# Author: Paul Fitzpatrick, paulfitz@ai.mit.edu
# Copyright (c) 2004 Paul Fitzpatrick
#
# This file is part of CosmicOS.
#
# CosmicOS is free software; you can redistribute it and / or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# CosmicOS is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with CosmicOS; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
# MATH introduce numbers (in unary notation)
# Here we count up, then count down, then go through primes, etc.
# There is a bunch of syntax around the numbers, but that
# can just be treated as noise at this point - it doesn't matter.
# Any 'words' written here are converted to arbitrary integers
# in the actual message. Any word ending in -in-unary will be given
# in unary rather than the binary code used in the main body
# of the message - this is simpler to start with.
[hear] (intro-in-unary 010);
[hear] (intro-in-unary 0110);
[hear] (intro-in-unary 01110);
[hear] (intro-in-unary 011110);
[hear] (intro-in-unary 0111110);
[hear] (intro-in-unary 01111110);
[hear] (intro-in-unary 011111110);
[hear] (intro-in-unary 0111111110);
[hear] (intro-in-unary 01111111110);
[hear] (intro-in-unary 011111111110);
[hear] (intro-in-unary 0111111111110);
[hear] (intro-in-unary 01111111111110);
[hear] (intro-in-unary 011111111111110);
[hear] (intro-in-unary 0111111111111110);
[hear] (intro-in-unary 01111111111111110);
[hear] (intro-in-unary 011111111111111110);
[hear] (intro-in-unary 0111111111111111110);
[hear] (intro-in-unary 01111111111111111110);
[hear] (intro-in-unary 011111111111111111110);
[hear] (intro-in-unary 0111111111111111111110);
[hear] (intro-in-unary 01111111111111111111110);
[hear] (intro-in-unary 011111111111111111111110);
[hear] (intro-in-unary 0111111111111111111111110);
[hear] (intro-in-unary 01111111111111111111111110);
[hear] (intro-in-unary 011111111111111111111111110);
[hear] (intro-in-unary 0111111111111111111111111110);
[hear] (intro-in-unary 01111111111111111111111111110);
[hear] (intro-in-unary 0111111111111111111111111110);
[hear] (intro-in-unary 011111111111111111111111110);
[hear] (intro-in-unary 01111111111111111111111110);
[hear] (intro-in-unary 0111111111111111111111110);
[hear] (intro-in-unary 011111111111111111111110);
[hear] (intro-in-unary 01111111111111111111110);
[hear] (intro-in-unary 0111111111111111111110);
[hear] (intro-in-unary 011111111111111111110);
[hear] (intro-in-unary 01111111111111111110);
[hear] (intro-in-unary 0111111111111111110);
[hear] (intro-in-unary 011111111111111110);
[hear] (intro-in-unary 01111111111111110);
[hear] (intro-in-unary 0111111111111110);
[hear] (intro-in-unary 011111111111110);
[hear] (intro-in-unary 01111111111110);
[hear] (intro-in-unary 0111111111110);
[hear] (intro-in-unary 011111111110);
[hear] (intro-in-unary 01111111110);
[hear] (intro-in-unary 0111111110);
[hear] (intro-in-unary 011111110);
[hear] (intro-in-unary 01111110);
[hear] (intro-in-unary 0111110);
[hear] (intro-in-unary 011110);
[hear] (intro-in-unary 01110);
[hear] (intro-in-unary 0110);
[hear] (intro-in-unary 010);
[hear] (intro-in-unary 0110);
[hear] (intro-in-unary 01110);
[hear] (intro-in-unary 0111110);
[hear] (intro-in-unary 011111110);
[hear] (intro-in-unary 0111111111110);
[hear] (intro-in-unary 011111111111110);
[hear] (intro-in-unary 0111111111111111110);
[hear] (intro-in-unary 011111111111111111110);
[hear] (intro-in-unary 0111111111111111111111110);
[hear] (intro-in-unary 010);
[hear] (intro-in-unary 011110);
[hear] (intro-in-unary 01111111110);
[hear] (intro-in-unary 011111111111111110);
[hear] (intro-in-unary 011111111111111111111111110);
[hear] (intro-in-unary 010);
[hear] (intro-in-unary 0111111110);
[hear] (intro-in-unary 01111111111111111111111111110);
# MATH introduce equality for unary numbers
# The intro operator does nothing essential, and could be
# omitted - it just tags the first use of a new operator.
# The = operator is introduced alongside a duplication of
# unary numbers. The meaning will not quite by nailed down
# until we see other relational operators.
[hear] (=-in-unary 010 010);
[hear] (=-in-unary 0110 0110);
[hear] (=-in-unary 01110 01110);
[hear] (=-in-unary 011110 011110);
[hear] (=-in-unary 0111110 0111110);
[hear] (=-in-unary 01111110 01111110);
[hear] (=-in-unary 011111110 011111110);
[hear] (=-in-unary 0111111110 0111111110);
[hear] (=-in-unary 010 010);
[hear] (=-in-unary 01111110 01111110);
[hear] (=-in-unary 0110 0110);
# MATH now introduce other relational operators
# After this lesson, it should be clear what contexts
# < > and = are appropriate in.
[hear] (>-in-unary 01111110 0110);
[hear] (>-in-unary 0110 00);
[hear] (>-in-unary 010 00);
[hear] (>-in-unary 01110 010);
[hear] (>-in-unary 010 00);
[hear] (>-in-unary 011110 00);
[hear] (>-in-unary 010 00);
[hear] (>-in-unary 0110 00);
[hear] (>-in-unary 010 00);
[hear] (>-in-unary 01111110 00);
[hear] (>-in-unary 0110 00);
[hear] (<-in-unary 0110 011110);
[hear] (<-in-unary 00 01111110);
[hear] (<-in-unary 01110 01111110);
[hear] (<-in-unary 00 01110);
[hear] (<-in-unary 0110 011110);
[hear] (<-in-unary 00 0110);
[hear] (<-in-unary 0110 011110);
[hear] (<-in-unary 010 01110);
[hear] (<-in-unary 0110 01111110);
[hear] (<-in-unary 0110 0111110);
[hear] (<-in-unary 00 0111110);
# drive the lesson home
[hear] (=-in-unary 00 00);
[hear] (<-in-unary 00 010);
[hear] (<-in-unary 00 0110);
[hear] (>-in-unary 010 00);
[hear] (=-in-unary 010 010);
[hear] (<-in-unary 010 0110);
[hear] (>-in-unary 0110 00);
[hear] (>-in-unary 0110 010);
[hear] (=-in-unary 0110 0110);
# switch to binary labelling
[hear] (= 00 00);
[hear] (< 00 010);
[hear] (< 00 0110);
[hear] (> 010 00);
[hear] (= 010 010);
[hear] (< 010 0110);
[hear] (> 0110 00);
[hear] (> 0110 010);
[hear] (= 0110 0110);
# a few more random examples
[hear] (> 0111110 010);
[hear] (> 0111110 0110);
[hear] (> 0111110 010);
[hear] (> 011110 00);
[hear] (< 0110 011110);
[hear] (< 0110 01110);
[hear] (< 010 01110);
[hear] (< 011110 0111110);
[hear] (< 00 0111110);
[hear] (< 01110 011110);
[hear] (< 010 01110);
# MATH introduce the NOT logical operator
[hear] (intro not);
[hear] (= 01110 01110);
[hear] (not / < 01110 01110);
[hear] (not / > 01110 01110);
[hear] (= 010 010);
[hear] (not / < 010 010);
[hear] (not / > 010 010);
[hear] (= 0110 0110);
[hear] (not / < 0110 0110);
[hear] (not / > 0110 0110);
[hear] (= 011110 011110);
[hear] (not / < 011110 011110);
[hear] (not / > 011110 011110);
[hear] (= 01110 01110);
[hear] (not / < 01110 01110);
[hear] (not / > 01110 01110);
[hear] (= 0110 0110);
[hear] (not / < 0110 0110);
[hear] (not / > 0110 0110);
[hear] (not / = 01110 011110);
[hear] (< 01110 011110);
[hear] (not / > 01110 011110);
[hear] (not / = 0111110 0111111110);
[hear] (< 0111110 0111111110);
[hear] (not / > 0111110 0111111110);
[hear] (not / = 0110 011110);
[hear] (< 0110 011110);
[hear] (not / > 0110 011110);
[hear] (not / = 00 010);
[hear] (< 00 010);
[hear] (not / > 00 010);
[hear] (not / = 00 01110);
[hear] (< 00 01110);
[hear] (not / > 00 01110);
[hear] (not / = 00 0110);
[hear] (< 00 0110);
[hear] (not / > 00 0110);
[hear] (not / = 0110 00);
[hear] (> 0110 00);
[hear] (not / < 0110 00);
[hear] (not / = 0111110 01110);
[hear] (> 0111110 01110);
[hear] (not / < 0111110 01110);
[hear] (not / = 01111110 011110);
