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topic-morp
Author | SHA1 | Date | |
---|---|---|---|
5d7668573a | |||
493b8a864c | |||
e0334f4d5c | |||
811adde1b9 | |||
42286bcadc | |||
b835cddcf1 | |||
486760f3e2 |
6 changed files with 590 additions and 2 deletions
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@ -2,7 +2,7 @@ use crate::bimap::Bimap;
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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#[derive(Eq, PartialEq, Hash, Clone, Debug)]
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#[derive(Eq, PartialEq, Hash, Clone, Copy, Debug)]
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pub enum TypeID {
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Fun(u64),
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Var(u64)
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@ -10,6 +10,8 @@ pub mod lnf;
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pub mod pnf;
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pub mod subtype;
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pub mod unification;
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pub mod morphism;
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pub mod steiner_tree;
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#[cfg(test)]
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mod test;
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@ -17,6 +19,7 @@ mod test;
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pub use {
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dict::*,
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term::*,
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unification::*
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unification::*,
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morphism::*
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};
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261
src/morphism.rs
Normal file
261
src/morphism.rs
Normal file
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@ -0,0 +1,261 @@
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use {
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crate::{
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TypeTerm, TypeID,
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unification::UnificationProblem,
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},
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std::collections::HashMap
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};
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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#[derive(Clone, PartialEq, Eq, Debug)]
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pub struct MorphismType {
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pub src_type: TypeTerm,
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pub dst_type: TypeTerm,
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}
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pub trait Morphism : Sized {
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fn get_type(&self) -> MorphismType;
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fn list_map_morphism(&self, list_typeid: TypeID) -> Option< Self >;
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fn weight(&self) -> u64 {
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1
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}
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}
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#[derive(Clone)]
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pub struct MorphismBase<M: Morphism + Clone> {
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morphisms: Vec< M >,
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list_typeid: TypeID
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}
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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impl MorphismType {
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pub fn normalize(self) -> Self {
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MorphismType {
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src_type: self.src_type.normalize(),
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dst_type: self.dst_type.normalize()
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}
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}
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}
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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impl<M: Morphism + Clone> MorphismBase<M> {
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pub fn new(list_typeid: TypeID) -> Self {
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MorphismBase {
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morphisms: Vec::new(),
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list_typeid
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}
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}
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pub fn add_morphism(&mut self, m: M) {
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self.morphisms.push( m );
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}
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pub fn enum_morphisms(&self, src_type: &TypeTerm)
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-> Vec< (HashMap<TypeID, TypeTerm>, TypeTerm) >
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{
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let mut dst_types = Vec::new();
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// first enumerate all "direct" morphisms,
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for m in self.morphisms.iter() {
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if let Ok(σ) = crate::unification::unify(
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&m.get_type().src_type,
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&src_type.clone().normalize()
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) {
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let dst_type =
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m.get_type().dst_type.clone()
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.apply_substitution( &|x| σ.get(x).cloned() )
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.clone();
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dst_types.push( (σ, dst_type) );
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}
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}
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// ..then all "list-map" morphisms.
