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This file: http://angg.twu.net/gab/README.html (find-gab "README") Author: Eduardo Ochs <eduardoochs@gmail.com> Varsion: 2012may15 Public domain. __ _ __ / / __ _ __ _| |__ \ \ | | / _` |/ _` | '_ \ | | < < | (_| | (_| | |_) | > > | | \__, |\__,_|_.__/ | | \_\ |___/ /_/ GabCalc - a calculator for mathematical expressions involving quantifiers and set comprehension, inspired by Andrej Bauer's PLZoo Note: this is not a proper README yet! I have only made one public announcement, for a TINY part of gab.lua... Because the rest is still a mess! See: http://angg.twu.net/gab/gab-lpeg.lua Introduction: examples ====================== This e-script*(eepitch-gab)*(eepitch-kill)*(eepitch-gab) pev "Fa a<-{2,3,4}. Ex b<-{2,3,4}. a*b>10" pev "{(x,y) | x<-{2,3}, y<-{3,4}, x<y}" pev "(\\ a. a*a)(5)" generates this transcript: Lua 5.1.4 Copyright (C) 1994-2008 Lua.org, PUC-Rio > pev "Fa a<-{2,3,4}. Ex b<-{2,3,4}. a*b>10" Fa a <- {2, 3, 4}. Ex b <- {2, 3, 4}. a*b > 10 Fa__________. | | <-_. Ex__________. | | | | a {}_.__. <-_. >_____. | | | | | | | 2 3 4 b {}_.__. *__. 10 | | | | | 2 3 4 a b F > pev "{(x,y) | x<-{2,3}, y<-{3,4}, x<y}" {(x, y) | x <- {2, 3}, y <- {3, 4}, x < y} So_______.________._____. | | | | <-_. <-_. <__. ()_. | | | | | | | | x {}_. y {}_. x y x y | | | | 2 3 3 4 {(2, 3), (2, 4), (3, 4)} > pev "(\\ a. a*a)(5)" (\a.a*a)(5) Ap_______. | | \__. 5 | | a *__. | | a a 25 > Files ===== Code: http://angg.twu.net/gab/gab.lua (find-gab "gab.lua") Tests: http://angg.twu.net/gab/gab-tests.lua (find-gab "gab-tests.lua") The LPeg tricks used in the parser: http://angg.twu.net/gab/gab-lpeg.lua (find-gab "gab-lpeg.lua") Old files (some are obsolete, some are garbage): http://angg.twu.net/gab/gab-oldparser.lua (find-gab "gab-oldparser.lua") http://angg.twu.net/gab/gabriela-app.lua (find-gab "gabriela-app.lua") http://angg.twu.net/gab/gabriela.lua (find-gab "gabriela.lua") The development is being made with eev and eepitch - see: http://angg.twu.net/eev-current/eepitch.el.html http://angg.twu.net/eev-current/eev-intro.el.html History ======= One of the courses that I teach at the university where I work is Discrete Mathematics ("MD"). The Teaching Assistant for MD in 2011, Gabriela Avila de Queiroz, chose to do as her reseach project a program that could interpret some expressions involving nested quantifiers, and calculate their results. She had some difficulties with Lua, and ended up writing it in C. In the beginning of 2012 I ported her program to Lua, and started learning ML with the intent of extending a language from PLZoo to add quantifiers to it - and, later, also adding categorical operations. But then I went back to Lua - possibly temporarily - and started adding features to the calculator in Lua - a printer that used infix notation, an evaluator, printers of expressions in a lisp-y form and in tree form, set comprehension, lambda forms and function application, definitions, a bare-bones way to calculate and print grids of values (like in spreasheets), a primitive recursive-descent parser written in Lua that required spaces between any two tokens, and a "real" parser written in LPeg. Some Medium-Term Goals ====================== If/then/else. Abbreviations. Sets of the form {a,...,b} (with ellipsis). Debugging tools. Set membership and equality. Better support for defining functions. Functions defined in Lua. Memoization. Inductive definitions. Substitution operators (like [x:=4](x*x)). Reduction rules and tools for operating on a certain subexpression. Expressions that keep their history. Plotting points. Full support for two-dimensional "modal" and "intuitionistic" truth-values - for toposes of the form Set^D, where is the poset generated by a subset of N×N. Interface with dednat5. Thunks and lazyness. The Logo ======== Here: http://angg.twu.net/gab/gab.png It was adapted from: http://www.pbs.org/design/2009/09/stealing-the-perfect-color-scheme.html http://www.pbs.org/design/images/rothko.jpg and created with Gimp's color picker and this: http://angg.twu.net/elisp/myxpm.el.html#gab (find-angg "elisp/myxpm.el" "gab") -- Local Variables: -- coding: raw-text-unix -- ee-anchor-format: "«%s»" -- End: