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This commit is contained in:
Devine Lu Linvega
commit
9d3384805b
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# Modal
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Modal is a language based a model of computation that uses pattern matching and replacement to rewrite trees.
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All Modal code is represented as a series of rules applied to a given tree, formatted textually as tokens delimited with parenthesis, which gets continually modified until no rules match any given part of the tree.
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A pattern/replacement can be:
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A token: foo, bar, baz
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A variable: ?foo, ?bar, ?baz
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A sequence of the above: (foo bar baz), (foo ?bar baz), foo (bar (baz))
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## Run
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```
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python3 ./modal.py
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```
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## Credits
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Created by [wryl](https://wryl.tech/), Immediate Mode Technologies.
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"""
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*------------------------------------------------------------*
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|modal.py : An Implementation of Modal in Python |
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| |
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|This is an implementation of Modal, a programming language |
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|based on term rewriting. This particular implementation |
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|is based on the idea of cyclic delimited string rewriting |
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|using a central queue and a dictionary of variable bindings.|
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|© 2019 imode, Immediate Mode Technologies |
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*------------------------------------------------------------*
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"""
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# `sys` for I/O and arguments.
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# `time` for measuring the runtime of the interpreter.
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import sys, time;
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# A decorator intended for measuring the runtime of a given function.
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def measure(function):
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def measurement(*arguments):
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start = time.time();
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result = function(*arguments);
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end = time.time();
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milliseconds = (end - start) * 1000.0;
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print("\nTook {:.3f}ms".format(milliseconds))
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return result;
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return measurement;
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# Enqueue an item by appending it to the queue.
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def enqueue(queue, item):
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return queue + item;
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# Dequeue an item by slicing the queue. The last item is the head.
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def dequeue(queue, length=1):
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if length > len(queue):
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return queue;
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return queue[length:];
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# Get the item(s) at the head of the queue.
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def peek(queue, length=1):
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if length > len(queue):
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return None;
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if length == 1:
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return queue[0];
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return queue[:length];
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# Roll/cycle the queue by a certain amount by slicing.
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# This dequeues and enqueues a number of items, "cycling" the queue.
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def roll(queue, length=1):
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if length > len(queue):
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return queue;
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return queue[length:] + queue[:length];
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# Seek to a certain position in the queue by repeatedly rolling it.
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def seek(queue, pattern):
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if pattern not in queue:
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return queue;
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while peek(queue, len(pattern)) != pattern:
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queue = roll(queue);
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return queue;
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# Extract a delimited fragment (subtree) from the queue.
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def extract(queue):
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results = [];
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depth = 0;
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for element in queue:
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if element[0] == "SRT":
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return [];
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if element[0] == "INC":
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depth = depth + 1;
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if element[0] == "DEC":
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if depth == 0:
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return results;
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depth = depth - 1;
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results.append(element);
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if depth == 0:
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return results;
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return results;
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# Generate a list of variable bindings from the current queue and a pattern.
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def match(pattern, queue, context=None):
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if context == None:
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context = {};
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if peek(queue) == None:
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return context;
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for element in pattern:
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if element[0] == "VAR":
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variable = element[1];
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value = extract(queue);
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if variable in context:
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if context[variable] != value:
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return None;
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queue = dequeue(queue, len(context[variable]));
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else:
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if len(value) == 0:
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return None;
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context[variable] = value;
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queue = dequeue(queue, len(context[variable]));
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elif element != peek(queue):
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return None;
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else:
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queue = dequeue(queue);
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return context;
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# Fill in a pattern with variables in it using a list of variable bindings.
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def construct(pattern, context):
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results = [];
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for element in pattern:
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if element[0] == "VAR":
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if element[1] in context:
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for element in context[element[1]]:
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results.append(element);
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else:
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results.append(element);
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else:
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results.append(element);
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return results;
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# Apply a pattern/replacement rule to the queue.