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// Check if we have a List type, and if so, see what the Item type is
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// TODO: function for generating fresh variables
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let item_variable = TypeID::Var(100);
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if let Ok(σ) = crate::unification::unify(
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&TypeTerm::App(vec![
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TypeTerm::TypeID(self.list_typeid),
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TypeTerm::TypeID(item_variable)
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]),
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&src_type.clone().param_normalize(),
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) {
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let src_item_type = σ.get(&item_variable).unwrap().clone();
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for (γ, dst_item_type) in self.enum_morphisms( &src_item_type ) {
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let dst_type =
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TypeTerm::App(vec![
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TypeTerm::TypeID(self.list_typeid),
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dst_item_type.clone()
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.apply_substitution(
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&|x| γ.get(x).cloned()
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).clone()
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]).normalize();
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dst_types.push( (γ.clone(), dst_type) );
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}
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}
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dst_types
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}
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pub fn enum_morphisms_with_subtyping(&self, src_type: &TypeTerm)
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-> Vec< (TypeTerm, TypeTerm) >
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{
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let mut src_lnf = src_type.clone().get_lnf_vec();
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let mut halo_lnf = vec![];
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let mut dst_types = Vec::new();
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while src_lnf.len() > 0 {
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let src_type = TypeTerm::Ladder( src_lnf.clone() );
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let halo_type = TypeTerm::Ladder( halo_lnf.clone() );
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for (σ, t) in self.enum_morphisms( &src_type ) {
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dst_types.push(
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(halo_type.clone()
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.apply_substitution(
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&|x| σ.get(x).cloned()
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).clone(),
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t.clone()
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.apply_substitution(
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&|x| σ.get(x).cloned()
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).clone()
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)
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);
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}
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// continue with next supertype
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halo_lnf.push(src_lnf.remove(0));
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}
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dst_types
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}
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/* try to find shortest morphism-path for a given type
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*/
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pub fn find_morphism_path(&self, ty: MorphismType)
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-> Option< Vec<TypeTerm> >
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{
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let ty = ty.normalize();
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let mut queue = vec![
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(0, vec![ ty.src_type.clone().normalize() ])
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];
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while ! queue.is_empty() {
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queue.sort_by( |&(w1,_),&(w2,_)| w2.cmp(&w1));
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if let Some((current_weight, current_path)) = queue.pop() {
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let current_type = current_path.last().unwrap();
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for (h, t) in self.enum_morphisms_with_subtyping(¤t_type) {
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let tt = TypeTerm::Ladder( vec![ h, t ] ).normalize();
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if ! current_path.contains( &tt ) {
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let unification_result = crate::unification::unify(&tt, &ty.dst_type);
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let morphism_weight = 1;
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/*
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{
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self.find_morphism( &tt ).unwrap().0.get_weight()
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};
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*/
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let new_weight = current_weight + morphism_weight;
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let mut new_path = current_path.clone();
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new_path.push( tt );
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if let Ok(σ) = unification_result {
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new_path = new_path.into_iter().map(
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|mut t: TypeTerm| t.apply_substitution(&|x| σ.get(x).cloned()).clone()
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).collect::<Vec<TypeTerm>>();
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return Some(new_path);
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} else {
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queue.push( (new_weight, new_path) );
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}
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}
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}
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}
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}
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None
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}
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pub fn find_morphism(&self, ty: &MorphismType)
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-> Option< ( M, HashMap<TypeID, TypeTerm> ) > {
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// try list-map morphism
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if let Ok(σ) = UnificationProblem::new(vec![
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(ty.src_type.clone().param_normalize(), TypeTerm::App(vec![ TypeTerm::TypeID(self.list_typeid), TypeTerm::TypeID(TypeID::Var(100)) ])),
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(ty.dst_type.clone().param_normalize(), TypeTerm::App(vec![ TypeTerm::TypeID(self.list_typeid), TypeTerm::TypeID(TypeID::Var(101)) ])),
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]).solve() {
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// TODO: use real fresh variable names
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let item_morph_type = MorphismType {
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src_type: σ.get(&TypeID::Var(100)).unwrap().clone(),
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dst_type: σ.get(&TypeID::Var(101)).unwrap().clone(),
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}.normalize();
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if let Some((m, σ)) = self.find_morphism( &item_morph_type ) {
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if let Some(list_morph) = m.list_map_morphism( self.list_typeid ) {
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return Some( (list_morph, σ) );
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}
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}
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}
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// otherwise
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for m in self.morphisms.iter() {
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let unification_problem = UnificationProblem::new(
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vec![
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( ty.src_type.clone().normalize(), m.get_type().src_type.clone() ),
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( ty.dst_type.clone().normalize(), m.get_type().dst_type.clone() )
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]
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);
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let unification_result = unification_problem.solve();
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if let Ok(σ) = unification_result {
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return Some((m.clone(), σ));
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}
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}
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None
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}
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pub fn find_morphism_with_subtyping(&self, ty: &MorphismType)
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-> Option<( M, TypeTerm, HashMap<TypeID, TypeTerm> )> {
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let mut src_lnf = ty.src_type.clone().get_lnf_vec();
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let mut dst_lnf = ty.dst_type.clone().get_lnf_vec();
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let mut halo = vec![];
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while src_lnf.len() > 0 && dst_lnf.len() > 0 {
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if let Some((m, σ)) = self.find_morphism(&MorphismType{
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src_type: TypeTerm::Ladder(src_lnf.clone()),
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dst_type: TypeTerm::Ladder(dst_lnf.clone())
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}) {
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halo.push(src_lnf.get(0).unwrap().clone());
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return Some((m,
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TypeTerm::Ladder(halo).apply_substitution(&|x| σ.get(x).cloned()).clone(),
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σ));
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} else {
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if src_lnf[0] == dst_lnf[0] {
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src_lnf.remove(0);
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halo.push(dst_lnf.remove(0));
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} else {
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return None;
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}
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}
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}
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None
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}
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}
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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162
src/steiner_tree.rs
Normal file
162
src/steiner_tree.rs
Normal file
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@ -0,0 +1,162 @@
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use {
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std::collections::HashMap,
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crate::{
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TypeID,
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TypeTerm,
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morphism::{
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MorphismType,
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Morphism,
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MorphismBase
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}
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}
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};
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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#[derive(Clone)]
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pub struct SteinerTree {
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weight: u64,
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goals: Vec< TypeTerm >,
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pub edges: Vec< MorphismType >,
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}
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impl SteinerTree {
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fn add_edge(&mut self, ty: MorphismType) {
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self.weight += 1;
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let ty = ty.normalize();
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// check if by adding this new edge, we reach a goal
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let mut new_goals = Vec::new();
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let mut added = false;
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for g in self.goals.clone() {
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if let Ok(σ) = crate::unify(&ty.dst_type, &g) {
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if !added {
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self.edges.push(ty.clone());
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// goal reached.
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for e in self.edges.iter_mut() {
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e.src_type = e.src_type.apply_substitution(&|x| σ.get(x).cloned()).clone();
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e.dst_type = e.dst_type.apply_substitution(&|x| σ.get(x).cloned()).clone();
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}
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added = true;
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} else {
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new_goals.push(g);
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}
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} else {
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new_goals.push(g);
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}
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}
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if !added {
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self.edges.push(ty.clone());
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}
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self.goals = new_goals;
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}
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fn is_solved(&self) -> bool {
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self.goals.len() == 0
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}
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fn contains(&self, t: &TypeTerm) -> Option< HashMap<TypeID, TypeTerm> > {
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for e in self.edges.iter() {
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if let Ok(σ) = crate::unify(&e.dst_type, t) {
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return Some(σ)
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}
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}
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None
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}
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}
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/* given a representation tree with the available
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* represenatations `src_types`, try to find
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* a sequence of morphisms that span up all
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* representations in `dst_types`.
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*/
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pub struct SteinerTreeProblem {
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src_types: Vec< TypeTerm >,
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queue: Vec< SteinerTree >
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}
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impl SteinerTreeProblem {
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pub fn new(
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src_types: Vec< TypeTerm >,
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dst_types: Vec< TypeTerm >
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) -> Self {
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SteinerTreeProblem {
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src_types: src_types.into_iter().map(|t| t.normalize()).collect(),
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queue: vec![
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SteinerTree {
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weight: 0,
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goals: dst_types.into_iter().map(|t| t.normalize()).collect(),
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edges: Vec::new()
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}
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]
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}
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}
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pub fn next(&mut self) -> Option< SteinerTree > {
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eprintln!("queue size = {}", self.queue.len());
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/* FIXME: by giving the highest priority to
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* candidate tree with the least remaining goals,
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* the optimality of the search algorithm
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* is probably destroyed, but it dramatically helps
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* to tame the combinatorical explosion in this algorithm.
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*/
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self.queue.sort_by(|t1, t2|
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if t1.goals.len() < t2.goals.len() {
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std::cmp::Ordering::Greater
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} else if t1.goals.len() == t2.goals.len() {
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if t1.weight < t2.weight {
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std::cmp::Ordering::Greater
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} else {
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std::cmp::Ordering::Less
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}
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} else {
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std::cmp::Ordering::Less
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}
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);
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self.queue.pop()
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}
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pub fn solve_bfs<M: Morphism + Clone>(&mut self, dict: &crate::dict::TypeDict, morphisms: &MorphismBase<M>) -> Option< SteinerTree > {
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// take the currently smallest tree and extend it by one step
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while let Some( mut current_tree ) = self.next() {
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// check if current tree is a solution
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if current_tree.goals.len() == 0 {
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return Some(current_tree);
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}
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// get all vertices spanned by this tree
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let mut current_nodes = self.src_types.clone();
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for e in current_tree.edges.iter() {
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current_nodes.push( e.dst_type.clone() );
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}
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// extend the tree by one edge and add it to the queue
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for src_type in current_nodes.iter() {
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for (dst_halo,dst_ty) in morphisms.enum_morphisms_with_subtyping( &src_type ) {
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let dst_type = TypeTerm::Ladder(vec![
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dst_halo, dst_ty
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]).normalize();
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if !current_nodes.contains( &dst_type ) {
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let mut new_tree = current_tree.clone();
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let src_type = src_type.clone();
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new_tree.add_edge(MorphismType { src_type, dst_type }.normalize());
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self.queue.push( new_tree );
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}
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}
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}
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}
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None
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}
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}
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|
|
@ -7,4 +7,5 @@ pub mod pnf;
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pub mod subtype;
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pub mod substitution;
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pub mod unification;
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pub mod morphism;
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|
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|
|
161
src/test/morphism.rs
Normal file
161
src/test/morphism.rs
Normal file
|
@ -0,0 +1,161 @@
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use {
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crate::{dict::*, morphism::*, steiner_tree::*, TypeTerm}
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};
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
|
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|
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#[derive(Clone, Debug, PartialEq)]
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struct DummyMorphism(MorphismType);
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impl Morphism for DummyMorphism {
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fn get_type(&self) -> MorphismType {
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self.0.clone().normalize()
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}
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fn list_map_morphism(&self, list_typeid: TypeID) -> Option<DummyMorphism> {
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Some(DummyMorphism(MorphismType {
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src_type: TypeTerm::App(vec![
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TypeTerm::TypeID( list_typeid ),
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self.0.src_type.clone()
|
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]),
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|
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dst_type: TypeTerm::App(vec![
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TypeTerm::TypeID( list_typeid ),
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self.0.dst_type.clone()
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])
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}))
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}
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}
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fn morphism_test_setup() -> ( TypeDict, MorphismBase<DummyMorphism> ) {
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let mut dict = TypeDict::new();
|
||||
let mut base = MorphismBase::<DummyMorphism>::new( dict.add_typename("Seq".into()) );
|
||||
|
||||
dict.add_varname("Radix".into());
|
||||
dict.add_varname("SrcRadix".into());
|
||||
dict.add_varname("DstRadix".into());
|
||||
|
||||
base.add_morphism(
|
||||
DummyMorphism(MorphismType{
|
||||
src_type: dict.parse("<Digit Radix> ~ Char").unwrap(),
|
||||
dst_type: dict.parse("<Digit Radix> ~ ℤ_2^64 ~ machine.UInt64").unwrap()
|
||||
})
|
||||
);
|
||||
base.add_morphism(
|
||||
DummyMorphism(MorphismType{
|
||||
src_type: dict.parse("<Digit Radix> ~ ℤ_2^64 ~ machine.UInt64").unwrap(),
|
||||
dst_type: dict.parse("<Digit Radix> ~ Char").unwrap()
|
||||
})
|
||||
);
|
||||
base.add_morphism(
|
||||
DummyMorphism(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()
|
||||
})
|
||||
);
|
||||
base.add_morphism(
|
||||
DummyMorphism(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()
|
||||
})
|
||||
);
|
||||
base.add_morphism(
|
||||
DummyMorphism(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()
|
||||
})
|
||||
);
|
||||
|
||||
(dict, base)
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_morphism_path() {
|
||||
let (mut dict, mut base) = morphism_test_setup();
|
||||
|
||||
assert_eq!(
|
||||
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()
|
||||
}),
|
||||
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(),
|
||||
]
|
||||
)
|
||||
);
|
||||
|
||||
assert_eq!(
|
||||
base.find_morphism_path(MorphismType {
|
||||
src_type: dict.parse("Symbol ~ ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ Char>").unwrap(),
|
||||
dst_type: dict.parse("Symbol ~ ℕ ~ <PosInt 16 BigEndian> ~ <Seq <Digit 16> ~ Char>").unwrap()
|
||||
}),
|
||||
Some(
|
||||
vec![
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ Char>").unwrap().normalize(),
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 10 LittleEndian> ~ <Seq <Digit 10> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 16 LittleEndian> ~ <Seq <Digit 16> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 16 BigEndian> ~ <Seq <Digit 16> ~ ℤ_2^64 ~ machine.UInt64>").unwrap().normalize(),
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 16 BigEndian> ~ <Seq <Digit 16> ~ Char>").unwrap().normalize(),
|
||||
]
|
||||
)
|
||||
);
|
||||
|
||||
assert_eq!(
|
||||
base.find_morphism_with_subtyping(
|
||||
&MorphismType {
|
||||
src_type: dict.parse("Symbol ~ ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ Char>").unwrap(),
|
||||
dst_type: dict.parse("Symbol ~ ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ ℤ_2^64 ~ machine.UInt64>").unwrap()
|
||||
}
|
||||
),
|
||||
|
||||
Some((
|
||||
DummyMorphism(MorphismType{
|
||||
src_type: dict.parse("<Seq <Digit Radix> ~ Char>").unwrap(),
|
||||
dst_type: dict.parse("<Seq <Digit Radix> ~ ℤ_2^64 ~ machine.UInt64>").unwrap()
|
||||
}),
|
||||
|
||||
dict.parse("Symbol ~ ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10>>").unwrap(),
|
||||
|
||||
vec![
|
||||
(dict.get_typeid(&"Radix".into()).unwrap(),
|
||||
dict.parse("10").unwrap())
|
||||
].into_iter().collect::<std::collections::HashMap<TypeID, TypeTerm>>()
|
||||
))
|
||||
);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_steiner_tree() {
|
||||
let (mut dict, mut base) = morphism_test_setup();
|
||||
|
||||
|
||||
let mut steiner_tree_problem = SteinerTreeProblem::new(
|
||||
// source reprs
|
||||
vec![
|
||||
dict.parse("ℕ ~ <PosInt 10 BigEndian> ~ <Seq <Digit 10> ~ Char>").unwrap(),
|
||||
],
|
||||
|
||||
// destination reprs
|
||||
vec![
|
||||
dict.parse("ℕ ~ <PosInt 2 BigEndian> ~ <Seq <Digit 2> ~ Char>").unwrap(),
|
||||
dict.parse("ℕ ~ <PosInt 10 LittleEndian> ~ <Seq <Digit 10> ~ Char>").unwrap(),
|
||||
dict.parse("ℕ ~ <PosInt 16 LittleEndian> ~ <Seq <Digit 16> ~ Char>").unwrap()
|
||||
]
|
||||
);
|
||||
|
||||
if let Some(solution) = steiner_tree_problem.solve_bfs( &dict, &base ) {
|
||||
for e in solution.edges.iter() {
|
||||
eprintln!(" :: {}\n--> {}", dict.unparse(&e.src_type), dict.unparse(&e.dst_type));
|
||||
}
|
||||
} else {
|
||||
eprintln!("no solution");
|
||||
}
|
||||
}
|
||||
|
Loading…
Reference in a new issue