1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183

//! A [Rust][0] library for representing, parsing, and computing with first-order [term rewriting systems][1].
//!
//! # Usage
//!
//! ```toml
//! [dependencies]
//! term_rewriting = "0.7"
//! ```
//!
//! # Example
//!
//! ```
//! use term_rewriting::{Signature, Term, parse_trs, parse_term};
//!
//! // We can parse a string representation of SK combinatory logic,
//! let mut sig = Signature::default();
//! let sk_rules = "S x_ y_ z_ = (x_ z_) (y_ z_); K x_ y_ = x_;";
//! let trs = parse_trs(&mut sig, sk_rules).expect("parsed TRS");
//!
//! // and we can also parse an arbitrary term.
//! let mut sig = Signature::default();
//! let term = "S K K (K S K)";
//! let parsed_term = parse_term(&mut sig, term).expect("parsed term");
//!
//! // These can also be constructed by hand.
//! let mut sig = Signature::default();
//! let s = sig.new_op(0, Some("S".to_string()));
//! let k = sig.new_op(0, Some("K".to_string()));
//! let app = sig.new_op(2, Some(".".to_string()));
//!
//! let constructed_term = Term::Application {
//!     op: app.clone(),
//!     args: vec![
//!         Term::Application {
//!             op: app.clone(),
//!             args: vec![
//!                 Term::Application {
//!                     op: app.clone(),
//!                     args: vec![
//!                         Term::Application { op: s.clone(), args: vec![] },
//!                         Term::Application { op: k.clone(), args: vec![] },
//!                     ]
//!                 },
//!                 Term::Application { op: k.clone(), args: vec![] }
//!             ]
//!         },
//!         Term::Application {
//!             op: app.clone(),
//!             args: vec![
//!                 Term::Application {
//!                     op: app.clone(),
//!                     args: vec![
//!                         Term::Application { op: k.clone(), args: vec![] },
//!                         Term::Application { op: s.clone(), args: vec![] },
//!                     ]
//!                 },
//!                 Term::Application { op: k.clone(), args: vec![] }
//!             ]
//!         }
//!     ]
//! };
//!
//! // This is the same output the parser produces.
//! assert_eq!(parsed_term, constructed_term);
//! ```
//!
//! # TRS syntax
//!
//! Several functions are available which parse TRS-related data structures
//! according to the following grammar (defined in [augmented Backus-Naur form]):
//!
//! - [`parse`]: a [`TRS`] and list of [`Term`s] (`program`)
//! - [`parse_trs`]: a [`TRS`] (`trs`)
//! - [`parse_term`]: a [`Term`] (`top-level-term`)
//! - [`parse_rule`]: a [`Rule`] (`rule`)
//! - [`parse_context`]: a [`Context`] (`top-level-context`)
//! - [`parse_rulecontext`]: a [`RuleContext`] (`rulecontext`)
//!
//! ```text
//! program = *wsp *( *comment statement ";" *comment ) *wsp
//!
//! statement = rule / top-level-term
//!
//! rule = top-level-term *wsp "=" *wsp top-level-term
//! rule /= rule *wsp "|" *wsp top-level-term
//!
//! top-level-term = term
//! top-level-term /= top-level-term 1*wsp top-level-term
//!
//! term = variable
//! term /= application
//! term /= "(" *wsp top-level-term *wsp ")"
//!
//! rulecontext = top-level-term *wsp "=" *wsp top-level-term
//! rulecontext /= rule *wsp "|" *wsp top-level-term
//!
//! top-level-context = context
//! top-level-context /= top-level-context 1*wsp top-level-context
//!
//! context = variable
//! context /= application
//! context /= hole
//! context /= "(" *wsp top-level-context *wsp ")"
//!
//! hole = "[!]"
//!
//! variable = identifier"_"
//!
//! application = identifier "(" [ term *( 1*wsp term ) ] ")"
//! application /= identifier
//! application /= binary-application
//!
//! ; binary application is the '.' operator with arity 2.
//! binary-application = "(" *wsp term *wsp term *wsp ")"
//!
//! identifier = 1*( ALPHA / DIGIT )
//!
//! comment = "#" *any-char-but-newline "\n"
//!
//! wsp = SP / TAB / CR / LF
//! ```
//!
//! # Term Rewriting Systems
//!
//! Term Rewriting Systems (TRS) are a simple formalism from theoretical
//! computer science used to model the behavior and evolution of tree-based
//! structures like natural langauge parse trees or abstract syntax trees.
//!
//! A TRS is defined as a pair _(S, R)_. _S_ is a set of symbols called the
//! signature and together with a disjoint and countably infinite set of
//! variables, defines the set of all possible trees, or terms, which the system
//! can consider. _R_ is a set of rewrite rules. A rewrite rule is an equation,
//! _s = t_, and is interpreted as follows: any term matching the pattern
//! described by _s_ can be rewritten according to the pattern described by _t_.
//! Together _S_ and _R_ define a TRS that describes a system of computation,
//! which can be considered as a sort of programming language.
//! `term_rewriting` provides a way to describe arbitrary first-order TRSs
//! (i.e. no lambda-binding in rules).
//!
//! ### Further Reading
//!
//! - Baader & Nipkow (1999). [Term rewriting and all that][2]. Cambridge University Press.
//! - Bezem, Klop, & de Vrijer (Eds.) (2003). [Term Rewriting Systems][3]. Cambridge University Press.
//! - [Rewriting][4]. (2017). Wikipedia.
//!
//! [0]: https://www.rust-lang.org
//!      "The Rust Programming Language"
//! [1]: https://en.wikipedia.org/wiki/Rewriting#Term_rewriting_systems
//!      "Wikipedia - Term Rewriting Systems"
//! [2]: http://www.cambridge.org/us/academic/subjects/computer-science/programming-languages-and-applied-logic/term-rewriting-and-all
//!      "Term Rewriting and All That"
//! [3]: http://www.cambridge.org/us/academic/subjects/computer-science/programming-languages-and-applied-logic/term-rewriting-systems
//!      "Term Rewriting Systems"
//! [4]: https://en.wikipedia.org/wiki/Rewriting
//!      "Wikipedia - Rewriting"
//! [augmented Backus-Naur form]: https://en.wikipedia.org/wiki/Augmented_Backus–Naur_form
//! [`parse`]: fn.parse.html
//! [`parse_trs`]: fn.parse_trs.html
//! [`parse_term`]: fn.parse_term.html
//! [`parse_rule`]: fn.parse_rule.html
//! [`parse_context`]: fn.parse_context.html
//! [`parse_rulecontext`]: fn.parse_rulecontext.html
//! [`TRS`]: struct.TRS.html
//! [`Term`s]: enum.Term.html
//! [`Term`]: enum.Term.html
//! [`Rule`]: struct.Rule.html
//! [`Context`]: enum.Context.html
//! [`RuleContext`]: struct.RuleContext.html

extern crate itertools;
#[macro_use]
extern crate nom;
extern crate rand;

mod parser;
mod pretty;
pub mod trace;
mod types;

pub use parser::{
    parse, parse_context, parse_rule, parse_rulecontext, parse_term, parse_trs, ParseError,
};
pub use types::*;