interpreter

4 files changed, 750 insertions, 0 deletions

diff --git a/README.md b/README.md
new file mode 100644
index 0000000..79361d7
--- /dev/null
+++ b/README.md
@@ -0,0 +1 @@
+usage: `bun repl.ts`
diff --git a/grammar.peggy b/grammar.peggy
new file mode 100644
index 0000000..c2dd580
--- /dev/null
+++ b/grammar.peggy
@@ -0,0 +1,14 @@
+LambdaTerm = Application / Abstraction / Variable
+
+Application = LPAREN _ left:LambdaTerm _ right:LambdaTerm RPAREN { return { application: { left, right } }; }
+
+Abstraction = LPAREN _ LAMBDA _ param:Variable _ DOT _ body:LambdaTerm RPAREN { return { abstraction: { param, body } }; }
+
+Variable = param:[a-zA-Z0-9]+ { return param.join(""); }
+
+LPAREN = "("
+RPAREN = ")"
+DOT = "."
+LAMBDA = "λ" / "\\"
+
+_ = ("\n" / " " / "\t" / "\r\n")*
diff --git a/parser.js b/parser.js
new file mode 100644
index 0000000..b57a127
--- /dev/null
+++ b/parser.js
@@ -0,0 +1,629 @@
+module.exports = // @generated by Peggy 4.0.0.
+//
+// https://peggyjs.org/
+(function() {
+  "use strict";
+
+function peg$subclass(child, parent) {
+  function C() { this.constructor = child; }
+  C.prototype = parent.prototype;
+  child.prototype = new C();
+}
+
+function peg$SyntaxError(message, expected, found, location) {
+  var self = Error.call(this, message);
+  // istanbul ignore next Check is a necessary evil to support older environments
+  if (Object.setPrototypeOf) {
+    Object.setPrototypeOf(self, peg$SyntaxError.prototype);
+  }
+  self.expected = expected;
+  self.found = found;
+  self.location = location;
+  self.name = "SyntaxError";
+  return self;
+}
+
+peg$subclass(peg$SyntaxError, Error);
+
+function peg$padEnd(str, targetLength, padString) {
+  padString = padString || " ";
+  if (str.length > targetLength) { return str; }
+  targetLength -= str.length;
+  padString += padString.repeat(targetLength);
+  return str + padString.slice(0, targetLength);
+}
+
+peg$SyntaxError.prototype.format = function(sources) {
+  var str = "Error: " + this.message;
+  if (this.location) {
+    var src = null;
+    var k;
+    for (k = 0; k < sources.length; k++) {
+      if (sources[k].source === this.location.source) {
+        src = sources[k].text.split(/\r\n|\n|\r/g);
+        break;
+      }
+    }
+    var s = this.location.start;
+    var offset_s = (this.location.source && (typeof this.location.source.offset === "function"))
+      ? this.location.source.offset(s)
+      : s;
+    var loc = this.location.source + ":" + offset_s.line + ":" + offset_s.column;
+    if (src) {
+      var e = this.location.end;
+      var filler = peg$padEnd("", offset_s.line.toString().length, ' ');
+      var line = src[s.line - 1];
+      var last = s.line === e.line ? e.column : line.length + 1;
+      var hatLen = (last - s.column) || 1;
+      str += "\n --> " + loc + "\n"
+          + filler + " |\n"
+          + offset_s.line + " | " + line + "\n"
+          + filler + " | " + peg$padEnd("", s.column - 1, ' ')
+          + peg$padEnd("", hatLen, "^");
+    } else {
+      str += "\n at " + loc;
+    }
+  }
+  return str;
+};
+
+peg$SyntaxError.buildMessage = function(expected, found) {
+  var DESCRIBE_EXPECTATION_FNS = {
+    literal: function(expectation) {
+      return "\"" + literalEscape(expectation.text) + "\"";
+    },