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def apply(queue, rules, pattern, replacement):
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context = match(pattern, queue);
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if context == None:
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return (False, roll(queue));
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pattern = construct(pattern, context);
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if not pattern:
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return (False, roll(queue));
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replacement = construct(replacement, context);
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if len(replacement) == 0:
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return (True, dequeue(queue, len(pattern)))
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if not replacement:
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return (True, roll(queue));
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return (True, enqueue(dequeue(queue, len(pattern)), replacement));
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def define(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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right = context["right"];
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if right and left:
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if len(left) > 1:
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left = left[1:][:-1];
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if len(right) > 1:
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right = right[1:][:-1];
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rules.append((left, apply, [right]));
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return (True, dequeue(queue, len(construct(pattern, context))));
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return (False, roll(queue));
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def undefine(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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if left:
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if len(left) > 1:
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left = left[1:][:-1];
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for rule, index in zip(rules, range(0, len(rules))):
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candidate , _, _ = rule;
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if candidate == left:
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del rules[index];
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return (True, dequeue(queue, len(construct(pattern, context))));
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return (False, roll(queue));
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def add(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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right = context["right"];
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if left and right:
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if left[0][0] == "NUM" and right[0][0] == "NUM":
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queue = dequeue(queue, len(construct(pattern, context)));
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queue = enqueue(queue, parse(str(left[0][1] + right[0][1])));
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return (True, queue);
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return (False, roll(queue));
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def subtract(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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right = context["right"];
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if left and right:
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if left[0][0] == "NUM" and right[0][0] == "NUM":
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queue = dequeue(queue, len(construct(pattern, context)));
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queue = enqueue(queue, parse(str(left[0][1] - right[0][1])));
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return (True, queue);
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return (False, roll(queue));
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def multiply(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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right = context["right"];
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if left and right:
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if left[0][0] == "NUM" and right[0][0] == "NUM":
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queue = dequeue(queue, len(construct(pattern, context)));
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queue = enqueue(queue, parse(str(left[0][1] * right[0][1])));
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return (True, queue);
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return (False, roll(queue));
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def divide(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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right = context["right"];
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if left and right:
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if left[0][0] == "NUM" and right[0][0] == "NUM":
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queue = dequeue(queue, len(construct(pattern, context)));
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queue = enqueue(queue, parse(str(left[0][1] // right[0][1])));
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return (True, queue);
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return (False, roll(queue));
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def modulo(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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right = context["right"];
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if left and right:
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if left[0][0] == "NUM" and right[0][0] == "NUM":
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queue = dequeue(queue, len(construct(pattern, context)));
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queue = enqueue(queue, parse(str(left[0][1] % right[0][1])));
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return (True, queue);
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return (False, roll(queue));
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def display(queue, rules, pattern):
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context = match(pattern, queue);
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left = context["left"];
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if left:
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if left[0][0] == "LIT" or left[0][0] == "NUM":
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if left[0][1] == "space":
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print(' ', end="");
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elif left[0][1] == "newline":
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print('\n', end="");
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elif left[0][1] == "tab":
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print('\t', end="");
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else:
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print(left[0][1], end="");
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return (True, dequeue(queue, len(construct(pattern, context))));
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return (False, roll(queue));
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def applicable(rules, queue):
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results = [];
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for pattern, operation, parameters in rules:
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if match(pattern, queue) != None:
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results.append((pattern, operation, parameters));
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return results;
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def pick(list):
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if len(list) == 0:
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return None;
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return list[0];
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def reconstruct(pattern):
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for element in pattern:
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if element[0] == "INC":
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yield '(';
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elif element[0] == "DEC":
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yield ')';
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elif element[0] == "NUM":
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yield str(element[1]);
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elif element[0] == "LIT":
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yield element[1];
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elif element[0] == "VAR":
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yield '?' + element[1];
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yield ' ';
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def number(string):
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try:
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|
result = int(string);
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return True;
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except:
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return False;
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|
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def literal(string, index=0):
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|
token = "";
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while index != len(string):
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character = string[index];
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if character in ['(', ')', '{', '}', '[', ']', '?', ' ', '\t', '\n', '\r']:
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break;
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|
else:
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token = token + string[index];
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index = index + 1;
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|
return (token, index);
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|
def parse(string, index=0):
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|
results = [];
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while index != len(string):
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|
character = string[index];
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if character in ['(', ')', '{', '}', '[', ']', '?', ' ', '\t', '\n', '\r']:
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index = index + 1;
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|
if character in ['(', '{', '[']:
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results.append(["INC"]);
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|
elif character in [')', '}', ']']:
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results.append(["DEC"]);
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|
elif character not in [' ', '\t', '\n', '\r']:
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|
token, index = literal(string, index);
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|
if character == '?':
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|
results.append(["VAR", token]);
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|
elif number(token):
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|
results.append(["NUM", int(token)]);
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|
else:
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|
results.append(["LIT", token]);
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|
return results;
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|
|
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|
@measure
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|
def run(rules, queue, limit=pow(2, 32)):
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|
steps = 0;
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|
failures = 0;
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|
queue = [["SRT"]] + queue;
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|
while failures != len(queue) and steps != limit:
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|
rule = pick(applicable(rules, queue));
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|
if rule == None:
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|
queue = roll(queue);
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|
failures = failures + 1;
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|
print("<>: ", inspect(queue))
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|
else:
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||||||
|
pattern, operation, parameters = rule;
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|
result, queue = operation(queue, rules, pattern, *parameters);
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||||||
|
if result == True:
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|
failures = 0;
|
||||||
|
#print("<>: ", inspect(seek(queue, ["SRT"])), ":::", inspect(pattern))
|
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|
print("<>: ", inspect(queue), ":::", inspect(pattern))
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|
#input()
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||||||
|
steps = steps + 1;
|
||||||
|
if steps == limit:
|
||||||
|
print("Execution limit reached.");
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||||||
|
return queue;
|
||||||
|
|
||||||
|
def read(file):
|
||||||
|
try:
|
||||||
|
with open(file) as file:
|
||||||
|
content = file.read();
|
||||||
|
return content;
|
||||||
|
except EnvironmentError:
|
||||||
|
return None;
|
||||||
|
|
||||||
|
def inspect(pattern):
|
||||||
|
return "".join(reconstruct(pattern));
|
||||||
|
|
||||||
|
def usage(name):
|
||||||
|
print(name + ':', "a programming language based on rewriting.");
|
||||||
|
print("Usage:");
|
||||||
|
print((' ' * 4) + name, "<file>");
|
||||||
|
|
||||||
|
def prompt(prompt):
|
||||||
|
try:
|
||||||
|
return input(prompt);
|
||||||
|
except:
|
||||||
|
return None;
|
||||||
|
|
||||||
|
def help():
|
||||||
|
prefix = ' ' * 4;
|
||||||
|
print("Commands:");
|
||||||
|
print(prefix + "rules : Display the current ruleset.");
|
||||||
|
print(prefix + "clear : Clear the current ruleset.");
|
||||||
|
print(prefix + "help : This message.");
|
||||||
|
print(prefix + "quit : Quit.");
|
||||||
|
|
||||||
|
def main():
|
||||||
|
defaults = [
|
||||||
|
(parse("define ?left ?right"), define, []),
|
||||||
|
(parse("undefine ?left"), undefine, []),
|
||||||
|
(parse("add (?left) (?right)"), add, []),
|
||||||
|
(parse("add (?left) ?right"), add, []),
|
||||||
|
(parse("add ?left (?right)"), add, []),
|
||||||
|
(parse("add ?left ?right"), add, []),
|
||||||
|
(parse("subtract (?left) (?right)"), subtract, []),
|
||||||
|
(parse("subtract (?left) ?right"), subtract, []),
|
||||||
|
(parse("subtract ?left (?right)"), subtract, []),
|
||||||
|
(parse("subtract ?left ?right"), subtract, []),
|
||||||
|
(parse("multiply (?left) (?right)"), multiply, []),
|
||||||
|
(parse("multiply (?left) ?right"), multiply, []),
|
||||||
|
(parse("multiply ?left (?right)"), multiply, []),
|
||||||
|
(parse("multiply ?left ?right"), multiply, []),
|
||||||
|
(parse("divide (?left) (?right)"), divide, []),
|
||||||
|
(parse("divide (?left) ?right"), divide, []),
|
||||||
|
(parse("divide ?left (?right)"), divide, []),
|
||||||
|
(parse("divide ?left ?right"), divide, []),
|
||||||
|
(parse("modulo (?left) (?right)"), modulo, []),
|
||||||
|
(parse("modulo (?left) ?right"), modulo, []),
|
||||||
|
(parse("modulo ?left (?right)"), modulo, []),
|
||||||
|
(parse("modulo ?left ?right"), modulo, []),
|
||||||
|
(parse("(?left) + (?right)"), add, []),
|
||||||
|
(parse("(?left) + ?right"), add, []),
|
||||||
|
(parse("?left + (?right)"), add, []),
|
||||||
|
(parse("?left + ?right"), add, []),
|
||||||
|
(parse("(?left) - (?right)"), subtract, []),
|
||||||
|
(parse("(?left) - ?right"), subtract, []),
|
||||||
|
(parse("?left - (?right)"), subtract, []),
|
||||||
|
(parse("?left - ?right"), subtract, []),
|
||||||
|
(parse("(?left) * (?right)"), multiply, []),
|
||||||
|
(parse("(?left) * ?right"), multiply, []),
|
||||||
|
(parse("?left * (?right)"), multiply, []),
|
||||||
|
(parse("?left * ?right"), multiply, []),
|
||||||
|
(parse("?left / ?right"), divide, []),
|
||||||
|
(parse("?left % ?right"), modulo, []),
|
||||||
|
(parse("display ?left"), display, []),
|
||||||
|
];
|
||||||
|
rules = defaults;
|
||||||
|
if len(sys.argv) >= 2:
|
||||||
|
content = read(sys.argv[1]);
|
||||||
|
if content == None:
|
||||||
|
print("No such file.");
|
||||||
|
return;
|
||||||
|
print("Initializating...");
|
||||||
|
run(rules, parse(content));
|
||||||
|
print("Modal v0.02");
|
||||||
|
help();
|
||||||
|
while True:
|
||||||
|
input = prompt("::> ");
|
||||||
|
if input == None:
|
||||||
|
break;
|
||||||
|
elif parse(input) == parse("rules"):
|
||||||
|
print("Rules:");
|
||||||
|
prefix = ' ' * 4;
|
||||||
|
for pattern, operation, parameters in rules:
|
||||||
|
if operation == apply:
|
||||||
|
print(prefix + inspect(pattern) + "-> " + inspect(parameters[0]));
|
||||||
|
elif parse(input) == parse("clear"):
|
||||||
|
rules = defaults;
|
||||||
|
elif parse(input) == parse("help"):
|
||||||
|
help();
|
||||||
|
elif parse(input) == parse("quit") or parse(input) == parse("exit"):
|
||||||
|
break;
|
||||||
|
else:
|
||||||
|
print("Reducing...");
|
||||||
|
print(inspect(seek(run(rules, parse(input)), ["SRT"])));
|
||||||
|
return;
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
main();
|
||||||
|
|
@ -0,0 +1,144 @@
|
||||||
|
1 -> (s (0));
|
||||||
|
|
||||||
|
|
||||||
|
neg (neg ?x) -> ?x;
|
||||||
|
neg (0) -> 0;
|
||||||
|
|
||||||
|
|
||||||
|
add (s ?x) (s ?y) -> s (add ?x (s ?y));
|
||||||
|
add (0) (s ?x) -> s ?x;
|
||||||
|
add (s ?x) (0) -> s ?x;
|
||||||
|
add (0) (0) -> 0;
|
||||||
|
|
||||||
|
|
||||||
|
?x + ?y + ?z -> (?x + ?y) + ?z;
|
||||||
|
|
||||||
|
|
||||||
|
?x + ?y -> add ?x ?y;
|
||||||
|
|
||||||
|
|
||||||
|
sub (s ?x) (s ?y) -> sub ?x ?y;
|
||||||
|
sub (s ?x) (0) -> s ?x;
|
||||||
|
sub (0) (s ?x) -> neg (s ?x);
|
||||||
|
sub (0) (0) -> 0;
|
||||||
|
|
||||||
|
|
||||||
|
?x - ?y -> sub ?x ?y;
|
||||||
|
|
||||||
|
|
||||||
|
mul (s ?x) (s ?y) -> (s ?x) + (mul (s ?x) ((s ?y) - 1));
|
||||||
|
mul (s ?x) (s (0)) -> s ?x;
|
||||||
|
mul (s ?x) (0) -> 0;
|
||||||
|
mul (0) (s ?x) -> 0;
|
||||||
|
|
||||||
|
|
||||||
|
?x * ?y -> mul ?x ?y;
|
||||||
|
|
||||||
|
|
||||||
|
Ensures that a list or a number has been reduced to its normal form. ;
|
||||||
|
|
||||||
|
reduced (0) -> true;
|
||||||
|
reduced (nil) -> true;
|
||||||
|
reduced (s ?x) -> reduced ?x;
|
||||||
|
reduced (?h : ?t) -> reduced ?t;
|
||||||
|
reduced ?x -> false;
|
||||||
|
|
||||||
|
|
||||||
|
Because there may be conflicts with expressions that
|
||||||
|
are currently being reduced, we need to fold over reduced
|
||||||
|
lists, i.e ones that have already been fully generated. ;
|
||||||
|
|
||||||
|
fold (?f) ?i ?l -> fold reduced ?l (?f) ?i ?l;
|
||||||
|
fold true (?f) ?i (nil) -> ?i;
|
||||||
|
fold true (?f) ?i (?h : (nil)) -> ?f ?i ?h;
|
||||||
|
fold true (?f) ?i (?h : ?t) -> ?f ?i (fold (?f) ?h ?t);
|
||||||
|
fold false (?f) ?i ?l -> fold (?f) ?i ?l;
|
||||||
|
|
||||||
|
|
||||||
|
factorial (s (0)) -> s (0);
|
||||||
|
factorial (s ?x) -> (s ?x) * (factorial ((s ?x) - 1));
|
||||||
|
|
||||||
|
|
||||||
|
sum (?h : ?t) -> fold (add) (0) (?h : ?t);
|
||||||
|
|
||||||
|
|
||||||
|
range ?x (s (0)) -> ?x : (nil);
|
||||||
|
range ?x (s ?y) -> ?x : (range (?x + 1) ((s ?y) - 1));
|
||||||
|
|
||||||
|
|
||||||
|
Disgusting (yet valid) hack for currying.
|
||||||
|
We need lambdas. ;
|
||||||
|
|
||||||
|
unpack (?h : nil) -> ?h;
|
||||||
|
unpack (?h : ?t) -> ?h unpack ?t;
|
||||||
|
unpack (?x) -> ?x;
|
||||||
|
unpack (?x . -> ?x unpack (;
|
||||||
|
|
||||||
|
|
||||||
|
:: (?f) ?a -> ?f unpack ?a;
|
||||||
|
|
||||||
|
|
||||||
|
mapp (?f) ?a (nil) -> nil;
|
||||||
|
mapp (?f) ?a (?h : (nil)) -> (?f unpack ?a ?h) : (nil);
|
||||||
|
mapp (?f) ?a (?h : ?t) -> (?f unpack ?a ?h) : (mapp (?f) ?a ?t);
|
||||||
|
|
||||||
|
|
||||||
|
map (?f) (nil) -> nil;
|
||||||
|
map (?f) (?h : nil) -> (?f ?h) : (nil);
|
||||||
|
map (?f) (?h : ?t) -> (?f ?h) : (map (?f) ?t);
|
||||||
|
|
||||||
|
|
||||||
|
product ?x -> fold (mul) 1 ?x;
|
||||||
|
|
||||||
|
|
||||||
|
factorial2 ?x -> product (range 1 ?x);
|
||||||
|
|
||||||
|
|
||||||
|
contains ?x (nil) -> false;
|
||||||
|
contains ?x (?x : ?t) -> true;
|
||||||
|
contains ?x (?h : ?t) -> contains ?x ?t;
|
||||||
|
|
||||||
|
|
||||||
|
unique (nil) -> nil;
|
||||||
|
unique false (?h : ?t) -> ?h : (unique ?t);
|
||||||
|
unique true (?h : ?t) -> unique ?t;
|
||||||
|
unique (?h : ?t) -> unique contains ?h ?t (?h : ?t);
|
||||||
|
|
||||||
|
|
||||||
|
length (nil) -> 0;
|
||||||
|
length (?h : ?t) -> s (length ?t);
|
||||||
|
|
||||||
|
|
||||||
|
zipWith (?f) (nil) (nil) -> nil;
|
||||||
|
zipWith (?f) (?h : ?t) (nil) -> nil;
|
||||||
|
zipWith (?f) (nil) (?h : ?t) -> nil;
|
||||||
|
zipWith (?f) (?h1 : ?t1) (?h2 : ?t2) -> (?f ?h1 ?h2) : (zipWith (?f) ?t1 ?t2);
|
||||||
|
|
||||||
|
|
||||||
|
evens ?x -> zipWith (add) (range (0) ?x) (range (0) ?x);
|
||||||
|
|
||||||
|
|
||||||
|
not (not ?x) -> ?x;
|
||||||
|
not true -> false;
|
||||||
|
not false -> true;
|
||||||
|
|
||||||
|
|
||||||
|
any ?x -> contains true ?x;
|
||||||
|
|
||||||
|
|
||||||
|
all ?x -> not contains false ?x;
|
||||||
|
|
||||||
|
|
||||||
|
none ?x -> not any ?x;
|
||||||
|
|
||||||
|
|
||||||
|
add1 ?x -> add ?x 1;
|
||||||
|
|
||||||
|
|
||||||
|
square ?x -> ?x * ?x;
|
||||||
|
|
||||||
|
|
||||||
|
reduce (s ?x) -> s (reduce ?x);
|
||||||
|
reduce (0) -> (0);
|
||||||
|
reduce (?h : ?t) -> ?h : (reduce ?t);
|
||||||
|
reduce (nil) -> nil;
|
||||||
Loading…
Reference in New Issue