[hear] (> 01111110 011110);
[hear] (not / < 01111110 011110);
[hear] (not / = 011110 01110);
[hear] (> 011110 01110);
[hear] (not / < 011110 01110);
[hear] (not / = 011111110 0111110);
[hear] (> 011111110 0111110);
[hear] (not / < 011111110 0111110);
[hear] (not / = 0111111110 0111110);
[hear] (> 0111111110 0111110);
[hear] (not / < 0111111110 0111110);
# MATH introduce the AND logical operator
[hear] (intro and);
[hear] (and (= 0110 0110) (= 01110 01110));
[hear] (and (> 0111110 0110) (> 0111110 011110));
[hear] (and (= 0111110 0111110) (= 011110 011110));
[hear] (and (< 00 010) (= 0111110 0111110));
[hear] (and (> 011110 01110) (= 011110 011110));
[hear] (and (< 0111110 0111111110) (< 010 01110));
[hear] (and (> 01111110 0111110) (> 011111110 0111110));
[hear] (and (> 0111110 01110) (> 011111110 011110));
[hear] (and (< 01110 011110) (= 010 010));
[hear] (and (< 0111110 01111110) (= 00 00));
[hear] (not / and (> 011110 010) (> 010 011110));
[hear] (not / and (< 0110 011110) (= 0110 0111110));
[hear] (not / and (< 0111110 011111110) (= 010 00));
[hear] (not / and (> 011110 01110) (< 0111110 0110));
[hear] (not / and (= 0110 0110) (> 010 010));
[hear] (not /
and (< 0111110 01110) (> 011111110 011110));
[hear] (not / and (> 00 010) (< 01110 0111110));
[hear] (not /
and (< 0111110 0110) (> 0111110 01110));
[hear] (not /
and (< 01111110 011110) (= 011110 011110));
[hear] (not /
and (< 01110 0110) (> 01111110 011110));
[hear] (not / and (< 0110 010) (= 0110 00));
[hear] (not / and (> 010 010) (< 011110 00));
[hear] (not /
and (< 01111110 0110) (> 011110 0111110));
[hear] (not / and (< 0111110 0110) (= 0111110 00));
[hear] (not / and (> 01110 01110) (> 010 0111110));
[hear] (and (< 01110 0111110) (< 010 01110));
[hear] (and (> 01110 010) (< 0110 011110));
[hear] (not / and (< 00 01110) (= 011110 00));
[hear] (not / and (= 00 0111110) (> 010 010));
[hear] (not / and (< 01111110 010) (> 01110 00));
[hear] (not / and (= 011110 011110) (> 0110 0110));
[hear] (and (< 0111110 011111110) (= 011110 011110));
[hear] (not / and (> 011110 0110) (> 00 01111110));
[hear] (not / and (> 01110 00) (= 011110 0110));
[hear] (not / and (= 011110 0110) (= 011110 01110));
# MATH introduce the OR logical operator
[hear] (intro or);
[hear] (or (< 011110 0111110) (> 011111110 0111110));
[hear] (or (= 01110 01110) (< 0111110 011111110));
[hear] (or (< 00 010) (> 011110 010));
[hear] (or (= 00 00) (< 011110 0111110));
[hear] (or (= 0111110 0111110) (= 0110 0110));
[hear] (or (= 00 00) (= 00 00));
[hear] (or (< 010 01110) (> 01111110 0111110));
[hear] (or (= 010 010) (> 01111110 011110));
[hear] (or (> 01110 00) (> 011111110 011110));
[hear] (or (< 010 0110) (> 01110 0110));
[hear] (or (> 0111110 0110) (= 00 010));
[hear] (or (< 01110 01111110) (= 0110 010));
[hear] (or (= 0111110 0111110) (= 01110 0110));
[hear] (or (< 011110 011111110) (< 0111110 011110));
[hear] (or (= 01110 01110) (> 00 011110));
[hear] (or (= 0111110 00) (< 011110 01111110));
[hear] (or (< 011110 01110) (= 0110 0110));
[hear] (or (< 011110 00) (< 00 0110));
[hear] (or (< 0111110 01110) (= 00 00));
[hear] (or (= 0111110 011110) (> 010 00));
[hear] (not / or (> 0110 01111110) (= 01110 010));
[hear] (not /
or (= 01110 011110) (< 01111110 011110));
[hear] (not /
or (> 00 0111110) (> 01111110 01111110));
[hear] (not / or (> 010 0111110) (= 011110 01110));
[hear] (not / or (= 0110 010) (> 01110 011110));
[hear] (or (= 011110 011110) (= 0111110 0111110));
[hear] (or (< 01111110 00) (> 0111110 0110));
[hear] (not / or (> 010 01110) (< 0111110 00));
[hear] (or (< 01111110 011110) (= 010 010));
[hear] (or (> 0110 01111110) (= 0111110 0111110));
[hear] (not / or (> 0110 0110) (> 010 0110));
[hear] (or (> 011110 0111110) (< 0111110 01111110));
[hear] (or (= 01110 01110) (< 0111110 0111111110));
[hear] (or (< 01110 010) (= 01110 01110));
[hear] (or (< 010 00) (= 011110 011110));
# MATH use equality for truth values
[hear] (= (= 00 00) (= 011110 011110));
[hear] (= (= 0110 0110) (> 0111110 01110));
[hear] (= (= 0111110 0111110) (< 0110 0111110));
[hear] (= (> 0111110 0110) (= 011110 011110));
[hear] (= (< 0110 01110) (> 01110 010));
[hear] (= (> 00 00) (= 0110 01110));
[hear] (= (< 0111110 01110) (< 01110 00));
[hear] (= (= 01110 00) (= 01110 0110));
[hear] (= (= 0110 010) (< 01110 010));
[hear] (= (> 010 01110) (< 01111110 00));
[hear] (not /
= (> 0111110 01111110) (> 011110 0110));
[hear] (not / = (= 010 0110) (< 010 01110));
[hear] (not / = (> 0110 0111110) (> 0111110 011110));
[hear] (not /
= (> 011110 0111110) (< 011110 01111110));
[hear] (not / = (< 0111110 01110) (< 010 01110));
[hear] (not / = (= 011110 011110) (> 0110 011110));
[hear] (not / = (< 00 0110) (> 00 011110));
[hear] (not / = (< 010 01110) (< 0111110 010));
[hear] (not / = (< 00 01110) (= 0110 01110));
[hear] (not / = (> 0111110 01110) (= 0110 0111110));
[hear] (intro true);
[hear] (intro false);
[hear] (= (true) (> 010 00));
[hear] (= (true) (< 01110 01111110));
[hear] (= (true) (< 0110 0111110));
[hear] (= (true) (> 01110 00));
[hear] (= (true) (> 011111110 011110));
[hear] (= (= 010 010) (true));
[hear] (= (< 01110 011110) (true));
[hear] (= (> 01111110 0111110) (true));
[hear] (= (< 011110 011111110) (true));
[hear] (= (< 0111110 0111111110) (true));
[hear] (= (false) (> 01110 0111110));
[hear] (= (false) (= 011110 010));
[hear] (= (false) (< 01110 010));
[hear] (= (false) (= 01110 011110));
[hear] (= (false) (> 00 00));
[hear] (= (< 010 00) (false));
[hear] (= (= 01110 0110) (false));
[hear] (= (> 010 011110) (false));
[hear] (= (= 0110 010) (false));
[hear] (= (= 0110 0111110) (false));
[hear] (= (true) (true));
[hear] (= (false) (false));
[hear] (not / = (true) (false));
[hear] (not / = (false) (true));
# MATH introduce addition
[hear] (intro +);
[hear] (= 0110 / + 010 010);
[hear] (= 01110 / + 010 0110);
[hear] (= 010 / + 010 00);
[hear] (= 011110 / + 010 01110);
[hear] (= 011110 / + 011110 00);
[hear] (= 0110 / + 0110 00);
[hear] (= 011110 / + 00 011110);
[hear] (= 01110 / + 010 0110);
[hear] (= 0110 / + 00 0110);
[hear] (= 010 / + 00 010);
# MATH introduce subtraction
[hear] (intro -);
[hear] (= 010 / - 010 00);
[hear] (= 010 / - 011110 01110);
[hear] (= 0110 / - 011110 0110);
[hear] (= 00 / - 011110 011110);
[hear] (= 011110 / - 0111110 010);
[hear] (= 010 / - 0110 010);
[hear] (= 010 / - 01110 0110);
[hear] (= 011110 / - 0111111110 011110);
[hear] (= 011110 / - 011111110 01110);
[hear] (= 010 / - 01110 0110);
# MATH introduce multiplication
[hear] (intro *);
[hear] (= 00 / * 00 00);
[hear] (= 00 / * 00 010);
[hear] (= 00 / * 00 0110);
[hear] (= 00 / * 00 01110);
[hear] (= 00 / * 010 00);
[hear] (= 010 / * 010 010);
[hear] (= 0110 / * 010 0110);
[hear] (= 01110 / * 010 01110);
[hear] (= 00 / * 0110 00);
[hear] (= 0110 / * 0110 010);
[hear] (= 011110 / * 0110 0110);
[hear] (= 01111110 / * 0110 01110);
[hear] (= 00 / * 01110 00);
[hear] (= 01110 / * 01110 010);
[hear] (= 01111110 / * 01110 0110);
[hear] (= 01111111110 / * 01110 01110);
[hear] (= 011110 / * 0110 0110);
[hear] (= 01111111110 / * 01110 01110);
[hear] (= 01111111110 / * 01110 01110);
[hear] (= 01110 / * 010 01110);
[hear] (= 00 / * 010 00);
[hear] (= 011110 / * 0110 0110);
[hear] (= 00 / * 00 010);
[hear] (= 00 / * 01110 00);
[hear] (= 0110 / * 010 0110);
[hear] (= 00 / * 01110 00);
