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-\documentclass{article}
-\usepackage{axiom}
-\begin{document}
-\title{\$SPAD/src/interp guess.boot}
-\author{The Axiom Team}
-\maketitle
-\begin{abstract}
-\end{abstract}
-\eject
-\tableofcontents
-\eject
-\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>>
-
-$minThreshold := 3
-$maxThreshold := 7
- 
---=======================================================================
---                        Build Directories
---=======================================================================
-buildOperationWordTable() ==
-  $opWordTable := buildWordTable [PNAME x for x in allOperations()]
- 
-buildWordTable u ==
-  table:= MAKE_-HASHTABLE 'ID
-  for s in u repeat
-    words := wordsOfString s
-    key := UPCASE s.0
-    HPUT(table,key,[[s,:words],:HGET(table,key)])
-  for key in HKEYS table repeat
-    HPUT(table,key,
-      listSort(function GLESSEQP,removeDupOrderedAlist
-        listSort(function GLESSEQP, HGET(table,key),function CAR),
-          function CADR))
-  table
-
-measureWordTable u ==
-  +/[+/[#entry for entry in HGET(u,key)] for key in HKEYS u]
-
-removeDupOrderedAlist u ==
-  -- removes duplicate entries in ordered alist
-  -- (where duplicates are adjacent)
-  for x in tails u repeat
-    (y := rest x) and first first x = first first y => RPLACD(x,rest y)
-  u
- 
-wordsOfString(s) == [UPCASE x for x in wordsOfStringKeepCase s]
- 
-wordsOfStringKeepCase s == wordsOfString1(s,0) or [COPY s]
- 
-wordsOfString1(s,j) ==
-  k := or/[i for i in j..SUB1(MAXINDEX(s)) | UPPER_-CASE_-P s.i] =>
-    tailWords:=
-      UPPER_-CASE_-P s.(k+1) =>
-        n:= or/[i for i in (k+2)..SUB1(MAXINDEX(s))|not UPPER_-CASE_-P s.i]
-        null n => [SUBSTRING(s,k,nil)]
-        n > k+1 => [SUBSTRING(s,k,n-k-1),:wordsOfString1(s,n-1)]
-      m := or/[i for i in (k+2)..SUB1(MAXINDEX(s)) | UPPER_-CASE_-P s.i] =>
-        [SUBSTRING(s,k,m-k),:wordsOfString1(s,m)]
-      [SUBSTRING(s,k,nil)]
-    k > j+1 => [SUBSTRING(s,j,k-j),:tailWords]
-    tailWords
-  nil
-
-wordKeys s == 
-  REMDUP [UPCASE s.0,:fn(s,1,-1,MAXINDEX s,nil)] where fn(s,i,lastKeyIndex,n,acc) ==
-    i > n => acc
-    UPPER_-CASE_-P s.i =>
---    i = lastKeyIndex + 1 => fn(s,i + 1,i,n,[s.i,:rest acc])
-      fn(s,i + 1,i,n,[s.i,:acc])
-    fn(s,i + 1,lastKeyIndex,n,acc)
-
---=======================================================================
---               Augment Function Directories
---=======================================================================
-add2WordFunctionTable fn ==
---called from DEF
-  $functionTable and
-    null LASSOC(s := PNAME fn,HGET($functionTable,(key := UPCASE s.0))) =>
-      HPUT($functionTable,key,[[s,:wordsOfString s],:HGET($functionTable,key)])
- 
---=======================================================================
---                       Guess Function Name
---=======================================================================
-findWords(word,table) == 
-  $lastWord := word
-  $lastTable:= table
-  $totalWords:= nil
-  $countThreshold := $minThreshold
-  $lastMinimum := -1
-  res := findApproximateWords(word,table) 
-  if null res then
-    $countThreshold := $countThreshold + 2
-    res := findApproximateWords(word,table) 
-  $lastAlist := mySort res =>
---    $lastMinimum := CAR LAST $lastAlist
---    $lastWords := wordSort CDAR $lastAlist
---    $totalWords:= $lastWords
---    $lastAlist := CDR  $lastAlist
---    $totalWords
-      $lastMinimum := CAAR $lastAlist
-      $lastWords := wordSort CDAR $lastAlist
-      $totalWords:= $lastWords
-      $lastAlist := CDR  $lastAlist
-      $totalWords
-  $lastWords := nil
-
-wordSort u == REMDUP listSort(function GLESSEQP,u)
-
-more() == moreWords($lastWord,$lastTable)
-
-moreWords(word,table) ==
-  $lastAlist =>
-     $lastMinimum := CAR LAST pp $lastAlist
-     numberOfLastWords := #$lastWords
-     $lastWords := "append"/(ASSOCRIGHT $lastAlist)
-     if #$lastWords > numberOfLastWords then 
-       trialLastAlist := 
-         [p for p in $lastAlist | p.0 < $maxThreshold]
-       trialLastWords := "append"/(ASSOCRIGHT trialLastAlist)
-       if #trialLastWords > numberOfLastWords then
-         $lastWords := trialLastWords         
-     $totalWords:= wordSort [:$lastWords,:$totalWords]
-     $lastAlist := nil
-     $totalWords
-  $countThreshold := $countThreshold + 2
-  $lastAlist := findApproximateWords(word,table)
-  moreWords(word,table)
-
-findApproximateWords(word,table) ==
-  count := $countThreshold
-  words:= wordsOfString word
-  upperWord:= UPCASE COPY word
-  n := #words
-  threshold:=
-    n = 1 => count
-    count+1
- 
-  --first try to break up as list of words
-  alist:= nil
-  for i in 1..#words repeat
-    $penalty :local := (i = 1 => 0; 1)
-    wordAlist:= HGET(table,UPCASE (first words).0)
-    for [x,:wordList] in wordAlist repeat
-      k := findApproxWordList(words,wordList,n,threshold,#wordList) 
-      k =>
-        k := k + $penalty
-        k <= $lastMinimum => 'skip
-        alist := consAlist(k,x,alist)
-      
-    if i = 1 and null alist then
-        --no winners, so try flattening to upper case and checking again
-        wordSize := SIZE word
-        lastThreshold := MAX(threshold - 1,wordSize/2)
-        for [x,:.] in wordAlist repeat
-          k := deltaWordEntry(upperWord,UPCASE x)
-          k < lastThreshold => alist := consAlist(k,x,alist)
-
-    rotateWordList words
-
-  alist
-
-consAlist(x,y,alist) ==
-  u := ASSOC(x,alist) => 
-    RPLACD(u,[y,:CDR u])
-    alist
-  [[x,y],:alist]
-
-findApproxWordList(words,wordList,n,threshold,w) ==
-  val := findApproxWordList1(words,wordList,n,threshold,w)
-  null val => val
---pp [val,:wordList]
-  val
-
-findApproxWordList1(words,wordList,n,threshold,w) ==
-  two := threshold - 2
-  n = w => 
-      k := findApproxSimple(words,wordList,threshold) => k 
-
-      n < 3 => false
-      threshold := threshold - 1
-      sum := 0      --next, throw out one bad word
-
-      badWord := false
-      for entry in wordList for part in words while sum < threshold repeat
-        k:= deltaWordEntry(part,entry)
-        k < two => sum:= sum + k
-        null badWord => badWord := true
-        sum := 1000
-      sum < threshold => 
---      pp [2,sum,wordList]
-        sum + 2
-
-  n+1 = w =>    --assume one word is missing
-      sum := 0
-      badWord := false
-      for entries in tails wordList for part in words
-           while sum < threshold repeat
-        entry := first entries
-        k:= deltaWordEntry(part,entry)
-        k < two => sum:= sum + k
-        null badWord =>
-          badWord := true
-          entries := rest entries      --skip this bad word
-          entry := first entries
-          k := deltaWordEntry(part,entry)
-          k < two => sum := sum + k
-          sum := 1000
-        sum := 1000
-      sum < threshold => 
---      pp [3,sum,wordList]
-        sum + 2
-      false
-  n-1 = w =>    --assume one word too many
-      sum := 0  --here: KEEP it hard to satisfy
-      badWord := false
-      for entry in wordList for parts in tails words
-           while sum < threshold repeat
-        part := first parts
-        k:= deltaWordEntry(part,entry)
-        k < 2 => sum:= sum + k
-        null badWord =>
-          badWord := true
-          parts := rest parts      --skip this bad word
-          part := first parts
-          k := deltaWordEntry(part,entry)
-          k < 2 => sum := sum + k
-          return (sum := 1000)
-        return (sum := 1000)
-      sum < threshold =>
---      pp [4,sum,wordList]
-        $penalty = 1 => sum
-        sum + 1
-      false
-  false
-
-findApproxSimple(words,wordList,threshold) ==
-  sum := 0
-  --first try matching words in order
-  for entry in wordList for part in words while sum < threshold repeat
-    sum:= sum + deltaWordEntry(part,entry)
-  sum < threshold => 
---  pp ['"--->",sum,:wordList]
-    sum
-  nil
-      
-rotateWordList u ==
-  v := u
-  p := CAR v
-  while QCDR v repeat
-    RPLACA(v,CADR v) 
-    v := QCDR v
-  RPLACA(v,p)
-  u
-
-deltaWordEntry(word,entry) ==
-  word = entry => 0
-  word.0 ^= entry.0 => 1000
-  #word > 2 and stringPrefix?(word,entry) => 1
-  ABS(diff := SIZE word - SIZE entry) > 4 => 1000
-  canForgeWord(word,entry)
- 
---+ Note these are optimized definitions below-- see commented out versions
---+   to understand the algorithm
-canForgeWord(word,entry) ==
-  forge(word,0,MAXINDEX word,entry,0,MAXINDEX entry,0)
- 
-forge(word,w,W,entry,e,E,n) ==
-  w > W =>
-    e > E => n
-    QSADD1 QSPLUS(E-e,n)
-  e > E => QSADD1 QSPLUS(W-w,n)
-  word.w = entry.e => forge(word,w+1,W,entry,e+1,E,n)
-  w=W or e=E => forge(word,w+1,W,entry,e+1,E,QSADD1 n)
-  word.w=entry.(e+1) =>
-    word.(w+1) = entry.e => forge(word,w+2,W,entry,e+2,E,QSADD1 n)
-    forge(word,w+1,W,entry,e+2,E,QSADD1 n)
-  word.(w+1)=entry.e => forge(word,w+2,W,entry,e+1,E,QSADD1 n)
- 
-  (deltaW := W-w) > 1 and (deltaE := E-e) > 1 =>
-    --if word is long, can we delete chars to match 2 consective chars
-    deltaW >= deltaE and
-      (k := or/[j for j in (w+2)..(W-1) | word.j = entry.e])
-        and word.(k+1) = entry.(e+1) =>
-          forge(word,k+2,W,entry,e+2,E,QSPLUS(k-w,n))
-    deltaW <= deltaE and
-    --if word is short, can we insert chars so as to match 2 consecutive chars
-      (k := or/[j for j in (e+2)..(E-1) | word.w = entry.j])
-        and word.(w+1) = entry.(k+1) =>
-          forge(word,w+2,W,entry,k+2,E,QSPLUS(n,k-e))
-    forge(word,w+1,W,entry,e+1,E,QSADD1 n)
-  --check for two consecutive matches down the line
-  forge(word,w+1,W,entry,e+1,E,QSADD1 n)
- 
---+ DO NOT REMOVE DEFINITIONS BELOW which explain the algorithm
---+ canForgeWord(word,entry) ==--
---+ [d,i,s,t] := forge(word,0,MAXINDEX word,entry,0,MAXINDEX entry,0,0,0,0)
---+ --d=deletions, i=insertions, s=substitutions, t=transpositions
---+ --list is formed only for tuning purposes-- remove later on
---+ d + i + s + t
- 
---+forge(word,w,W,entry,e,E,d,i,s,t) ==
---+  w > W =>
---+    e > E => [d,i,s,t]
---+    [d,E-e+i+1,s,t]
---+  e > E => [W-w+d+1,i,s,t]
---+  word.w = entry.e => forge(word,w+1,W,entry,e+1,E,d,i,s,t)
---+  w=W or e=E => forge(word,w+1,W,entry,e+1,E,d,i,s+1,t)
---+  word.w=entry.(e+1) =>
---+    word.(w+1) = entry.e => forge(word,w+2,W,entry,e+2,E,d,i,s,t+1)
---+    forge(word,w+1,W,entry,e+2,E,d,i+1,s,t)
---+  word.(w+1)=entry.e => forge(word,w+2,W,entry,e+1,E,d+1,i,s,t)
---+
---+  (deltaW := W-w) > 1 and (deltaE := E-e) > 1 =>
---+    --if word is long, can we delete chars to match 2 consective chars
---+    deltaW >= deltaE and
---+      (k := or/[j for j in (w+2)..(W-1) | word.j = entry.e])
---+        and word.(k+1) = entry.(e+1) =>
---+          forge(word,k+2,W,entry,e+2,E,d+k-w,i,s,t)
---+    deltaW <= deltaE and
---+    --if word is short, can we insert chars so as to match 2 consecutive chars
---+      (k := or/[j for j in (e+2)..(E-1) | word.w = entry.j])
---+        and word.(w+1) = entry.(k+1) =>
---+          forge(word,w+2,W,entry,k+2,E,d,i+k-e,s,t)
---+    forge(word,w+1,W,entry,e+1,E,d,i,s+1,t)
---+  --check for two consecutive matches down the line
---+  forge(word,w+1,W,entry,e+1,E,d,i,s+1,t)
- 
-mySort u == listSort(function GLESSEQP,u)
-@
-\eject
-\begin{thebibliography}{99}
-\bibitem{1} nothing
-\end{thebibliography}
-\end{document}