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Diffstat (limited to 'src/algebra/formula.spad.pamphlet')
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diff --git a/src/algebra/formula.spad.pamphlet b/src/algebra/formula.spad.pamphlet deleted file mode 100644 index 750bf710..00000000 --- a/src/algebra/formula.spad.pamphlet +++ /dev/null @@ -1,515 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra formula.spad} -\author{Robert S. Sutor} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\section{domain FORMULA ScriptFormulaFormat} -<<domain FORMULA ScriptFormulaFormat>>= -)abbrev domain FORMULA ScriptFormulaFormat -++ Author: Robert S. Sutor -++ Date Created: 1987 through 1990 -++ Change History: -++ Basic Operations: coerce, convert, display, epilogue, -++ formula, new, prologue, setEpilogue!, setFormula!, setPrologue! -++ Related Constructors: ScriptFormulaFormat1 -++ Also See: TexFormat -++ AMS Classifications: -++ Keywords: output, format, SCRIPT, BookMaster, formula -++ References: -++ SCRIPT Mathematical Formula Formatter User's Guide, SH20-6453, -++ IBM Corporation, Publishing Systems Information Development, -++ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 80301-9191. -++ Description: -++ \spadtype{ScriptFormulaFormat} provides a coercion from -++ \spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. -++ The basic SCRIPT formula format object consists of three parts: a -++ prologue, a formula part and an epilogue. The functions -++ \spadfun{prologue}, \spadfun{formula} and \spadfun{epilogue} -++ extract these parts, respectively. The central parts of the expression -++ go into the formula part. The other parts can be set -++ (\spadfun{setPrologue!}, \spadfun{setEpilogue!}) so that contain the -++ appropriate tags for printing. For example, the prologue and -++ epilogue might simply contain ":df." and ":edf." so that the -++ formula section will be printed in display math mode. - -ScriptFormulaFormat(): public == private where - E ==> OutputForm - I ==> Integer - L ==> List - S ==> String - - public == Join(SetCategory, CoercibleFrom E) with - convert: (E,I) -> % - ++ convert(o,step) changes o in standard output format to - ++ SCRIPT formula format and also adds the given step number. - ++ This is useful if you want to create equations with given numbers - ++ or have the equation numbers correspond to the interpreter step - ++ numbers. - display: (%, I) -> Void - ++ display(t,width) outputs the formatted code t so that each - ++ line has length less than or equal to \spadvar{width}. - display: % -> Void - ++ display(t) outputs the formatted code t so that each - ++ line has length less than or equal to the value set by - ++ the system command \spadsyscom{set output length}. - epilogue: % -> L S - ++ epilogue(t) extracts the epilogue section of a formatted object t. - formula: % -> L S - ++ formula(t) extracts the formula section of a formatted object t. - new: () -> % - ++ new() create a new, empty object. Use \spadfun{setPrologue!}, - ++ \spadfun{setFormula!} and \spadfun{setEpilogue!} to set the - ++ various components of this object. - prologue: % -> L S - ++ prologue(t) extracts the prologue section of a formatted object t. - setEpilogue!: (%, L S) -> L S - ++ setEpilogue!(t,strings) sets the epilogue section of a - ++ formatted object t to strings. - setFormula!: (%, L S) -> L S - ++ setFormula!(t,strings) sets the formula section of a - ++ formatted object t to strings. - setPrologue!: (%, L S) -> L S - ++ setPrologue!(t,strings) sets the prologue section of a - ++ formatted object t to strings. - - private == add - import OutputForm - import Character - import Integer - import List OutputForm - import List String - - Rep := Record(prolog : L S, formula : L S, epilog : L S) - - -- local variables declarations and definitions - - expr: E - prec,opPrec: I - str: S - blank : S := " @@ " - - maxPrec : I := 1000000 - minPrec : I := 0 - - splitChars : S := " <>[](){}+*=,-%" - - unaryOps : L S := ["-","^"]$(L S) - unaryPrecs : L I := [700,260]$(L I) - - -- the precedence of / in the following is relatively low because - -- the bar obviates the need for parentheses. - binaryOps : L S := ["+->","|","**","/","<",">","=","OVER"]$(L S) - binaryPrecs : L I := [0,0,900, 700,400,400,400, 700]$(L I) - - naryOps : L S := ["-","+","*",blank,",",";"," ","ROW","", - " habove "," here "," labove "]$(L S) - naryPrecs : L I := [700,700,800, 800,110,110, 0, 0, 0, - 0, 0, 0]$(L I) --- naryNGOps : L S := ["ROW"," here "]$(L S) - naryNGOps : L S := nil$(L S) - - plexOps : L S := ["SIGMA","PI","INTSIGN","INDEFINTEGRAL"]$(L S) - plexPrecs : L I := [ 700, 800, 700, 700]$(L I) - - specialOps : L S := ["MATRIX","BRACKET","BRACE","CONCATB", _ - "AGGLST","CONCAT","OVERBAR","ROOT","SUB", _ - "SUPERSUB","ZAG","AGGSET","SC","PAREN"] - - -- the next two lists provide translations for some strings for - -- which the formula formatter provides special variables. - - specialStrings : L S := - ["5","..."] - specialStringsInFormula : L S := - [" alpha "," ellipsis "] - - -- local function signatures - - addBraces: S -> S - addBrackets: S -> S - group: S -> S - formatBinary: (S,L E, I) -> S - formatFunction: (S,L E, I) -> S - formatMatrix: L E -> S - formatNary: (S,L E, I) -> S - formatNaryNoGroup: (S,L E, I) -> S - formatNullary: S -> S - formatPlex: (S,L E, I) -> S - formatSpecial: (S,L E, I) -> S - formatUnary: (S, E, I) -> S - formatFormula: (E,I) -> S - parenthesize: S -> S - precondition: E -> E - postcondition: S -> S - splitLong: (S,I) -> L S - splitLong1: (S,I) -> L S - stringify: E -> S - - -- public function definitions - - new() : % == [[".eq set blank @",":df."]$(L S), - [""]$(L S), [":edf."]$(L S)]$Rep - - coerce(expr : E): % == - f : % := new()$% - f.formula := [postcondition - formatFormula(precondition expr, minPrec)]$(L S) - f - - convert(expr : E, stepNum : I): % == - f : % := new()$% - f.formula := concat(["<leqno lparen ",string(stepNum)$S, - " rparen>"], [postcondition - formatFormula(precondition expr, minPrec)]$(L S)) - f - - display(f : %, len : I) == - s,t : S - for s in f.prolog repeat sayFORMULA(s)$Lisp - for s in f.formula repeat - for t in splitLong(s, len) repeat sayFORMULA(t)$Lisp - for s in f.epilog repeat sayFORMULA(s)$Lisp - - display(f : %) == - display(f, _$LINELENGTH$Lisp pretend I) - - prologue(f : %) == f.prolog - formula(f : %) == f.formula - epilogue(f : %) == f.epilog - - setPrologue!(f : %, l : L S) == f.prolog := l - setFormula!(f : %, l : L S) == f.formula := l - setEpilogue!(f : %, l : L S) == f.epilog := l - - coerce(f : %): E == - s,t : S - l : L S := nil - for s in f.prolog repeat l := concat(s,l) - for s in f.formula repeat - for t in splitLong(s, (_$LINELENGTH$Lisp pretend Integer) - 4) repeat - l := concat(t,l) - for s in f.epilog repeat l := concat(s,l) - (reverse l) :: E - - -- local function definitions - - postcondition(str: S): S == - len : I := #str - len < 4 => str - plus : Character := char "+" - minus: Character := char "-" - for i in 1..(len-1) repeat - if (str.i =$Character plus) and (str.(i+1) =$Character minus) - then setelt(str,i,char " ")$S - str - - stringify expr == object2String(expr)$Lisp pretend S - - splitLong(str : S, len : I): L S == - -- this blocks into lines - if len < 20 then len := _$LINELENGTH$Lisp - splitLong1(str, len) - - splitLong1(str : S, len : I) == - l : List S := nil - s : S := "" - ls : I := 0 - ss : S - lss : I - for ss in split(str,char " ") repeat - lss := #ss - if ls + lss > len then - l := concat(s,l)$List(S) - s := "" - ls := 0 - lss > len => l := concat(ss,l)$List(S) - ls := ls + lss + 1 - s := concat(s,concat(ss," ")$S)$S - if positive? ls then l := concat(s,l)$List(S) - reverse l - - group str == - concat ["<",str,">"] - - addBraces str == - concat ["left lbrace ",str," right rbrace"] - - addBrackets str == - concat ["left lb ",str," right rb"] - - parenthesize str == - concat ["left lparen ",str," right rparen"] - - precondition expr == - outputTran(expr)$Lisp - - formatSpecial(op : S, args : L E, prec : I) : S == - op = "AGGLST" => - formatNary(",",args,prec) - op = "AGGSET" => - formatNary(";",args,prec) - op = "CONCATB" => - formatNary(" ",args,prec) - op = "CONCAT" => - formatNary("",args,prec) - op = "BRACKET" => - group addBrackets formatFormula(first args, minPrec) - op = "BRACE" => - group addBraces formatFormula(first args, minPrec) - op = "PAREN" => - group parenthesize formatFormula(first args, minPrec) - op = "OVERBAR" => - null args => "" - group concat [formatFormula(first args, minPrec)," bar"] - op = "ROOT" => - null args => "" - tmp : S := formatFormula(first args, minPrec) - null rest args => group concat ["sqrt ",tmp] - group concat ["midsup adjust(u 1.5 r 9) ", - formatFormula(first rest args, minPrec)," sqrt ",tmp] - op = "SC" => - formatNary(" labove ",args,prec) - op = "SUB" => - group concat [formatFormula(first args, minPrec)," sub ", - formatSpecial("AGGLST",rest args,minPrec)] - op = "SUPERSUB" => - -- variable name - form : List S := [formatFormula(first args, minPrec)] - -- subscripts - args := rest args - null args => concat form - tmp : S := formatFormula(first args, minPrec) - if tmp ~= "" then form := append(form,[" sub ",tmp])$(List S) - -- superscripts - args := rest args - null args => group concat form - tmp : S := formatFormula(first args, minPrec) - if tmp ~= "" then form := append(form,[" sup ",tmp])$(List S) - -- presuperscripts - args := rest args - null args => group concat form - tmp : S := formatFormula(first args, minPrec) - if tmp ~= "" then form := append(form,[" presup ",tmp])$(List S) - -- presubscripts - args := rest args - null args => group concat form - tmp : S := formatFormula(first args, minPrec) - if tmp ~= "" then form := append(form,[" presub ",tmp])$(List S) - group concat form - op = "MATRIX" => formatMatrix rest args --- op = "ZAG" => --- concat ["\zag{",formatFormula(first args, minPrec),"}{", --- formatFormula(first rest args,minPrec),"}"] - concat ["not done yet for ",op] - - formatPlex(op : S, args : L E, prec : I) : S == - hold : S - p : I := position(op,plexOps) - p < 1 => error "unknown Script Formula Formatter unary op" - opPrec := plexPrecs.p - n : I := #args - (n ~= 2) and (n ~= 3) => error "wrong number of arguments for plex" - s : S := - op = "SIGMA" => "sum" - op = "PI" => "product" - op = "INTSIGN" => "integral" - op = "INDEFINTEGRAL" => "integral" - "????" - hold := formatFormula(first args,minPrec) - args := rest args - if op ~= "INDEFINTEGRAL" then - if hold ~= "" then - s := concat [s," from",group concat ["\displaystyle ",hold]] - if not null rest args then - hold := formatFormula(first args,minPrec) - if hold ~= "" then - s := concat [s," to",group concat ["\displaystyle ",hold]] - args := rest args - s := concat [s," ",formatFormula(first args,minPrec)] - else - hold := group concat [hold," ",formatFormula(first args,minPrec)] - s := concat [s," ",hold] - if opPrec < prec then s := parenthesize s - group s - - formatMatrix(args : L E) : S == - -- format for args is [[ROW ...],[ROW ...],[ROW ...]] - group addBrackets formatNary(" habove ",args,minPrec) - - formatFunction(op : S, args : L E, prec : I) : S == - group concat [op, " ", parenthesize formatNary(",",args,minPrec)] - - formatNullary(op : S) == - op = "NOTHING" => "" - group concat [op,"()"] - - formatUnary(op : S, arg : E, prec : I) == - p : I := position(op,unaryOps) - p < 1 => error "unknown Script Formula Formatter unary op" - opPrec := unaryPrecs.p - s : S := concat [op,formatFormula(arg,opPrec)] - opPrec < prec => group parenthesize s - op = "-" => s - group s - - formatBinary(op : S, args : L E, prec : I) : S == - p : I := position(op,binaryOps) - p < 1 => error "unknown Script Formula Formatter binary op" - op := - op = "**" => " sup " - op = "/" => " over " - op = "OVER" => " over " - op - opPrec := binaryPrecs.p - s : S := formatFormula(first args, opPrec) - s := concat [s,op,formatFormula(first rest args, opPrec)] - group - op = " over " => s - opPrec < prec => parenthesize s - s - - formatNary(op : S, args : L E, prec : I) : S == - group formatNaryNoGroup(op, args, prec) - - formatNaryNoGroup(op : S, args : L E, prec : I) : S == - null args => "" - p : I := position(op,naryOps) - p < 1 => error "unknown Script Formula Formatter nary op" - op := - op = "," => ", @@ " - op = ";" => "; @@ " - op = "*" => blank - op = " " => blank - op = "ROW" => " here " - op - l : L S := nil - opPrec := naryPrecs.p - for a in args repeat - l := concat(op,concat(formatFormula(a,opPrec),l)$L(S))$L(S) - s : S := concat reverse rest l - opPrec < prec => parenthesize s - s - - formatFormula(expr,prec) == - i : Integer - not %pair?