+
+    class: function(expectation) {
+      var escapedParts = expectation.parts.map(function(part) {
+        return Array.isArray(part)
+          ? classEscape(part[0]) + "-" + classEscape(part[1])
+          : classEscape(part);
+      });
+
+      return "[" + (expectation.inverted ? "^" : "") + escapedParts.join("") + "]";
+    },
+
+    any: function() {
+      return "any character";
+    },
+
+    end: function() {
+      return "end of input";
+    },
+
+    other: function(expectation) {
+      return expectation.description;
+    }
+  };
+
+  function hex(ch) {
+    return ch.charCodeAt(0).toString(16).toUpperCase();
+  }
+
+  function literalEscape(s) {
+    return s
+      .replace(/\\/g, "\\\\")
+      .replace(/"/g,  "\\\"")
+      .replace(/\0/g, "\\0")
+      .replace(/\t/g, "\\t")
+      .replace(/\n/g, "\\n")
+      .replace(/\r/g, "\\r")
+      .replace(/[\x00-\x0F]/g,          function(ch) { return "\\x0" + hex(ch); })
+      .replace(/[\x10-\x1F\x7F-\x9F]/g, function(ch) { return "\\x"  + hex(ch); });
+  }
+
+  function classEscape(s) {
+    return s
+      .replace(/\\/g, "\\\\")
+      .replace(/\]/g, "\\]")
+      .replace(/\^/g, "\\^")
+      .replace(/-/g,  "\\-")
+      .replace(/\0/g, "\\0")
+      .replace(/\t/g, "\\t")
+      .replace(/\n/g, "\\n")
+      .replace(/\r/g, "\\r")
+      .replace(/[\x00-\x0F]/g,          function(ch) { return "\\x0" + hex(ch); })
+      .replace(/[\x10-\x1F\x7F-\x9F]/g, function(ch) { return "\\x"  + hex(ch); });
+  }
+
+  function describeExpectation(expectation) {
+    return DESCRIBE_EXPECTATION_FNS[expectation.type](expectation);
+  }
+
+  function describeExpected(expected) {
+    var descriptions = expected.map(describeExpectation);
+    var i, j;
+
+    descriptions.sort();
+
+    if (descriptions.length > 0) {
+      for (i = 1, j = 1; i < descriptions.length; i++) {
+        if (descriptions[i - 1] !== descriptions[i]) {
+          descriptions[j] = descriptions[i];
+          j++;
+        }
+      }
+      descriptions.length = j;
+    }
+
+    switch (descriptions.length) {
+      case 1:
+        return descriptions[0];
+
+      case 2:
+        return descriptions[0] + " or " + descriptions[1];
+
+      default:
+        return descriptions.slice(0, -1).join(", ")
+          + ", or "
+          + descriptions[descriptions.length - 1];
+    }
+  }
+
+  function describeFound(found) {
+    return found ? "\"" + literalEscape(found) + "\"" : "end of input";
+  }
+
+  return "Expected " + describeExpected(expected) + " but " + describeFound(found) + " found.";
+};
+
+function peg$parse(input, options) {
+  options = options !== undefined ? options : {};
+
+  var peg$FAILED = {};
+  var peg$source = options.grammarSource;
+
+  var peg$startRuleFunctions = { LambdaTerm: peg$parseLambdaTerm };
+  var peg$startRuleFunction = peg$parseLambdaTerm;
+
+  var peg$c0 = "(";
+  var peg$c1 = ")";
+  var peg$c2 = ".";
+  var peg$c3 = "\r\n";
+
+  var peg$r0 = /^[a-zA-Z0-9]/;
+  var peg$r1 = /^[\\\u03BB]/;
+  var peg$r2 = /^[\t-\n ]/;
+
+  var peg$e0 = peg$classExpectation([["a", "z"], ["A", "Z"], ["0", "9"]], false, false);
+  var peg$e1 = peg$literalExpectation("(", false);
+  var peg$e2 = peg$literalExpectation(")", false);
+  var peg$e3 = peg$literalExpectation(".", false);
+  var peg$e4 = peg$classExpectation(["\\", "\u03BB"], false, false);
+  var peg$e5 = peg$classExpectation([["\t", "\n"], " "], false, false);
+  var peg$e6 = peg$literalExpectation("\r\n", false);
+
+  var peg$f0 = function(left, right) { return { application: { left, right } }; };
+  var peg$f1 = function(param, body) { return { abstraction: { param, body } }; };
+  var peg$f2 = function(param) { return param.join(""); };
+  var peg$currPos = options.peg$currPos | 0;
+  var peg$savedPos = peg$currPos;
+  var peg$posDetailsCache = [{ line: 1, column: 1 }];
+  var peg$maxFailPos = peg$currPos;
+  var peg$maxFailExpected = options.peg$maxFailExpected || [];
+  var peg$silentFails = options.peg$silentFails | 0;
+
+  var peg$result;
+
+  if (options.startRule) {
+    if (!(options.startRule in peg$startRuleFunctions)) {
+      throw new Error("Can't start parsing from rule \"" + options.startRule + "\".");
+    }
+
+    peg$startRuleFunction = peg$startRuleFunctions[options.startRule];
+  }
+
+  function text() {
+    return input.substring(peg$savedPos, peg$currPos);
+  }
+
+  function offset() {
+    return peg$savedPos;
+  }
+
+  function range() {
+    return {
+      source: peg$source,
+      start: peg$savedPos,
+      end: peg$currPos
+    };
+  }
+
+  function location() {
+    return peg$computeLocation(peg$savedPos, peg$currPos);
+  }
+
+  function expected(description, location) {
+    location = location !== undefined
+      ? location
+      : peg$computeLocation(peg$savedPos, peg$currPos);
+
+    throw peg$buildStructuredError(
+      [peg$otherExpectation(description)],
+      input.substring(peg$savedPos, peg$currPos),
+      location
+    );
+  }
+
+  function error(message, location) {
+    location = location !== undefined
+      ? location
+      : peg$computeLocation(peg$savedPos, peg$currPos);
+
+    throw peg$buildSimpleError(message, location);
+  }
+
+  function peg$literalExpectation(text, ignoreCase) {
+    return { type: "literal", text: text, ignoreCase: ignoreCase };
+  }
+
+  function peg$classExpectation(parts, inverted, ignoreCase) {
+    return { type: "class", parts: parts, inverted: inverted, ignoreCase: ignoreCase };
+  }
+
+  function peg$anyExpectation() {
+    return { type: "any" };
+  }
+
+  function peg$endExpectation() {
+    return { type: "end" };
+  }
+
+  function peg$otherExpectation(description) {
+    return { type: "other", description: description };
+  }
+
+  function peg$computePosDetails(pos) {
+    var details = peg$posDetailsCache[pos];
+    var p;
+
+    if (details) {
+      return details;
+    } else {
+      if (pos >= peg$posDetailsCache.length) {
+        p = peg$posDetailsCache.length - 1;
+      } else {
+        p = pos;
+        while (!peg$posDetailsCache[--p]) {}
+      }
+
+      details = peg$posDetailsCache[p];
+      details = {
+        line: details.line,
+        column: details.column
+      };
+
+      while (p < pos) {
+        if (input.charCodeAt(p) === 10) {
+          details.line++;
+          details.column = 1;
+        } else {
+          details.column++;
+        }
+
+        p++;
+      }
+
+      peg$posDetailsCache[pos] = details;
+
+      return details;
+    }
+  }
+
+  function peg$computeLocation(startPos, endPos, offset) {
+    var startPosDetails = peg$computePosDetails(startPos);
+    var endPosDetails = peg$computePosDetails(endPos);
+
+    var res = {
+      source: peg$source,
+      start: {
+        offset: startPos,
+        line: startPosDetails.line,
+        column: startPosDetails.column
+      },
+      end: {
+        offset: endPos,
+        line: endPosDetails.line,
+        column: endPosDetails.column
+      }
+    };
+    if (offset && peg$source && (typeof peg$source.offset === "function")) {
+      res.start = peg$source.offset(res.start);
+      res.end = peg$source.offset(res.end);
+    }
+    return res;
+  }
+
+  function peg$fail(expected) {
+    if (peg$currPos < peg$maxFailPos) { return; }
+
+    if (peg$currPos > peg$maxFailPos) {
+      peg$maxFailPos = peg$currPos;
+      peg$maxFailExpected = [];
+    }
+
+    peg$maxFailExpected.push(expected);
+  }
+
+  function peg$buildSimpleError(message, location) {
+    return new peg$SyntaxError(message, null, null, location);
+  }
+
+  function peg$buildStructuredError(expected, found, location) {
+    return new peg$SyntaxError(
+      peg$SyntaxError.buildMessage(expected, found),
+      expected,
+      found,
+      location
+    );
+  }
+
+  function peg$parseLambdaTerm() {
+    var s0;
+
+    s0 = peg$parseApplication();
+    if (s0 === peg$FAILED) {
+      s0 = peg$parseAbstraction();
+      if (s0 === peg$FAILED) {
+        s0 = peg$parseVariable();
+      }
+    }
+
+    return s0;
+  }
+
+  function peg$parseApplication() {
+    var s0, s1, s2, s3, s4, s5, s6;
+
+    s0 = peg$currPos;
+    s1 = peg$parseLPAREN();
+    if (s1 !== peg$FAILED) {
+      s2 = peg$parse_();
+      s3 = peg$parseLambdaTerm();
+      if (s3 !== peg$FAILED) {
+        s4 = peg$parse_();
+        s5 = peg$parseLambdaTerm();
+        if (s5 !== peg$FAILED) {
+          s6 = peg$parseRPAREN();
+          if (s6 !== peg$FAILED) {
+            peg$savedPos = s0;
+            s0 = peg$f0(s3, s5);
+          } else {
+            peg$currPos = s0;
+            s0 = peg$FAILED;
+          }
+        } else {
+          peg$currPos = s0;
+          s0 = peg$FAILED;
+        }
+      } else {
+        peg$currPos = s0;
+        s0 = peg$FAILED;
+      }
+    } else {
+      peg$currPos = s0;
+      s0 = peg$FAILED;
+    }
+
+    return s0;
+  }
+
+  function peg$parseAbstraction() {
+    var s0, s1, s2, s3, s4, s5, s6, s7, s8, s9, s10;
+
+    s0 = peg$currPos;
+    s1 = peg$parseLPAREN();
+    if (s1 !== peg$FAILED) {
+      s2 = peg$parse_();
+      s3 = peg$parseLAMBDA();
+      if (s3 !== peg$FAILED) {
+        s4 = peg$parse_();
+        s5 = peg$parseVariable();
+        if (s5 !== peg$FAILED) {
+          s6 = peg$parse_();
+          s7 = peg$parseDOT();
+          if (s7 !== peg$FAILED) {
+            s8 = peg$parse_();
+            s9 = peg$parseLambdaTerm();
+            if (s9 !== peg$FAILED) {
+              s10 = peg$parseRPAREN();
+              if (s10 !== peg$FAILED) {
+                peg$savedPos = s0;
+                s0 = peg$f1(s5, s9);
+              } else {
+                peg$currPos = s0;
+                s0 = peg$FAILED;
+              }
+            } else {
+              peg$currPos = s0;
+              s0 = peg$FAILED;
+            }
+          } else {
+            peg$currPos = s0;
+            s0 = peg$FAILED;
+          }
+        } else {
+          peg$currPos = s0;
+          s0 = peg$FAILED;
+        }
+      } else {
+        peg$currPos = s0;
+        s0 = peg$FAILED;
+      }
+    } else {
+      peg$currPos = s0;
+      s0 = peg$FAILED;
+    }
+
+    return s0;
+  }
+
+  function peg$parseVariable() {
+    var s0, s1, s2;
+
+    s0 = peg$currPos;
+    s1 = [];
+    s2 = input.charAt(peg$currPos);
+    if (peg$r0.test(s2)) {
+      peg$currPos++;
+    } else {
+      s2 = peg$FAILED;
+      if (peg$silentFails === 0) { peg$fail(peg$e0); }
+    }
+    if (s2 !== peg$FAILED) {
+      while (s2 !== peg$FAILED) {
+        s1.push(s2);
+        s2 = input.charAt(peg$currPos);
+        if (peg$r0.test(s2)) {
+          peg$currPos++;
+        } else {
+          s2 = peg$FAILED;
+          if (peg$silentFails === 0) { peg$fail(peg$e0); }
+        }
+      }
+    } else {
+      s1 = peg$FAILED;
+    }
+    if (s1 !== peg$FAILED) {
+      peg$savedPos = s0;
+      s1 = peg$f2(s1);
+    }
+    s0 = s1;
+
+    return s0;
+  }
+
+  function peg$parseLPAREN() {
+    var s0;
+
+    if (input.charCodeAt(peg$currPos) === 40) {
+      s0 = peg$c0;
+      peg$currPos++;
+    } else {
+      s0 = peg$FAILED;
+      if (peg$silentFails === 0) { peg$fail(peg$e1); }
+    }
+
+    return s0;
+  }
+
+  function peg$parseRPAREN() {
+    var s0;
+
+    if (input.charCodeAt(peg$currPos) === 41) {
+      s0 = peg$c1;
+      peg$currPos++;
+    } else {
+      s0 = peg$FAILED;
+      if (peg$silentFails === 0) { peg$fail(peg$e2); }
+    }
+
+    return s0;
+  }
+
+  function peg$parseDOT() {
+    var s0;
+
+    if (input.charCodeAt(peg$currPos) === 46) {
+      s0 = peg$c2;
+      peg$currPos++;
+    } else {
+      s0 = peg$FAILED;
+      if (peg$silentFails === 0) { peg$fail(peg$e3); }
+    }
+
+    return s0;
+  }
+
+  function peg$parseLAMBDA() {
+    var s0;
+
+    s0 = input.charAt(peg$currPos);
+    if (peg$r1.test(s0)) {
+      peg$currPos++;
+    } else {
+      s0 = peg$FAILED;
+      if (peg$silentFails === 0) { peg$fail(peg$e4); }
+    }
+
+    return s0;
+  }
+
+  function peg$parse_() {
+    var s0, s1;
+
+    s0 = [];
+    s1 = input.charAt(peg$currPos);
+    if (peg$r2.test(s1)) {
+      peg$currPos++;
+    } else {
+      s1 = peg$FAILED;
+      if (peg$silentFails === 0) { peg$fail(peg$e5); }
+    }
+    if (s1 === peg$FAILED) {
+      if (input.substr(peg$currPos, 2) === peg$c3) {
+        s1 = peg$c3;
+        peg$currPos += 2;
+      } else {
+        s1 = peg$FAILED;
+        if (peg$silentFails === 0) { peg$fail(peg$e6); }
+      }
+    }
+    while (s1 !== peg$FAILED) {
+      s0.push(s1);
+      s1 = input.charAt(peg$currPos);
+      if (peg$r2.test(s1)) {
+        peg$currPos++;
+      } else {
+        s1 = peg$FAILED;
+        if (peg$silentFails === 0) { peg$fail(peg$e5); }
+      }
+      if (s1 === peg$FAILED) {
+        if (input.substr(peg$currPos, 2) === peg$c3) {
+          s1 = peg$c3;
+          peg$currPos += 2;
+        } else {
+          s1 = peg$FAILED;
+          if (peg$silentFails === 0) { peg$fail(peg$e6); }
+        }
+      }
+    }
+
+    return s0;
+  }
+
+  peg$result = peg$startRuleFunction();
+
+  if (options.peg$library) {
+    return /** @type {any} */ ({
+      peg$result,
+      peg$currPos,
+      peg$FAILED,
+      peg$maxFailExpected,
+      peg$maxFailPos
+    });
+  }
+  if (peg$result !== peg$FAILED && peg$currPos === input.length) {
+    return peg$result;
+  } else {
+    if (peg$result !== peg$FAILED && peg$currPos < input.length) {
+      peg$fail(peg$endExpectation());
+    }
+
+    throw peg$buildStructuredError(
+      peg$maxFailExpected,
+      peg$maxFailPos < input.length ? input.charAt(peg$maxFailPos) : null,
+      peg$maxFailPos < input.length
+        ? peg$computeLocation(peg$maxFailPos, peg$maxFailPos + 1)
+        : peg$computeLocation(peg$maxFailPos, peg$maxFailPos)
+    );
+  }
+}
+
+  return {
+    StartRules: ["LambdaTerm"],
+    SyntaxError: peg$SyntaxError,
+    parse: peg$parse
+  };
+})()
+;
diff --git a/repl.ts b/repl.ts
new file mode 100644
index 0000000..6a67e50
--- /dev/null
+++ b/repl.ts
@@ -0,0 +1,106 @@
+const peggy = require("./parser.js");
+
+const isVariable = (ast: any) => typeof ast === "string";
+const isApplication = (ast: any) =>
+  typeof ast === "object" && "application" in ast;
+const isAbstraction = (ast: any) =>
+  typeof ast === "object" && "abstraction" in ast;
+
+const emitCode = (ast: any) => {
+  if (isVariable(ast)) {
+    return ast;
+  }
+
+  if (isApplication(ast)) {
+    const { application } = ast;
+    const { left, right } = application;
+    return `( ${emitCode(left)} ${emitCode(right)} )`;
+  }
+
+  const { abstraction } = ast;
+  const { param, body } = abstraction;
+
+  return `(λ ${emitCode(param)} . ${emitCode(body)})`;
+};
+
+const substitute = (param: string, term: any, result: any) => {
+  if (isVariable(term)) {
+    if (term === param) {
+      return result;
+    }
+    return term;
+  }
+
+  if (isApplication(term)) {
+    const { application } = term;
+    const { left, right } = application;
+
+    return {
+      application: {
+        left: substitute(param, left, result),
+        right: substitute(param, right, result),
+      },
+    };
+  }
+
+  const { abstraction } = term;
+  const { body } = abstraction;
+  return {
+    abstraction: {
+      param: abstraction.param,
+      body: substitute(param, body, result),
+    },
+  };
+};
+
+const betaReduce = (ast: any) => {
+  if (isVariable(ast)) {
+    return ast;
+  }
+
+  if (isApplication(ast)) {
+    const { application } = ast;
+    const { left, right } = application;
+
+    if (isAbstraction(left)) {
+      const { abstraction } = left;
+      const { param } = abstraction;
+
+      return substitute(param, right);
+    }
+
+    return {
+      application: {
+        left: betaReduce(left),
+        right: betaReduce(right),
+      },
+    };
+  }
+
+  // it's an abstraction
+  const { abstraction } = ast;
+  const { param, body } = abstraction;
+  return { param: betaReduce(param), body: betaReduce(body) };
+};
+
+const evaluate = (lambdaTerm: string) => {
+  const ast = peggy.parse(lambdaTerm);
+
+  const fullBetaReduction = betaReduce(ast);
+  return emitCode(fullBetaReduction);
+};
+
+const doRepl = async () => {
+  const prompt = ">>> ";
+  process.stdout.write(prompt);
+
+  for await (const line of console) {
+    const result = evaluate(line);
+    console.log(result);
+    break;
+  }
+
+  await doRepl();
+};
+
+await doRepl();