# MATH introduce a simple form of binary notation
# After this lesson, in the higher-level version of the message,
# will expand decimal to stand for the binary notation given.
# It wouldn't be hard to accompany this lesson with a more
# formal definition once functions are introduced (below)
# so maybe the transition to binary shouldbe delayed?
[hear] (= 00 (.));
[hear] (= 010 (:));
[hear] (= 0110 (:.));
[hear] (= 01110 (::));
[hear] (= 011110 (:..));
[hear] (= 0111110 (:.:));
[hear] (= 01111110 (::.));
[hear] (= 011111110 (:::));
[hear] (= 0111111110 (:...));
[hear] (= 01111111110 (:..:));
[hear] (= 011111111110 (:.:.));
[hear] (= 0111111111110 (:.::));
[hear] (= 01111111111110 (::..));
[hear] (= 011111111111110 (::.:));
[hear] (= 0111111111111110 (:::.));
[hear] (= 01111111111111110 (::::));
[hear] (= (::.) 01111110);
[hear] (= (:::) 011111110);
[hear] (= (:::.) 0111111111111110);
[hear] (= (.) 00);
[hear] (= (:) 010);
[hear] (= (:..) 011110);
[hear] (= (:) 010);
[hear] (= (::..) 01111111111110);
[hear] (= (:::) 011111110);
[hear] (= (::::) 01111111111111110);
[hear] (= (:::) 011111110);
[hear] (= (:...) 0111111110);
[hear] (= (::::) 01111111111111110);
[hear] (= (::.) 01111110);
[hear] (= (:.:) 0111110);
[hear] (= (:...) 0111111110);
[hear] (= (:...) /
+ (:...) (.));
[hear] (= (:.::) /
+ (::) (:...));
[hear] (= (:::) / + (:::) (.));
[hear] (= (:..::) /
+ (:.:.) (:..:));
[hear] (= (:..:) /
+ (:) (:...));
[hear] (= (:.::.) /
+ (::..) (:.:.));
[hear] (= (:..::) /
+ (:.::) (:...));
[hear] (= (::..) /
+ (:..:) (::));
[hear] (= (::::.) /
* (:.:) (::.));
[hear] (= (::.:.) /
* (::.:) (:.));
[hear] (= (::::..) /
* (::.) (:.:.));
[hear] (= (::::::) /
* (:::) (:..:));
[hear] (= (:....:) /
* (::) (:.::));
[hear] (= (::..:) /
* (:.:) (:.:));
[hear] (= (:...) /
* (:..) (:.));
[hear] (= (:.::.:.) /
* (::.) (::::));
# MATH show local assignment
[hear] (assign 20 0 / = (20) 0);
[hear] (assign 20 1 / = (20) 1);
[hear] (assign 20 2 / = (20) 2);
[hear] (assign 21 0 / = (21) 0);
[hear] (assign 21 1 / = (21) 1);
[hear] (assign 21 2 / = (21) 2);
[hear] (assign 22 0 / = (22) 0);
[hear] (assign 22 1 / = (22) 1);
[hear] (assign 22 2 / = (22) 2);
[hear] (= 0 (assign 20 0 (20)));
[hear] (= 0 (assign 20 0 / 20));
[hear] (= 0 / assign 20 0 / 20);
[hear] (= 20 / assign 20 0 20);
[hear] (= 5 / assign 20 0 5);
[hear] (= 5 / assign 20 0 / assign 23 5 / 23);
[hear] (= 23 / assign 20 0 / assign 23 5 23);
[hear] (= 1 (assign 20 1 (20)));
[hear] (= 1 (assign 20 1 / 20));
[hear] (= 1 / assign 20 1 / 20);
[hear] (= 20 / assign 20 1 20);
[hear] (= 5 / assign 20 1 5);
[hear] (= 5 / assign 20 1 / assign 23 5 / 23);
[hear] (= 23 / assign 20 1 / assign 23 5 23);
[hear] (= 2 (assign 20 2 (20)));
[hear] (= 2 (assign 20 2 / 20));
[hear] (= 2 / assign 20 2 / 20);
[hear] (= 20 / assign 20 2 20);
[hear] (= 5 / assign 20 2 5);
[hear] (= 5 / assign 20 2 / assign 23 5 / 23);
[hear] (= 23 / assign 20 2 / assign 23 5 23);
[hear] (= 0 (assign 21 0 (21)));
[hear] (= 0 (assign 21 0 / 21));
[hear] (= 0 / assign 21 0 / 21);
[hear] (= 21 / assign 21 0 21);
[hear] (= 5 / assign 21 0 5);
[hear] (= 5 / assign 21 0 / assign 23 5 / 23);
[hear] (= 23 / assign 21 0 / assign 23 5 23);
[hear] (= 1 (assign 21 1 (21)));
[hear] (= 1 (assign 21 1 / 21));
[hear] (= 1 / assign 21 1 / 21);
[hear] (= 21 / assign 21 1 21);
[hear] (= 5 / assign 21 1 5);
[hear] (= 5 / assign 21 1 / assign 23 5 / 23);
[hear] (= 23 / assign 21 1 / assign 23 5 23);
[hear] (= 2 (assign 21 2 (21)));
[hear] (= 2 (assign 21 2 / 21));
[hear] (= 2 / assign 21 2 / 21);
[hear] (= 21 / assign 21 2 21);
[hear] (= 5 / assign 21 2 5);
[hear] (= 5 / assign 21 2 / assign 23 5 / 23);
[hear] (= 23 / assign 21 2 / assign 23 5 23);
[hear] (= 0 (assign 22 0 (22)));
[hear] (= 0 (assign 22 0 / 22));
[hear] (= 0 / assign 22 0 / 22);
[hear] (= 22 / assign 22 0 22);
[hear] (= 5 / assign 22 0 5);
[hear] (= 5 / assign 22 0 / assign 23 5 / 23);
[hear] (= 23 / assign 22 0 / assign 23 5 23);
[hear] (= 1 (assign 22 1 (22)));
[hear] (= 1 (assign 22 1 / 22));
[hear] (= 1 / assign 22 1 / 22);
[hear] (= 22 / assign 22 1 22);
[hear] (= 5 / assign 22 1 5);
[hear] (= 5 / assign 22 1 / assign 23 5 / 23);
[hear] (= 23 / assign 22 1 / assign 23 5 23);
[hear] (= 2 (assign 22 2 (22)));
[hear] (= 2 (assign 22 2 / 22));
[hear] (= 2 / assign 22 2 / 22);
[hear] (= 22 / assign 22 2 22);
[hear] (= 5 / assign 22 2 5);
[hear] (= 5 / assign 22 2 / assign 23 5 / 23);
[hear] (= 23 / assign 22 2 / assign 23 5 23);
# Now for functions.
[hear] (assign 33 (? 28 5) / = 5 (33 2));
[hear] (assign 26 (? 24 5) / = 5 (26 3));
[hear] (assign 20 (? 21 6) / = 6 (20 2));
[hear] (assign 32 (? 31 6) / = 6 (32 3));
[hear] (assign 23 (? 21 (21)) / = 2 (23 2));
[hear] (assign 28 (? 35 (35)) / = 3 (28 3));
[hear] (assign 21 (? 37 (37)) / = 2 (21 2));
[hear] (assign 32 (? 27 (27)) / = 3 (32 3));
[hear] (assign 28 (? 37 / + (37) 1) / = 3 (28 2));
[hear] (assign 35 (? 23 / + (23) 1) / = 4 (35 3));
[hear] (assign 31 (? 25 / + (25) 1) / = 3 (31 2));
[hear] (assign 31 (? 21 / + (21) 1) / = 4 (31 3));
[hear] (assign y (? x / + (x) 8) / = (y 15) 23);
[hear] (= ((? x / + (x) 8) 15) 23);
[hear] (assign y (? x / + (x) 4) / = (y 15) 19);
[hear] (= ((? x / + (x) 4) 15) 19);
[hear] (assign y (? x / + (x) 2) / = (y 2) 4);
[hear] (= ((? x / + (x) 2) 2) 4);
[hear] (assign y (? x / + (x) 15) / = (y 5) 20);
[hear] (= ((? x / + (x) 15) 5) 20);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= (z 15 10) 151);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= ((z 15) 10) 151);
[hear] (= ((? x / ? y / + 1 / * (x) (y)) 15 10)
151);
[hear] (= (((? x / ? y / + 1 / * (x) (y)) 15) 10)
151);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= (z 5 12) 61);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= ((z 5) 12) 61);
[hear] (= ((? x / ? y / + 1 / * (x) (y)) 5 12) 61);
[hear] (= (((? x / ? y / + 1 / * (x) (y)) 5) 12)
61);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= (z 9 3) 28);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= ((z 9) 3) 28);
[hear] (= ((? x / ? y / + 1 / * (x) (y)) 9 3) 28);
[hear] (= (((? x / ? y / + 1 / * (x) (y)) 9) 3)
28);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= (z 12 12) 145);
[hear] (assign z (? x / ? y / + 1 / * (x) (y)) /
= ((z 12) 12) 145);
[hear] (= ((? x / ? y / + 1 / * (x) (y)) 12 12)
145);
[hear] (= (((? x / ? y / + 1 / * (x) (y)) 12) 12)
145);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 14 10 24);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 5 11 16);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 1 3 4);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 7 9 16);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 15 7 22);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 12 7 19);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 8 4 12);
[hear] (assign
w
(? x /
? y /
? z /
= (z) /
+ (x) (y)) /
w 12 4 16);
# MATH demonstrate existence of memory
[hear] (define forty-something 42);
[hear] (= 42 (forty-something));
# now introduce a function
[hear] (assign square (? x / * (x) (x)) /
= 25 (square 5));
[hear] (assign square (? x / * (x) (x)) /
= 0 (square 0));
[hear] (assign square (? x / * (x) (x)) /
= 25 (square 5));
[hear] (assign square (? x / * (x) (x)) /
= 9 (square 3));
# show that functions can be remembered across statements
[hear] (define square / ? x / * (x) (x));
[hear] (= (square 5) 25);
[hear] (= (square 4) 16);
[hear] (= (square 9) 81);
[hear] (= (square 3) 9);
[hear] (define plusone / ? x / + (x) 1);
[hear] (= (plusone 4) 5);
[hear] (= (plusone 9) 10);
[hear] (= (plusone 4) 5);
[hear] (= (plusone 3) 4);
# MATH show mechanisms for branching
[hear] (intro if);
[hear] (= (if (> 4 1) 29 22) 29);
[hear] (= (if (> 5 4) 24 28) 24);
[hear] (= (if (> 4 4) 20 20) 20);
[hear] (= (if (> 6 3) 28 28) 28);
[hear] (= (if (< 5 6) 22 23) 22);
[hear] (= (if (= 3 3) 25 20) 25);
[hear] (= (if (< 1 2) 27 21) 27);
[hear] (= (if (= 3 3) 25 25) 25);
[hear] (define max /
? x /
? y /
if (> (x) (y)) (x) (y));
[hear] (define min /
? x /
? y /
if (< (x) (y)) (x) (y));
[hear] (= 0 (max 0 0));
[hear] (= 0 (min 0 0));
[hear] (= 1 (max 0 1));
[hear] (= 0 (min 0 1));
[hear] (= 2 (max 0 2));
[hear] (= 0 (min 0 2));
[hear] (= 1 (max 1 0));
[hear] (= 0 (min 1 0));
[hear] (= 1 (max 1 1));
[hear] (= 1 (min 1 1));
[hear] (= 2 (max 1 2));
[hear] (= 1 (min 1 2));
[hear] (= 2 (max 2 0));
[hear] (= 0 (min 2 0));
[hear] (= 2 (max 2 1));
[hear] (= 1 (min 2 1));
[hear] (= 2 (max 2 2));
[hear] (= 2 (min 2 2));
[hear] (define factorial /
? n /
if (<= (n) 1) 1 /
* (n) /
factorial /
- (n) 1);
[hear] (= 1 / factorial 1);
[hear] (= 2 / factorial 2);
[hear] (= 6 / factorial 3);
[hear] (= 24 / factorial 4);
[hear] (= 120 / factorial 5);
# MATH illustrate pairs
[hear] (assign x (cons 3 4) / = (car / x) 3);
[hear] (assign x (cons 3 4) / = (cdr / x) 4);
[hear] (assign x (cons 9 1) / = (car / x) 9);
[hear] (assign x (cons 9 1) / = (cdr / x) 1);
[hear] (assign x (cons 7 8) / = (car / x) 7);
[hear] (assign x (cons 7 8) / = (cdr / x) 8);
[hear] (assign x (cons 16 / cons 6 13) /
= (car / x) 16);
[hear] (assign x (cons 16 / cons 6 13) /
= (car / cdr / x) 6);
[hear] (assign x (cons 16 / cons 6 13) /
= (cdr / cdr / x) 13);
[hear] (assign x (cons 14 / cons 11 5) /
= (car / x) 14);
[hear] (assign x (cons 14 / cons 11 5) /
= (car / cdr / x) 11);
[hear] (assign x (cons 14 / cons 11 5) /
= (cdr / cdr / x) 5);
[hear] (assign x (cons 2 / cons 9 7) /
= (car / x) 2);
[hear] (assign x (cons 2 / cons 9 7) /
= (car / cdr / x) 9);
[hear] (assign x (cons 2 / cons 9 7) /
= (cdr / cdr / x) 7);
[hear] (assign
x
(cons 1 /
cons 4 /
cons 3 /
cons 0 2) /
and (= 1 / car / x) /
and (= 4 / car / cdr / x) /
and (= 3 / car / cdr / cdr / x) /
and (= 0 /
car /
cdr /
cdr /
cdr /
x)
(= 2 /
cdr /
cdr /
cdr /
cdr /
x));
# MATH introduce mutable objects, and side-effects
[hear] (intro make-cell);
[hear] (intro set!);
[hear] (intro get!);
[hear] (define demo-mut1 / make-cell 0);
[hear] (set! (demo-mut1) 15);
[hear] (= (get! / demo-mut1) 15);
[hear] (set! (demo-mut1) 5);
[hear] (set! (demo-mut1) 7);
[hear] (= (get! / demo-mut1) 7);
[hear] (define demo-mut2 / make-cell 11);
[hear] (= (get! / demo-mut2) 11);
[hear] (set! (demo-mut2) 22);
[hear] (= (get! / demo-mut2) 22);
[hear] (= (get! / demo-mut1) 7);
[hear] (= (+ (get! / demo-mut1) (get! / demo-mut2))
29);
[hear] (if (= (get! / demo-mut1) 7)
(set! (demo-mut1) 88)
(set! (demo-mut1) 99));
[hear] (= (get! / demo-mut1) 88);
[hear] (if (= (get! / demo-mut1) 7)
(set! (demo-mut1) 88)
(set! (demo-mut1) 99));
[hear] (= (get! / demo-mut1) 99);
# MATH illustrate lists and some list operators
# to make list describable as a function, need to preceed lists
# ... with an argument count
# Lists keep an explicit record of their length
# this is to avoid the need for using a special 'nil' symbol
# ... which cannot itself be placed in the list.
#
# missing - intro to cons, car, cdr
# used to be pure-cons pure-car pure-cdr but changed for better interface to scheme
# also should introduce number? check function
#
[hear] (define list-helper /
? n /
? ret /
if (> (n) 1)
(? x /
list-helper
(- (n) 1)
(? y /
? z /
ret (+ 1 (y)) (cons (x) (z))))
(? x /
ret 1 (x)));
[hear] (define list /
? n /
if (= (n) 0)
(cons 0 0)
(list-helper (n) (? y / ? z / cons (y) (z))));
[hear] (define head /
? lst /
if (= (car / lst) 0)
(undefined)
(if (= (car / lst) 1)
(cdr /
lst)
(car /
cdr /
lst)));
[hear] (define tail /
? lst /
if (= (car / lst) 0)
(undefined)
(if (= (car / lst) 1)
(cons 0 0)
(cons (- (car / lst) 1) (cdr / cdr / lst))));
[hear] (define list-length / ? lst / car / lst);
[hear] (define list-ref /
? lst /
? n /
if (= (list-ref / lst) 0)
(undefined)
(if (= (n) 0)
(head /
lst)
(list-ref (tail / lst) (- (n) 1))));
[hear] (define prepend /
? x /
? lst /
if (= (list-length / lst) 0)
(cons 1 (x))
(cons (+ (list-length / lst) 1)
(cons (x) (cdr / lst))));
[hear] (define equal /
? x /
? y /
if (= (number? (x)) (number? (y)))
(if (number? (x)) (= (x) (y)) (list= (x) (y)))
(false));
[hear] (define list= /
? x /
? y /
if (= (list-length / x) (list-length / y))
(if (> (list-length / x) 0)
(and (equal (head / x) (head / y))
(list= (tail / x) (tail / y)))
(true))
(false));
[hear] (= (list-length / (list 5) 8 5 9 2 3) 5);
[hear] (= (list-length / (list 0)) 0);
[hear] (= (list-length / (list 4) 6 5 8 4) 4);
[hear] (= (list-length / (list 8) 8 3 1 6 0 2 7 4) 8);
[hear] (= (list-length / (list 1) 3) 1);
[hear] (= (head / (list 8) 2 4 7 5 14 14 16 1) 2);
[hear] (list= (tail /
(list 8) 2 4 7 5 14 14 16 1)
((list 7) 4 7 5 14 14 16 1));
[hear] (= (head / (list 9) 6 15 18 17 2 12 12 16 8) 6);
[hear] (list= (tail /
(list 9) 6 15 18 17 2 12 12 16 8)
((list 8) 15 18 17 2 12 12 16 8));
[hear] (= (head / (list 2) 16 13) 16);
[hear] (list= (tail / (list 2) 16 13) ((list 1) 13));
[hear] (= (head / (list 8) 18 9 10 15 2 12 15 17) 18);
[hear] (list= (tail /
(list 8) 18 9 10 15 2 12 15 17)
((list 7) 9 10 15 2 12 15 17));
[hear] (= (head / (list 2) 1 15) 1);
[hear] (list= (tail / (list 2) 1 15) ((list 1) 15));
[hear] (= (head /
(list 10) 1 14 7 3 5 11 1 17 13 15)
1);
[hear] (list= (tail /
(list 10) 1 14 7 3 5 11 1 17 13 15)
((list 9) 14 7 3 5 11 1 17 13 15));
[hear] (= (head / (list 4) 10 19 16 4) 10);
[hear] (list= (tail /
(list 4) 10 19 16 4)
((list 3) 19 16 4));
[hear] (= (head / (list 1) 15) 15);
[hear] (list= (tail / (list 1) 15) ((list 0)));
[hear] (= (head / (list 8) 11 5 11 8 5 8 3 14) 11);
[hear] (list= (tail /
(list 8) 11 5 11 8 5 8 3 14)
((list 7) 5 11 8 5 8 3 14));
[hear] (= (head / (list 5) 6 2 13 5 1) 6);
[hear] (list= (tail /
(list 5) 6 2 13 5 1)
((list 4) 2 13 5 1));
[hear] (= (list-ref ((list 1) 18) 0) 18);
[hear] (= (list-ref ((list 3) 3 15 16) 2) 16);
[hear] (= (list-ref ((list 5) 12 0 0 0 8) 0) 12);
[hear] (= (list-ref ((list 1) 3) 0) 3);
[hear] (= (list-ref ((list 2) 16 16) 0) 16);
[hear] (= (list-ref ((list 1) 0) 0) 0);
[hear] (= (list-ref ((list 2) 9 0) 1) 0);
[hear] (= (list-ref ((list 7) 11 5 7 19 9 18 2) 2) 7);
[hear] (= (list-ref ((list 3) 18 9 12) 1) 9);
[hear] (= (list-ref ((list 1) 0) 0) 0);
[hear] (list= ((list 0)) ((list 0)));
[hear] (list= ((list 1) 10) ((list 1) 10));
[hear] (list= ((list 2) 12 8) ((list 2) 12 8));
[hear] (list= ((list 3) 5 5 0) ((list 3) 5 5 0));
[hear] (list= ((list 4) 4 10 12 11)
((list 4) 4 10 12 11));
# this next batch of examples are a bit misleading, should streamline
[hear] (not / list= ((list 0)) ((list 1) 4));
[hear] (not / list= ((list 0)) ((list 1) 4));
[hear] (not / list= ((list 1) 5) ((list 2) 8 5));
[hear] (not / list= ((list 1) 5) ((list 2) 5 3));
[hear] (not /
list= ((list 2) 11 15) ((list 3) 4 11 15));
[hear] (not /
list= ((list 2) 11 15) ((list 3) 11 15 3));
[hear] (not /
list= ((list 3) 11 19 16) ((list 4) 4 11 19 16));
[hear] (not /
list= ((list 3) 11 19 16) ((list 4) 11 19 16 1));
[hear] (not /
list= ((list 4) 14 18 5 11)
((list 5) 6 14 18 5 11));
[hear] (not /
list= ((list 4) 14 18 5 11)
((list 5) 14 18 5 11 9));
# some helpful functions
[hear] (list= (prepend 6 ((list 0))) ((list 1) 6));
[hear] (list= (prepend 6 ((list 1) 11)) ((list 2) 6 11));
[hear] (list= (prepend 17 ((list 2) 11 4))
((list 3) 17 11 4));
[hear] (list= (prepend 18 ((list 3) 6 17 4))
((list 4) 18 6 17 4));
[hear] (list= (prepend 3 ((list 4) 8 11 1 10))
((list 5) 3 8 11 1 10));
[hear] (list= (prepend 7 ((list 5) 8 3 2 8 0))
((list 6) 7 8 3 2 8 0));
[hear] (list= (prepend 17 ((list 6) 14 15 14 19 9 3))
((list 7) 17 14 15 14 19 9 3));
[hear] (list= (prepend 17 ((list 7) 10 19 8 2 7 4 1))
((list 8) 17 10 19 8 2 7 4 1));
[hear] (define pair /
? x /
? y /
(list 2) (x) (y));
[hear] (define first / ? lst / head / lst);
[hear] (define second /
? lst /
head /
tail /
lst);
[hear] (list= (pair 2 8) ((list 2) 2 8));
[hear] (= (first / pair 2 8) 2);
[hear] (= (second / pair 2 8) 8);
[hear] (list= (pair 6 0) ((list 2) 6 0));
[hear] (= (first / pair 6 0) 6);
[hear] (= (second / pair 6 0) 0);
[hear] (list= (pair 9 3) ((list 2) 9 3));
[hear] (= (first / pair 9 3) 9);
[hear] (= (second / pair 9 3) 3);
[hear] (define list-find-helper /
? lst /
? key /
? fail /
? idx /
if (= (list-length / lst) 0)
(fail 0)
(if (equal (head / lst) (key))
(idx)
(list-find-helper
(tail /
lst)
(key)
(fail)
(+ (idx) 1))));
[hear] (define list-find /
? lst /
? key /
? fail /
list-find-helper (lst) (key) (fail) 0);
[hear] (define example-fail / ? x 100);
[hear] (= (list-find ((list 1) 13) 13 (example-fail)) 0);
[hear] (= (list-find
((list 9) 15 17 16 12 3 15 2 4 13)
15
(example-fail))
0);
[hear] (= (list-find
((list 9) 19 0 14 18 9 11 12 5 19)
11
(example-fail))
5);
[hear] (= (list-find ((list 2) 15 1) 15 (example-fail))
0);
[hear] (= (list-find ((list 4) 0 7 19 1) 7 (example-fail))
1);
[hear] (= (list-find
((list 6) 9 9 1 10 5 19)
10
(example-fail))
3);
[hear] (= (list-find ((list 2) 17 1) 1 (example-fail))
1);
[hear] (= (list-find
((list 8) 0 3 16 13 19 13 18 11)
13
(example-fail))
3);
[hear] (= (list-find ((list 4) 15 6 2 1) 1 (example-fail))
3);
[hear] (= (list-find ((list 1) 3) 3 (example-fail)) 0);
[hear] (= (list-find ((list 4) 4 6 0 10) 1 (example-fail))
100);
[hear] (= (list-find
((list 6) 5 7 8 16 1 0)
13
(example-fail))
100);
[hear] (= (list-find
((list 8) 13 17 16 0 7 10 11 3)
15
(example-fail))
100);
# HACK describe changes to the implicit interpreter to allow new special forms
[hear] (define base-translate / translate);
[hear] (define translate /
? x /
if (= (x) 10) 15 (base-translate / x));
[hear] (= 10 15);
[hear] (= (+ 10 15) 30);
[hear] (define translate / base-translate);
[hear] (not / = 10 15);
[hear] (= (+ 10 15) 25);
# now can create a special form for lists
[hear] (define translate /
? x /
if (number? /
x)
(base-translate /
x)
(if (= (head / x) vector)
(translate /
prepend
((list 2) list (list-length / tail / x))
(tail /
x))
(base-translate /
x)));
[hear] (= (vector 1 2 3) ((list 3) 1 2 3));
# now to desugar let expressions
[hear] (define translate-with-vector / translate);
[hear] (define translate-let-form /
? x /
? body /
if (= (list-length / x) 0)
(translate /
body)
(translate-let-form
(tail /
x)
(vector
(vector ? (head / head / x) (body))
(head /
tail /
head /
x))));
[hear] (define translate /
? x /
if (number? /
x)
(translate-with-vector /
x)
(if (= (head / x) let)
(translate-let-form
(head /
tail /
x)
(head /
tail /
tail /
x))
(translate-with-vector /
x)));
[hear] (let ((x 20)) (= (x) 20));
[hear] (let ((x 50) (y 20)) (= (- (x) (y)) 30));
# the is-list function is now on dubious ground
# this stuff will be replaced with typing ASAP
[hear] (define is-list /
? x /
not /
number? /
x);
[hear] (is-list / (list 2) 1 3);
[hear] (is-list / (list 0));
[hear] (not / is-list 23);
[hear] (is-list /
(list 3) ((list 2) 2 3) 1 (? x / + (x) 10));
# MATH introduce sugar for let
# if would be good to introduce desugarings more rigorously, but for now...
# ... just a very vague sketch
[hear] (intro let);
[hear] (= (let ((x 10)) (+ (x) 5))
((? x / + (x) 5) 10));
[hear] (= (let ((x 10) (y 5)) (+ (x) (y)))
(((? x / ? y / + (x) (y)) 10) 5));
# MATH build up functions of several variables
[hear] (= ((? x / ? y / - (x) (y)) 7 4) 3);
[hear] (= ((? x / ? y / - (x) (y)) 12 8) 4);
[hear] (= ((? x / ? y / - (x) (y)) 12 8) 4);
[hear] (= ((? x / ? y / - (x) (y)) 8 2) 6);
[hear] (= ((? x / ? y / - (x) (y)) 14 5) 9);
[hear] (define last /
? x /
list-ref (x) (- (list-length / x) 1));
[hear] (define except-last /
? x /
if (> (list-length / x) 1)
(prepend
(head /
x)
(except-last /
tail /
x))
(vector));
# test last and except-last
[hear] (= 15 (last / vector 4 5 15));
[hear] (list= (vector 4 5)
(except-last /
vector 4 5 15));
[hear] (intro lambda);
[hear] (define prev-translate / translate);
[hear] (define translate /
let ((prev (prev-translate)))
(? x /
if (number? /
x)
(prev /
x)
(if (= (head / x) lambda)
(let ((formals (head / tail / x))
(body (head / tail / tail / x)))
(if (> (list-length / formals) 0)
(translate
(vector
lambda
(except-last /
formals)
(vector ? (last / formals) (body))))
(translate (body))))
(prev /
x))));
# test lambda
[hear] (= ((lambda (x y) (- (x) (y))) 3 2) 1);
[hear] (= ((lambda (x y) (- (x) (y))) 6 6) 0);
[hear] (= ((lambda (x y) (- (x) (y))) 14 8) 6);
[hear] (= ((lambda (x y) (- (x) (y))) 10 8) 2);
[hear] (= ((lambda (x y) (- (x) (y))) 11 5) 6);
[hear] (define apply /
lambda (x y)
(if (list= (y) (vector))
(x)
(apply ((x) (head / y)) (tail / y))));
[hear] (= (apply (lambda (x y) (- (x) (y))) (vector 14 9))
5);
[hear] (= (apply (lambda (x y) (- (x) (y))) (vector 3 3))
0);
[hear] (= (apply (lambda (x y) (- (x) (y))) (vector 7 1))
6);
[hear] (= (apply (lambda (x y) (- (x) (y))) (vector 9 4))
5);
[hear] (= (apply (lambda (x y) (- (x) (y))) (vector 5 5))
0);
# MATH show map function for applying a function across the elements of a list
[hear] (define map /
lambda (p lst)
(if (> (list-length / lst) 0)
(prepend
(p (head / lst))
(map (p) (tail / lst)))
(vector)));
[hear] (= (map (? x / * (x) 2) (vector 12 4 13))
(vector 24 8 26));
[hear] (= (map (? x / * (x) 2) (vector 7 15 19 14))
(vector 14 30 38 28));
[hear] (= (map (? x / * (x) 2) (vector 2 4 17 6 8))
(vector 4 8 34 12 16));
[hear] (= (map (? x / * (x) 2) (vector 15 18 17 10 16 4))
(vector 30 36 34 20 32 8));
[hear] (= (map (? x 42) (vector 1 19 5))
(vector 42 42 42));
[hear] (= (map (? x 42) (vector 8 9 10 3))
(vector 42 42 42 42));
[hear] (= (map (? x 42) (vector 6 12 11 13 8))
(vector 42 42 42 42 42));
[hear] (= (map (? x 42) (vector 1 7 10 0 18 9))
(vector 42 42 42 42 42 42));
[hear] (define crunch /
lambda (p lst)
(if (>= (list-length / lst) 2)
(p (head / lst) (crunch (p) (tail / lst)))
(if (= (list-length / lst) 1)
(head /
lst)
(undefined))));
[hear] (= (crunch (+) (vector 13 9 14)) 36);
[hear] (= (crunch (+) (vector 14 8 6 19)) 47);
[hear] (= (crunch (+) (vector 17 10 4 16 15)) 62);
[hear] (= (crunch (+) (vector 18 15 4 3 8 10)) 58);
# NOTE end of part 1, start of part 2
# The following parts of the message are experimental, and not
# carefully integrated with the main body
[hear] (intro part2);
# MATH show an example of recursive evaluation
# skipping over a lot of definitions and desugarings
[hear] (define easy-factorial /
? f /
? x /
if (> (x) 0) (* (x) / f (f) (- (x) 1)) 1);
[hear] (define factorial /
? x /
if (> (x) 0)
(* (x) /
factorial /
- (x) 1)
1);
[hear] (= (easy-factorial (easy-factorial) 0) 1);
[hear] (= (easy-factorial (easy-factorial) 1) 1);
[hear] (= (easy-factorial (easy-factorial) 2) 2);
[hear] (= (easy-factorial (easy-factorial) 3) 6);
[hear] (= (easy-factorial (easy-factorial) 4) 24);
[hear] (= (easy-factorial (easy-factorial) 5) 120);
[hear] (= (factorial 0) 1);
[hear] (= (factorial 1) 1);
[hear] (= (factorial 2) 2);
[hear] (= (factorial 3) 6);
[hear] (= (factorial 4) 24);
[hear] (= (factorial 5) 120);
# MATH some pure lambda calculus definitions - optional
# these definitions are not quite what we want
# since thinking of everything as a function requires headscratching
# it would be better to use these as a parallel means of evaluation
# ... for expressions
[hear] (define pure-if /
? x /
? y /
? z /
x (y) (z));
[hear] (define pure-true / ? y / ? z / y);
[hear] (define pure-false / ? y / ? z / z);
[hear] (define pure-cons /
? x /
? y /
? z /
pure-if (z) (x) (y));
[hear] (define pure-car / ? x / x (pure-true));
[hear] (define pure-cdr / ? x / x (pure-false));
[hear] (define zero / ? f / ? x / x);
[hear] (define one / ? f / ? x / f (x));
[hear] (define two / ? f / ? x / f (f (x)));
[hear] (define succ /
? n /
? f /
? x /
f ((n (f)) (x)));
[hear] (define add / ? a / ? b / (a (succ)) (b));
[hear] (define mult /
? a /
? b /
(a (add / b)) (zero));
[hear] (define pred /
? n /
pure-cdr /
(n (? p /
pure-cons
(succ /
pure-car /
p)
(pure-car /
p)))
(pure-cons (zero) (zero)));
[hear] (define is-zero /
? n /
(n (? dummy / pure-false) (pure-true)));
[hear] (define fixed-point /
? f /
(? x / f (x (x))) (? x / f (x (x))));
# .. but for rest of message will assume that define does fixed-point for us
# now build a link between numbers and church number functions
[hear] (define unchurch /
? c /
c (? x / + (x) 1) 0);
[hear] (= 0 (unchurch / zero));
[hear] (= 1 (unchurch / one));
[hear] (= 2 (unchurch / two));
[hear] (define church /
? x /
if (= 0 (x))
(zero)
(succ /
church /
- (x) 1));
# MATH introduce universal quantifier
# really need to link with sets for true correctness
# and the examples here are REALLY sparse, need much more
[hear] (intro forall);
[hear] (< 5 (+ 5 1));
[hear] (< 4 (+ 4 1));
[hear] (< 3 (+ 3 1));
[hear] (< 2 (+ 2 1));
[hear] (< 1 (+ 1 1));
[hear] (< 0 (+ 0 1));
[hear] (forall (? x / < (x) (+ (x) 1)));
[hear] (< 5 (* 5 2));
[hear] (< 4 (* 4 2));
[hear] (< 3 (* 3 2));
[hear] (< 2 (* 2 2));
[hear] (< 1 (* 1 2));
[hear] (not / < 0 (* 0 2));
[hear] (not / forall (? x / < (x) (* (x) 2)));
# MATH introduce existential quantifier
# really need to link with sets for true correctness
# and the examples here are REALLY sparse, need much more
[hear] (not / = 5 (* 2 2));
[hear] (= 4 (* 2 2));
[hear] (not / = 3 (* 2 2));
[hear] (not / = 2 (* 2 2));
[hear] (not / = 1 (* 2 2));
[hear] (not / = 0 (* 2 2));
[hear] (intro exists);
[hear] (exists (? x / = (x) (* 2 2)));
[hear] (not / = 5 (+ 5 2));
[hear] (not / = 4 (+ 4 2));
[hear] (not / = 3 (+ 3 2));
[hear] (not / = 2 (+ 2 2));
[hear] (not / = 1 (+ 1 2));
[hear] (not / = 0 (+ 0 2));
[hear] (not (exists (? x / = (x) (+ (x) 2))));
# MATH introduce logical implication
[hear] (intro =>);
[hear] (define => /
? x /
? y /
not /
and (x) (not / y));
[hear] (=> (true) (true));
[hear] (not / => (true) (false));
[hear] (=> (false) (true));
[hear] (=> (false) (false));
[hear] (forall
(? x /
forall
(? y /
=> (=> (x) (y)) (=> (not / y) (not / x)))));
# MATH introduce sets and set membership
[hear] (intro element);
[hear] (define element /
? x /
? lst /
not /
= (list-find-helper (lst) (x) (? y 0) 1) 0);
[hear] (element 2 (vector 8 9 2));
[hear] (element 8 (vector 8 9 2));
[hear] (element 9 (vector 8 9 2));
[hear] (element 4 (vector 6 1 4 9));
[hear] (element 1 (vector 6 1 4 9));
[hear] (element 6 (vector 6 1 4 9));
[hear] (element 1 (vector 8 1 0 3 5));
[hear] (element 3 (vector 8 1 0 3 5));
[hear] (element 0 (vector 8 1 0 3 5));
[hear] (element 3 (vector 4 0 3 7 9));
[hear] (element 0 (vector 4 0 3 7 9));
[hear] (element 9 (vector 4 0 3 7 9));
[hear] (element 3 (vector 4 1 3 9));
[hear] (element 9 (vector 4 1 3 9));
[hear] (element 4 (vector 4 1 3 9));
[hear] (not / element 8 (vector 4 1 0 9));
[hear] (not / element 8 (vector 6 4 0 7 5));
[hear] (not / element 1 (vector 0 7));
[hear] (not / element 4 (vector 1 3 2 5));
[hear] (not / element 8 (vector 3 7 2 5));
# rules for set equality
[hear] (define set-subset /
? x /
? y /
if (> (list-length / x) 0)
(and (element (head / x) (y))
(set-subset (tail / x) (y)))
(true));
[hear] (define set= /
? x /
? y /
and (set-subset (x) (y)) (set-subset (y) (x)));
[hear] (set= (vector 1 5 9) (vector 5 1 9));
[hear] (set= (vector 1 5 9) (vector 9 1 5));
[hear] (not / set= (vector 1 5 9) (vector 1 5));
# let's go leave ourselves wide open to Russell's paradox
# ... by using characteristic functions
# ... since it doesn't really matter for communication purposes
# ... and so far this is just used / tested with sets of integers really
[hear] (element 5 (all (? x / = (+ (x) 10) 15)));
[hear] (element 3 (all (? x / = (* (x) 3) (+ (x) 6))));
[hear] (define empty-set / vector);
[hear] (element 0 (natural-set));
[hear] (forall
(? x /
=> (element (x) (natural-set))
(element (+ (x) 1) (natural-set))));
[hear] (element 1 (natural-set));
[hear] (element 2 (natural-set));
[hear] (element 3 (natural-set));
[hear] (element 4 (natural-set));
[hear] (element 5 (natural-set));
[hear] (element 6 (natural-set));
[hear] (element 7 (natural-set));
[hear] (element 8 (natural-set));
[hear] (element 9 (natural-set));
[hear] (define boolean-set / vector (true) (false));
[hear] (element (true) (boolean-set));
[hear] (element (false) (boolean-set));
# actually, to simplify semantics elsewhere, true and false
# are now just 0 and 1 so they are not distinct from ints
[hear] (define even-natural-set /
all /
? x /
exists /
? y /
and (element (y) (natural-set))
(= (* 2 (y)) (x)));
[hear] (element 0 (natural-set));
[hear] (element 0 (even-natural-set));
[hear] (element 1 (natural-set));
[hear] (not / element 1 (even-natural-set));
[hear] (element 2 (natural-set));
[hear] (element 2 (even-natural-set));
[hear] (element 3 (natural-set));
[hear] (not / element 3 (even-natural-set));
[hear] (element 4 (natural-set));
[hear] (element 4 (even-natural-set));
[hear] (element 5 (natural-set));
[hear] (not / element 5 (even-natural-set));
[hear] (element 6 (natural-set));
[hear] (element 6 (even-natural-set));
# MATH introduce graph structures
[hear] (define make-graph /
lambda (nodes links) (pair (nodes) (links)));
[hear] (define test-graph /
make-graph
(vector 1 2 3 4)
(vector (vector 1 2) (vector 2 3) (vector 1 4)));
[hear] (define graph-linked /
lambda (g n1 n2)
(exists /
? idx /
if (and (>= (idx) 0)
(< (idx) (list-length / list-ref (g) 1)))
(list= (list-ref (list-ref (g) 1) (idx))
(vector (n1) (n2)))
(false)));
[hear] (= (graph-linked (test-graph) 1 2) (true));
[hear] (= (graph-linked (test-graph) 1 3) (false));
[hear] (= (graph-linked (test-graph) 2 4) (false));
# 'if' is used a lot in the next definition in place of and / or
# this is because I haven't established lazy evaluation forms for and / or
# so this very inefficient algorithm completely bogs down when combined
# ... during testing with a dumb implementation for 'exists'.
[hear] (define graph-linked* /
lambda (g n1 n2)
(if (= (n1) (n2))
(true)
(if (graph-linked (g) (n1) (n2))
(true)
(exists
(? n3 /
if (graph-linked (g) (n1) (n3))
(graph-linked* (g) (n3) (n2))
(false))))));
[hear] (= (graph-linked* (test-graph) 1 2) (true));
[hear] (= (graph-linked* (test-graph) 1 3) (true));
[hear] (= (graph-linked* (test-graph) 2 4) (false));
# MATH show how to execute a sequence of instructions
[hear] (intro begin);
[hear] (define prev-translate / translate);
[hear] (define reverse /
? x /
if (>= (list-length / x) 1)
(prepend
(last /
x)
(reverse /
except-last /
x))
(x));
# test reverse
[hear] (list= (vector 1 2 3) (reverse / vector 3 2 1));
[hear] (define translate /
let ((prev (prev-translate)))
(? x /
if (number? /
x)
(prev /
x)
(if (= (head / x) begin)
(translate
(vector
(vector ? x (vector head (vector x)))
(prepend vector (reverse / tail / x))))
(prev /
x))));
[hear] (= (begin 1 7 2 4) 4);
[hear] (= (begin
(set! (demo-mut1) 88)
(set! (demo-mut1) 6)
(get! /
demo-mut1))
6);
[hear] (= (begin
(set! (demo-mut2) 88)
(set! (demo-mut1) 6)
(get! /
demo-mut2))
88);
[hear] (= (begin
(set! (demo-mut1) 88)
(set! (demo-mut1) 6)
(get! /
demo-mut1)
4)
4);
# MATH introduce environment / hashmap structure
# this section needs a LOT more examples :-
# note that at the time of writing (h 1 2) is same as ((h) 1 2)
[hear] (define hash-add /
lambda (h x y z)
(if (equal (z) (x)) (y) (h (z))));
[hear] (define hash-ref / lambda (h x) (h (x)));
[hear] (define hash-null / ? x / undefined);
[hear] (define hash-default /
? default /
? x /
default);
[hear] (define test-hash /
hash-add (hash-add (hash-null) 3 2) 4 9);
[hear] (= (hash-ref (test-hash) 4) 9);
[hear] (= (hash-ref (test-hash) 3) 2);
[hear] (= (hash-ref (test-hash) 8) (undefined));
[hear] (= (hash-ref (test-hash) 15) (undefined));
[hear] (= (hash-ref (hash-add (test-hash) 15 33) 15) 33);
[hear] (= (hash-ref (test-hash) 15) (undefined));
[hear] (define make-hash /
? x /
if (list= (x) (vector))
(hash-null)
(hash-add
(make-hash (tail / x))
(first /
head /
x)
(second /
head /
x)));
[hear] (= (hash-ref
(make-hash /
vector (pair 3 10) (pair 2 20) (pair 1 30))
3)
10);
[hear] (= (hash-ref
(make-hash /
vector (pair 3 10) (pair 2 20) (pair 1 30))
1)
30);
# OBJECT introduce simple mutable structures
[hear] (define mutable-struct /
? lst /
let ((data (map (? x / make-cell 0) (lst))))
(? key /
list-ref (data) (list-find (lst) (key) (? x 0))));
[hear] (define test-struct1 /
mutable-struct /
vector item1 item2 item3);
[hear] (set! (test-struct1 item1) 15);
[hear] (= (get! / test-struct1 item1) 15);
# OBJECT introduce method handler wrappers
[hear] (define add-method /
lambda (object name method)
(hash-add
(object)
(name)
(? dummy /
method /
object)));
[hear] (define call / ? x / x 0);
[hear] (define test-struct2 /
mutable-struct /
vector x y);
[hear] (set! (test-struct2 x) 10);
[hear] (set! (test-struct2 y) 20);
[hear] (= (get! / test-struct2 x) 10);
[hear] (= (get! / test-struct2 y) 20);
[hear] (define test-struct3 /
add-method
(test-struct2)
sum
(? self /
+ (get! / self x) (get! / self y)));
[hear] (= (get! / test-struct3 x) 10);
[hear] (= (get! / test-struct3 y) 20);
[hear] (= (call / test-struct3 sum) 30);
[hear] (set! (test-struct3 y) 10);
[hear] (= (call / test-struct3 sum) 20);
[hear] (set! (test-struct2 y) 5);
[hear] (= (call / test-struct3 sum) 15);
# TURING introduce turing machine model
# just for fun!
[hear] (define safe-tail /
? x /
if (> (list-length / x) 0)
(if (> (list-length / x) 1)
(tail /
x)
(vector /
vector))
(? vector /
vector));
[hear] (define safe-head /
? x /
if (> (list-length / x) 0)
(head /
x)
(vector));
[hear] (define tape-read /
? tape /
let ((x (second / tape)))
(if (> (list-length / x) 0)
(head /
x)
(vector)));
[hear] (define tape-transition /
lambda (tape shift value)
(if (= (shift) 1)
(pair (prepend (value) (first / tape))
(safe-tail /
second /
tape))
(if (= (shift) 0)
(pair (safe-tail /
first /
tape)
(prepend
(safe-head /
first /
tape)
(prepend (value) (safe-tail / second / tape))))
(pair (first /
tape)
(prepend (value) (safe-tail / second / tape))))));
[hear] (define turing /
lambda (machine current last tape)
(if (= (current) (last))
(tape)
(let ((next (machine (current) (tape-read / tape))))
(turing
(machine)
(list-ref (next) 0)
(last)
(tape-transition
(tape)
(list-ref (next) 1)
(list-ref (next) 2))))));
[hear] (define make-tape /
? x /
pair (vector) (x));
[hear] (define remove-trail /
? x /
? lst /
if (> (list-length / lst) 0)
(if (= (last / lst) (x))
(remove-trail (x) (except-last / lst))
(lst))
(lst));
[hear] (define extract-tape /
? x /
remove-trail (vector) (second / x));
[hear] (define tm-binary-increment /
make-hash /
vector
(pair right
(make-hash /
vector
(pair 0 (vector right 1 0))
(pair 1 (vector right 1 1))
(pair (vector) (vector inc 0 (vector)))))
(pair inc
(make-hash /
vector
(pair 0 (vector noinc 0 1))
(pair 1 (vector inc 0 0))
(pair (vector) (vector halt 2 1))))
(pair noinc
(make-hash /
vector
(pair 0 (vector noinc 0 0))
(pair 1 (vector noinc 0 1))
(pair (vector) (vector halt 1 (vector)))))
(pair halt (make-hash / vector)));
[hear] (= (extract-tape /
turing
(tm-binary-increment)
right
halt
(make-tape /
vector 1 0 0 1))
(vector 1 0 1 0));
[hear] (= (extract-tape /
turing
(tm-binary-increment)
right
halt
(make-tape /
vector 1 1 1))
(vector 1 0 0 0));
[hear] (= (extract-tape /
turing
(tm-binary-increment)
right
halt
(make-tape /
vector 1 1 1 0 0 0 1 1 1))
(vector 1 1 1 0 0 1 0 0 0));
# OBJECT introduce simple form of typing, for ease of documentation.
# An object is simply a function that takes an argument.
# The argument is the method to call on the object.
# Types are here taken to be just the existence of a particular method,
# with that method returning an object of the appropriate type.
[hear] (define make-integer
(lambda (v)
(lambda (x)
(if (= (x) int)
(v)
0))));
[hear] (define objectify
(? x
(if (number? (x))
(make-integer (x))
(x))));
[hear] (define instanceof
(lambda (T t)
(if (number? (t))
(= (T) int)
(not (number? ((objectify (t)) (T)))))));
# add version of lambda that allows types to be declared
[hear] (define prev-translate (translate));
[hear] (define translate
(let ((prev (prev-translate)))
(? x
(if (number? (x))
(prev (x))
(if (= (head (x)) lambda)
(let ((formals (head (tail (x))))
(body (head (tail (tail (x))))))
(if (> (list-length (formals)) 0)
(if (number? (last (formals)))
(translate
(vector
lambda
(except-last (formals))
(vector ? (last (formals)) (body))))
(let ((formal-name (first (last (formals))))
(formal-type (second (last (formals)))))
(translate
(vector
lambda
(except-last (formals))
(vector
?
(formal-name)
(vector
let
(vector (vector
(formal-name)
(vector
(vector objectify (vector (formal-name)))
(formal-type))))
(body)))))))
(translate (body))))
(prev (x)))))));
# add conditional form
[hear] (define prev-translate (translate));
[hear] (define translate
(let ((prev (prev-translate)))
(? x
(if (number? (x))
(prev (x))
(if (= (head (x)) cond)
(let ((cnd (head (tail (x))))
(rem (tail (tail (x)))))
(if (> (list-length (rem)) 0)
(translate
(vector
if
(first (cnd))
(second (cnd))
(prepend cond (rem))))
(translate (cnd))))
(prev (x)))))));
[hear] (= 99 (cond 99));
[hear] (= 8 (cond ((true) 8) 11));
[hear] (= 11 (cond ((false) 8) 11));
[hear] (= 7 (cond ((false) 3) ((true) 7) 11));
[hear] (= 3 (cond ((true) 3) ((true) 7) 11));
[hear] (= 11 (cond ((false) 3) ((false) 7) 11));
[hear] (define remove-match
(lambda (test lst)
(if (> (list-length (lst)) 0)
(if (test (head (lst)))
(remove-match (test) (tail (lst)))
(prepend (head (lst)) (remove-match (test) (tail (lst)))))
(lst))));
[hear] (define remove-element
(lambda (x)
(remove-match (lambda (y) (= (y) (x))))));
[hear] (list= (vector 1 2 3 5) (remove-element 4 (vector 1 2 3 4 5)));
[hear] (list= (vector 1 2 3 5) (remove-element 4 (vector 1 4 2 4 3 4 5)));
[hear] (define return
(lambda (T t)
(let ((obj (objectify (t))))
(obj (T)))));
[hear] (define tester
(lambda ((x int) (y int))
(return int (+ (x) (y)))));
[hear] (= 42 (tester (make-integer 10) (make-integer 32)));
[hear] (= 42 (tester 10 32));
[hear] (define reflective
(lambda (f)
((lambda (x)
(f (lambda (y) ((x (x)) (y)))))
(lambda (x)
(f (lambda (y) ((x (x)) (y))))))));
# OBJECT an example object -- a 2D point
[hear] (define point
(lambda (x y)
(reflective
(lambda (self msg)
(cond ((= (msg) x) (x))
((= (msg) y) (y))
((= (msg) point) (self))
((= (msg) +)
(lambda ((p point))
(point (+ (x) (p x))
(+ (y) (p y)))))
((= (msg) =)
(lambda ((p point))
(and (= (x) (p x))
(= (y) (p y)))))
0)))));
[hear] (define point1 (point 1 11));
[hear] (define point2 (point 2 22));
[hear] (= 1 (point1 x));
[hear] (= 22 (point2 y));
[hear] (= 11 ((point 11 12) x));
[hear] (= 11 (((point 11 12) point) x));
[hear] (= 16 (((point 16 17) point) x));
[hear] (= 33 (point1 + (point2) y));
[hear] (point1 + (point2) = (point 3 33));
[hear] (point2 + (point1) = (point 3 33));
[hear] ((point 100 200) + (point 200 100) = (point 300 300));
[hear] (instanceof point (point1));
[hear] (not (instanceof int (point1)));
[hear] (instanceof int 5);
[hear] (not (instanceof point 5));
# OBJECT an example object -- a container
[hear] (define container
(lambda (x)
(let ((contents (make-cell (vector))))
(reflective
(lambda (self msg)
(cond ((= (msg) container) (self))
((= (msg) inventory) (get! (contents)))
((= (msg) add)
(lambda (x)
(if (not (element (x) (get! (contents))))
(set! (contents) (prepend (x) (get! (contents))))
(false))))
((= (msg) remove)
(lambda (x)
(set! (contents) (remove-element (x) (get! (contents))))))
((= (msg) =)
(lambda ((c container))
(set= (self inventory) (c inventory))))
0))))));
# Can pass anything to container function to create an object
# Should eventually use a consistent protocol for all objects,
# but all this stuff is still in flux
[hear] (define pocket (container new));
[hear] (pocket add 77);
[hear] (pocket add 88);
[hear] (pocket add 99);
[hear] (set= (pocket inventory) (vector 77 88 99));
[hear] (pocket remove 88);
[hear] (set= (pocket inventory) (vector 77 99));
[hear] (define pocket2 (container new));
[hear] (pocket2 add 77);
[hear] (pocket2 add 99);
[hear] (pocket2 = (pocket));
# OBJECT expressing inheritance
# counter-container adds one method to container: count
[hear] (define counter-container
(lambda (x)
(let ((super (container new)))
(reflective
(lambda (self msg)
(cond ((= (msg) counter-container) (self))
((= (msg) count) (list-length (super inventory)))
(super (msg))))))));
[hear] (define cc1 (counter-container new));
[hear] (= 0 (cc1 count));
[hear] (cc1 add 4);
[hear] (= 1 (cc1 count));
[hear] (cc1 add 5);
[hear] (= 2 (cc1 count));
# OBJECT adding a special form for classes
# need a bunch of extra machinery first, will push this
# back into previous sections eventually, and simplify
[hear] (define list-append
(lambda (lst1 lst2)
(if (> (list-length (lst1)) 0)
(list-append (except-last (lst1))
(prepend (last (lst1)) (lst2)))
(lst2))));
[hear] (= (list-append (vector 1 2 3) (vector 4 5 6)) (vector 1 2 3 4 5 6));
[hear] (define append
(? x
(? lst
(if (> (list-length (lst)) 0)
(prepend (head (lst)) (append (x) (tail (lst))))
(vector (x))))));
[hear] (= (append 5 (vector 1 2)) (vector 1 2 5));
[hear] (define select-match
(lambda (test lst)
(if (> (list-length (lst)) 0)
(if (test (head (lst)))
(prepend (head (lst)) (select-match (test) (tail (lst))))
(select-match (test) (tail (lst))))
(lst))));
[hear] (define unique
(let ((store (make-cell 0)))
(lambda (x)
(let ((id (get! (store))))
(begin
(set! (store) (+ (id) 1))
(id))))));
[hear] (= (unique new) 0);
[hear] (= (unique new) 1);
[hear] (= (unique new) 2);
[hear] (not (= (unique new) (unique new)));
# okay, here it comes. don't panic!
# I need to split this up into helpers, and simplify.
# It basically just writes code for classes like we saw in
# a previous section.
[hear] (define prev-translate (translate));
[hear] (define translate
(let ((prev (prev-translate)))
(? x
(if (number? (x))
(prev (x))
(if (= (head (x)) class)
(let ((name (list-ref (x) 1))
(args (list-ref (x) 2))
(fields (tail (tail (tail (x))))))
(translate
(vector
define
(name)
(vector
lambda
(prepend method (args))
(vector
let
(append
(vector unique-id (vector unique new))
(map
(tail)
(select-match (? x (= (first (x)) field)) (fields))))
(vector
let
(vector
(vector
self
(vector
reflective
(vector
lambda
(vector self method)
(list-append
(prepend
cond
(list-append
(map
(? x
(vector
(vector = (vector method) (first (x)))
(second (x))))
(map (tail)
(select-match
(? x (= (first (x)) method))
(fields))))
(map
(? x
(vector
(vector = (vector method) (x))
(vector (x))))
(map (second)
(select-match
(? x (= (first (x)) field))
(fields))))))
(vector
(vector
(vector = (vector method) self)
(vector self))
(vector
(vector = (vector method) (name))
(vector self self))
(vector
(vector = (vector method) unknown)
(vector lambda (vector x) 0))
(vector
(vector = (vector method) new)
0)
(vector
(vector = (vector method) unique-id)
(vector unique-id))
(vector
(vector = (vector method) ==)
(vector
lambda
(vector x)
(vector =
(vector unique-id)
(vector x unique-id))))
(vector self unknown (vector method))))))))
(vector
begin
(vector self (vector method))
(vector self))))))))
(prev (x)))))));
# revisit the point class example
[hear] (class point (x y)
(method x (x))
(method y (y))
(method + (lambda ((p point))
(point new
(+ (x) (p x))
(+ (y) (p y))))