TypeTerm)
+    -> Vec< (HashMap<TypeID, TypeTerm>, TypeTerm) >
+    {
+        let mut dst_types = Vec::new();
+
+        // first enumerate all "direct" morphisms,
+        for (ty,m) in self.morphisms.iter() {
+            if let Ok(σ) = crate::unification::unify(
+                &ty.src_type,
+                &src_type.clone().normalize()
+            ) {
+                let dst_type = 
+                    ty.dst_type.clone()
+                        .apply_substitution(
+                            &|x| σ.get(x).cloned()
+                        )
+                        .clone();
+
+                dst_types.push( (σ, dst_type) );
+            }
+        }
+
+        // ..then all "list-map" morphisms.
+        // Check if we have a List type, and if so, see what the Item type is
+
+        // TODO: function for generating fresh variables
+        let item_variable = TypeID::Var(100);
+
+        if let Ok(σ) = crate::unification::unify(
+            &TypeTerm::App(vec![
+                TypeTerm::TypeID(self.list_typeid),
+                TypeTerm::TypeID(item_variable)
+            ]),
+            &src_type.clone().param_normalize(),
+        ) {
+            let src_item_type = σ.get(&item_variable).unwrap().clone();
+
+            for (γ, dst_item_type) in self.enum_morphisms( &src_item_type ) {
+                let dst_type =
+                        TypeTerm::App(vec![
+                            TypeTerm::TypeID(self.list_typeid),
+                            dst_item_type.clone()
+                                .apply_substitution(
+                                    &|x| γ.get(x).cloned()
+                                ).clone()
+                        ]).normalize();
+
+                dst_types.push( (γ.clone(), dst_type) );
+            }
+        }
+
+        dst_types
+    }
+
+    pub fn enum_morphisms_with_subtyping(&self, src_type: &TypeTerm)
+    -> Vec< (TypeTerm, TypeTerm) >
+    {
+        let mut src_lnf = src_type.clone().get_lnf_vec();
+        let mut halo_lnf = vec![];
+        let mut dst_types = Vec::new();
+
+        while src_lnf.len() > 0 {
+            let src_type = TypeTerm::Ladder( src_lnf.clone() );
+            let halo_type = TypeTerm::Ladder( halo_lnf.clone() );
+
+            for (σ, t) in self.enum_morphisms( &src_type ) {
+                dst_types.push(
+                    (halo_type.clone()
+                        .apply_substitution(
+                            &|x| σ.get(x).cloned()
+                        ).clone(),
+                    t.clone()
+                        .apply_substitution(
+                            &|x| σ.get(x).cloned()
+                        ).clone()
+                    )
+                );
+            }
+
+            // continue with next supertype
+            halo_lnf.push(src_lnf.remove(0));
+        }
+
+        dst_types
+    }
+
+    /* performs DFS to find a morphism-path for a given type
+     * will return the first matching path, not the shortest
+     */
+    pub fn find_morphism_path(&self, ty: MorphismType)
+    -> Option< Vec<TypeTerm> >
+    {
+        let ty = ty.normalize();
+        let mut visited = Vec::new();
+        let mut queue = vec![
+            vec![ ty.src_type.clone().normalize() ]
+        ];
+
+        while let Some(current_path) = queue.pop() {       
+            let current_type = current_path.last().unwrap();
+
+            if ! visited.contains( current_type ) {
+                visited.push( current_type.clone() );
+
+                for (h, t) in self.enum_morphisms_with_subtyping(&current_type) {
+                    let tt = TypeTerm::Ladder( vec![ h, t ] ).normalize();
+
+                    if ! visited.contains( &tt ) {
+                        let unification_result = crate::unification::unify(&tt, &ty.dst_type);
+                        let mut new_path = current_path.clone();
+
+                        new_path.push( tt );
+
+                        if let Ok(σ) = unification_result {
+                            new_path = new_path.into_iter().map(
+                                |mut t: TypeTerm| t.apply_substitution(&|x| σ.get(x).cloned()).clone()
+                            ).collect::<Vec<TypeTerm>>();
+
+                            return Some(new_path);
+                        } else {
+                            queue.push( new_path );
+                        }
+                    }
+                }
+            }
+        }
+
+        None
+    }
+
+    pub fn find_morphism(&self, ty: &MorphismType)
+    -> Option< Morphism > {
+
+        // TODO
+
+        None
+    }
+
+    pub fn find_list_map_morphism(&self, item_ty: &MorphismType)
+    -> Option< Morphism > {
+
+        // TODO
+
+        None
+    }
+
+    pub fn find_morphism_with_subtyping(&self, ty: &MorphismType)
+    -> Option<( Morphism, TypeTerm, HashMap<TypeID, TypeTerm> )> {
+
+        // TODO
+
+        None
+    }
+}
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
+

src/test/mod.rs

@@ -6,4 +6,5 @@ pub mod lnf;
 pub mod subtype;
 pub mod substitution;
 pub mod unification;
+pub mod morphism;
 

src/test/morphism.rs

@@ -0,0 +1,73 @@
+use {
+    crate::{dict::*, morphism::*}
+};
+
+//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
+
+#[test]
+fn test_morphism_path() {
+    let mut dict = TypeDict::new();
+    let mut base = MorphismBase::<u64>::new( dict.add_typename("Seq".into()) );
+
+    dict.add_varname("Radix".into());
+    dict.add_varname("SrcRadix".into());
+    dict.add_varname("DstRadix".into());
+
+    base.add_morphism(
+        MorphismType{
+            src_type: dict.parse("<Digit Radix> ~ Char").unwrap(),
+            dst_type: dict.parse("<Digit Radix> ~ ℤ_2^64 ~ machine.UInt64").unwrap()
+        },
+        11
+    );
+    base.add_morphism(
+        MorphismType{
+            src_type: dict.parse("<Digit Radix> ~ ℤ_2^64 ~ machine.UInt64").unwrap(),
+            dst_type: dict.parse("<Digit Radix> ~ Char").unwrap()
+        },
+        22
+    );
+    base.add_morphism(
+        MorphismType{
+            src_type: dict.parse("ℕ ~ <PosInt Radix BigEndian> ~ <Seq <Digit Radix>~ℤ_2^64~machine.UInt64>").unwrap(),
+            dst_type: dict.parse("ℕ ~ <PosInt Radix LittleEndian> ~ <Seq <Digit Radix>~ℤ_2^64~machine.UInt64>").unwrap()
+        },
+        333
+    );
+    base.add_morphism(
+        MorphismType{
+            src_type: dict.parse("ℕ ~ <PosInt Radix LittleEndian> ~ <Seq <Digit Radix>~ℤ_2^64~machine.UInt64>").unwrap(),
+            dst_type: dict.parse("ℕ ~ <PosInt Radix BigEndian> ~ <Seq <Digit Radix>~ℤ_2^64~machine.UInt64>").unwrap()
+        },
+        444
+    );
+    base.add_morphism(
+        MorphismType{
+            src_type: dict.parse("ℕ ~ <PosInt SrcRadix LittleEndian> ~ <Seq <Digit SrcRadix>~ℤ_2^64~machine.UInt64>").unwrap(),
+            dst_type: dict.parse("ℕ ~ <PosInt DstRadix LittleEndian> ~ <Seq <Digit DstRadix>~ℤ_2^64~machine.UInt64>").unwrap()
+        },
+        555
+    );
+
+
+    let path = base.find_morphism_path(MorphismType {
+        src_type: dict.parse("ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ Char>").unwrap(),
+        dst_type: dict.parse("ℕ ~ <PosInt 16 BigEndian> ~ <Seq <Digit 16> ~ Char>").unwrap()
+    });
+
+    assert_eq!(
+        path,
+
+        Some(
+            vec![
+                dict.parse("ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ Char>").unwrap().normalize(),
+                dict.parse("ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
+                dict.parse("ℕ ~ <PosInt 10 LittleEndian> ~ <Seq <Digit 10> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
+                dict.parse("ℕ ~ <PosInt 16 LittleEndian> ~ <Seq <Digit 16> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
+                dict.parse("ℕ ~ <PosInt 16 BigEndian> ~ <Seq <Digit 16> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
+                dict.parse("ℕ ~ <PosInt 16 BigEndian> ~ <Seq <Digit 16> ~ Char>").unwrap().normalize(),
+            ]
+        )
+    );
+}
+