(expr)$Foreign(Builtin) => - str := stringify expr - %integer?(expr)$Foreign(Builtin) => - i := expr : Integer - if negative? i or (i > 9) then group str else str - positive?(i := position(str,specialStrings)) => - specialStringsInFormula.i - str - l : L E := (expr pretend L E) - null l => blank - op : S := stringify first l - args : L E := rest l - nargs : I := #args - - -- special cases - member?(op, specialOps) => formatSpecial(op,args,prec) - member?(op, plexOps) => formatPlex(op,args,prec) - - -- nullary case - 0 = nargs => formatNullary op - - -- unary case - (1 = nargs) and member?(op, unaryOps) => - formatUnary(op, first args, prec) - - -- binary case - (2 = nargs) and member?(op, binaryOps) => - formatBinary(op, args, prec) - - -- nary case - member?(op,naryNGOps) => formatNaryNoGroup(op,args, prec) - member?(op,naryOps) => formatNary(op,args, prec) - op := formatFormula(first l,minPrec) - formatFunction(op,args,prec) - -@ -\section{package FORMULA1 ScriptFormulaFormat1} -<<package FORMULA1 ScriptFormulaFormat1>>= -)abbrev package FORMULA1 ScriptFormulaFormat1 -++ Author: Robert S. Sutor -++ Date Created: 1987 through 1990 -++ Change History: -++ Basic Operations: coerce -++ Related Constructors: ScriptFormulaFormat -++ Also See: TexFormat, TexFormat1 -++ AMS Classifications: -++ Keywords: output, format, SCRIPT, BookMaster, formula -++ References: -++ SCRIPT Mathematical Formula Formatter User's Guide, SH20-6453, -++ IBM Corporation, Publishing Systems Information Development, -++ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 80301-9191. -++ Description: -++ \spadtype{ScriptFormulaFormat1} provides a utility coercion for -++ changing to SCRIPT formula format anything that has a coercion to -++ the standard output format. - -ScriptFormulaFormat1(S : SetCategory): public == private where - public == with - coerce: S -> ScriptFormulaFormat() - ++ coerce(s) provides a direct coercion from an expression s of domain S to - ++ SCRIPT formula format. This allows the user to skip the step of - ++ first manually coercing the object to standard output format - ++ before it is coerced to SCRIPT formula format. - - private == add - import ScriptFormulaFormat() - - coerce(s : S): ScriptFormulaFormat == - coerce(s :: OutputForm)$ScriptFormulaFormat - -@ -\section{License} -<<license>>= ---Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. ---All rights reserved. --- ---Redistribution and use in source and binary forms, with or without ---modification, are permitted provided that the following conditions are ---met: --- --- - Redistributions of source code must retain the above copyright --- notice, this list of conditions and the following disclaimer. --- --- - Redistributions in binary form must reproduce the above copyright --- notice, this list of conditions and the following disclaimer in --- the documentation and/or other materials provided with the --- distribution. --- --- - Neither the name of The Numerical ALgorithms Group Ltd. nor the --- names of its contributors may be used to endorse or promote products --- derived from this software without specific prior written permission. --- ---THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS ---IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED ---TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A ---PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER ---OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, ---EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, ---PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR ---PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF ---LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING ---NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ---SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -@ -<<*>>= -<<license>> - -<<domain FORMULA ScriptFormulaFormat>> -<<package FORMULA1 ScriptFormulaFormat1>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |