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6 changed files with 58 additions and 199 deletions
57
README.md
57
README.md
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@ -5,6 +5,8 @@ Rust Implementation of Ladder-Types (parsing, unification, rewriting, etc)
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## Ladder Types
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### Motivation
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In order to implement complex datastructures and algorithms, usually
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many layers of abstraction are built ontop of each other.
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Consequently higher-level data types are encoded into lower-level data
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@ -57,6 +59,48 @@ this:
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1696093021:1696093039:1528324679:1539892301:1638141920:1688010253
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```
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### Syntax
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In their core form, type-terms can be one of the following:
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- (**Atomic Type**) | `SomeTypeName`
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- (**Literal Integer**) | `0` | `1` | `2` | ...
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- (**Literal Character**) | `'a'` | `'b'` | `'c'` | ...
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- (**Literal String**) | `"abc"`
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- (**Parameter Application**) | `<T1 T2>` given `T1` and `T2` are type-terms
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- (**Ladder**) | `T1 ~ T2` given `T1` and `T2` are type-terms
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Ontop of that, the following syntax-sugar is defined:
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#### Complex Types
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- `[ T ]` <===> `<Seq T>`
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- `{ a:A b:B }` <===> `<Struct <"a" A> <"b" B>>`
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- `a:A | b:B` <===> `<Enum <"a" A> <"b" B>>`
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#### Function Types
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- `A -> B` <===> `<Fn A B>`
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#### Reference Types
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- `*A` <===> `<Ptr A>`
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- `&A` <===> `<ConstRef A>`
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- `&!A` <===> `<MutRef A>`
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### Equivalences
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#### Currying
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`<<A B> C>` <===> `<A B C>`
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#### Ladder-Normal-Form
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exhaustively apply `<A B~C>` ===> `<A B>~<A C>`
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e.g. `[<Digit 10>]~[Char]~[Ascii]` is in **LNF**
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#### Parameter-Normal-Form
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exhaustively apply `<A B>~<A C>` ===> `<A B~C>`
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e.g. `[<Digit 10>~Char~Ascii]` is in **PNF**
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## How to use this crate
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```rust
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@ -73,6 +117,19 @@ fn main() {
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}
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```
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## Roadmap
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- [x] (Un-)Parsing
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- [x] (De-)Currying
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- [x] Unification
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- [x] Ladder-Normal-Form
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- [x] Parameter-Normal-Form
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- [ ] (De)-Sugaring
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- [ ] Seq
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- [ ] Enum
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- [ ] Struct
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- [ ] References
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- [ ] Function
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## License
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[GPLv3](COPYING)
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@ -7,7 +7,6 @@ pub mod parser;
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pub mod unparser;
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pub mod curry;
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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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113
src/pnf.rs
113
src/pnf.rs
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@ -1,113 +0,0 @@
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use crate::term::TypeTerm;
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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impl TypeTerm {
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/// transmute type into Parameter-Normal-Form (PNF)
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///
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/// Example:
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/// ```ignore
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/// <Seq <Digit 10>>~<Seq Char>
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/// ⇒ <Seq <Digit 10>~Char>
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/// ```
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pub fn param_normalize(self) -> Self {
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match self {
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TypeTerm::Ladder(mut rungs) => {
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if rungs.len() > 0 {
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// normalize all rungs separately
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for r in rungs.iter_mut() {
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*r = r.clone().param_normalize();
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}
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// take top-rung
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match rungs.remove(0) {
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TypeTerm::App(params_top) => {
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let mut params_ladders = Vec::new();
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let mut tail : Vec<TypeTerm> = Vec::new();
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// append all other rungs to ladders inside
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// the application
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for p in params_top {
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params_ladders.push(vec![ p ]);
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}
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for r in rungs {
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match r {
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TypeTerm::App(mut params_rung) => {
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if params_rung.len() > 0 {
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let mut first_param = params_rung.remove(0);
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if first_param == params_ladders[0][0] {
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for (l, p) in params_ladders.iter_mut().skip(1).zip(params_rung) {
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l.push(p.param_normalize());
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}
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} else {
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params_rung.insert(0, first_param);
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tail.push(TypeTerm::App(params_rung));
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}
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}
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}
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TypeTerm::Ladder(mut rs) => {
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for r in rs {
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tail.push(r.param_normalize());
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}
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}
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atomic => {
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tail.push(atomic);
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}
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}
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}
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let head = TypeTerm::App(
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params_ladders.into_iter()
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.map(
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|mut l| {
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l.dedup();
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match l.len() {
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0 => TypeTerm::unit(),
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1 => l.remove(0),
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_ => TypeTerm::Ladder(l).param_normalize()
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}
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}
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)
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.collect()
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);
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if tail.len() > 0 {
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tail.insert(0, head);
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TypeTerm::Ladder(tail)
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} else {
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head
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}
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}
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TypeTerm::Ladder(mut r) => {
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r.append(&mut rungs);
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TypeTerm::Ladder(r)
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}
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atomic => {
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rungs.insert(0, atomic);
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TypeTerm::Ladder(rungs)
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}
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}
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} else {
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TypeTerm::unit()
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}
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}
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TypeTerm::App(params) => {
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TypeTerm::App(
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params.into_iter()
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.map(|p| p.param_normalize())
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.collect())
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}
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atomic => atomic
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}
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}
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}
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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@ -2,49 +2,7 @@ use crate::term::TypeTerm;
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//<<<<>>>><<>><><<>><<<*>>><<>><><<>><<<<>>>>\\
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impl TypeTerm {
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pub fn find_semantic_subtype_matches(&self, expected_type: &TypeTerm)
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-> Option<(TypeTerm, TypeTerm, TypeTerm)>
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{
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let provided_lnf = self.clone().get_lnf_vec();
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let expected_lnf = expected_type.clone().get_lnf_vec();
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for i in 0..provided_lnf.len() {
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if provided_lnf[i] == expected_lnf[0] {
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// found first match.
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// now find first mismatch.
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for j in i..usize::min(provided_lnf.len(), i+expected_lnf.len()) {
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if provided_lnf[j] != expected_lnf[ j-i ] {
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eprintln!("found match at {}, mismatch at {}", i, j);
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let syntactic_subladder = TypeTerm::Ladder( provided_lnf[ 0 .. j ].into_iter().cloned().collect() );
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let provided_reprladder = TypeTerm::Ladder( provided_lnf[ j .. ].into_iter().cloned().collect() );
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let expected_reprladder = TypeTerm::Ladder( expected_lnf[ j-i .. ].into_iter().cloned().collect() );
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return Some((syntactic_subladder, provided_reprladder, expected_reprladder));
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}
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}
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eprintln!("only syntactic subtype");
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// syntactic subtype
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let n = {
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if provided_lnf.len() + i < expected_lnf.len() {
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1
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} else {
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2
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}
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};
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let syntactic_subladder = TypeTerm::Ladder( provided_lnf[ 0 .. provided_lnf.len()-1 ].into_iter().cloned().collect() );
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let provided_reprladder = TypeTerm::Ladder( provided_lnf[ provided_lnf.len()-n .. ].into_iter().cloned().collect() );
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let expected_reprladder = TypeTerm::Ladder( expected_lnf[ provided_lnf.len()-n-i .. ].into_iter().cloned().collect() );
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return Some((syntactic_subladder, provided_reprladder, expected_reprladder));
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}
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}
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None
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}
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impl TypeTerm {
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// returns ladder-step of first match and provided representation-type
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pub fn is_semantic_subtype_of(&self, expected_type: &TypeTerm) -> Option<(usize, TypeTerm)> {
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let provided_lnf = self.clone().get_lnf_vec();
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@ -3,7 +3,6 @@ pub mod lexer;
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pub mod parser;
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pub mod curry;
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pub mod lnf;
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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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@ -1,41 +0,0 @@
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use crate::dict::TypeDict;
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#[test]
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fn test_param_normalize() {
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let mut dict = TypeDict::new();
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assert_eq!(
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dict.parse("A~B~C").expect("parse error"),
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dict.parse("A~B~C").expect("parse error").param_normalize(),
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);
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assert_eq!(
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dict.parse("<A B>~C").expect("parse error"),
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dict.parse("<A B>~C").expect("parse error").param_normalize(),
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);
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assert_eq!(
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dict.parse("<A B~C>").expect("parse error"),
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dict.parse("<A B>~<A C>").expect("parse error").param_normalize(),
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);
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assert_eq!(
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dict.parse("<A B~C D~E>").expect("parse error"),
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dict.parse("<A B D>~<A C D>~<A C E>").expect("parse errror").param_normalize(),
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);
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assert_eq!(
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dict.parse("<Seq <Digit 10>~Char>").expect("parse error"),
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dict.parse("<Seq <Digit 10>>~<Seq Char>").expect("parse errror").param_normalize(),
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);
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assert_eq!(
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dict.parse("<A <B C~D~E> F~G H H>").expect("parse error"),
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dict.parse("<A <B C> F H H>
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~<A <B D> F H H>
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~<A <B E> F H H>
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~<A <B E> G H H>").expect("parse errror")
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.param_normalize(),
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);
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}
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