# HG changeset patch
# User ryokka
# Date 1544607859 -32400
# Node ID df1552e4ac7a29bb0d245698b71394fba54982e4
# Parent 6e03fff298c584f111e0d00b9ebbda4782f3290c
add mindmap, some figs
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/.DS_Store
Binary file Paper/pic/.DS_Store has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/00.graffle
Binary file Paper/pic/00.graffle has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/03.graffle
Binary file Paper/pic/03.graffle has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/06.eps
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/06.eps Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,2719 @@
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+%%Creator: (Unknown)
+%%CreationDate: (Unknown)
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+%%BeginFile: cg-pdf.ps
+%%Copyright: Copyright 2000-2004 Apple Computer Incorporated.
+%%Copyright: All Rights Reserved.
+currentpacking true setpacking
+/cg_md 141 dict def
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+%dup (number of ld's = )print == flush % *** how many
+{ld}repeat pop
+/SC{ % CSname
+ /ColorSpace fr scs
+}bd
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+/soprm /setoverprintmode where{pop/setoverprintmode}{/pop}ifelse ld
+/cgmtx matrix def
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+/CM {cgmtx setmatrix}bd % pop the ctm: our gstate ctm on host is now identity
+/cm {cmmtx astore CM concat}bd % reset the matrix and then concat
+/W{clip newpath}bd
+/W*{eoclip newpath}bd
+
+statusdict begin product end dup (HP) anchorsearch{
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+ true
+}{
+ pop % previous search result
+ (hp) anchorsearch{
+ pop pop true
+ }{
+ pop false
+ }ifelse
+}ifelse
+
+{ % HP is the product: we use this method of stroking because of a bug in their clone printers with certain T3 fonts
+ {
+ { % charCode Wx Wy
+ pop pop % charCode
+ (0)dup 0 4 -1 roll put
+ F charpath
+ }cshow
+ }
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+/re{4 2 roll m 1 index 0 rlineto 0 exch rlineto neg 0 rlineto h}bd
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+/cg_BeginEPSF{
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+ false setstrokeadjust false setoverprint % don't use F
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+ cg_dict_array 3 1 index length 3 sub getinterval
+ {begin}forall
+ count userdict/cg_op_count get sub{pop}repeat
+ userdict/cg_b4_Inc_state get restore
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+ /ImageBandData 0 def
+ /cg_mibiproc{
+ string/ImageBandMask xs
+ string/ImageBandData xs
+ /ImageDataSource{[currentfile/RunLengthDecode filter dup ImageBandMask/readstring cvx
+ /pop cvx dup ImageBandData/readstring cvx/pop cvx]cvx bind}bd
+ }bd
+ /cg_miaiproc{
+ string/ImageBandMask xs
+ string/ImageBandData xs
+ /ImageDataSource{[currentfile/ASCII85Decode filter/RunLengthDecode filter
+ dup ImageBandMask/readstring cvx
+ /pop cvx dup ImageBandData/readstring cvx/pop cvx]cvx bind}bd
+ }bd
+}ifelse
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+dict begin
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+pop % remove mark
+/ImageType 1 def
+/ImageMatrix[Width 0 0 Height neg 0 Height]def
+currentdict dup/ImageMask known{ImageMask}{F}ifelse exch
+% currentdict on stack
+L3?{
+ dup/MaskedImage known
+ {
+ pop
+ <<
+ /ImageType 3
+ /InterleaveType 2
+ /DataDict currentdict
+ /MaskDict
+ << /ImageType 1
+ /Width Width
+ /Height Height
+ /ImageMatrix ImageMatrix
+ /BitsPerComponent 1
+ /Decode [0 1]
+ currentdict/Interpolate known
+ {/Interpolate Interpolate}if
+ >>
+ >>
+ }if
+}if
+exch
+{imagemask}{image}ifelse
+end % pop imagedict from dict stack
+}bd
+
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+}bd
+/t_array 0 def
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+/x_proc{ % x y
+ exch t_array t_i get add exch moveto
+ /t_i t_i 1 add store
+}bd
+/y_proc{ % x y
+ t_array t_i get add moveto
+ /t_i t_i 1 add store
+}bd
+/xy_proc{
+ % x y
+ t_array t_i 2 copy 1 add get 3 1 roll get
+ 4 -1 roll add 3 1 roll add moveto
+ /t_i t_i 2 add store
+}bd
+/sop 0 def % don't bind sop
+/cp_proc/x_proc ld % default moveto proc is for xwidths only
+/base_charpath % string array
+{
+ /t_array xs
+ /t_i 0 def
+ { % char
+ t_c 0 3 -1 roll put
+ currentpoint
+ t_c cply sop
+ cp_proc
+ }forall
+ /t_array 0 def
+}bd
+/sop/stroke ld % default sop is stroke. Done here so we don't bind in /base_charpath
+
+% default sop is stroke
+/nop{}def
+/xsp/base_charpath ld
+/ysp{/cp_proc/y_proc ld base_charpath/cp_proc/x_proc ld}bd
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+findfont dup length dict copy dup
+/Encoding 4 -1 roll put
+definefont pop
+}bd
+/renmfont{ % newname fontname
+findfont dup length dict copy definefont pop
+}bd
+
+L3? dup dup{save exch}if
+
+% languagelevel2 ONLY code goes here
+
+/Range 0 def
+/DataSource 0 def
+/val 0 def
+/nRange 0 def
+/mulRange 0 def
+/d0 0 def
+/r0 0 def
+/di 0 def
+/ri 0 def
+/a0 0 def
+/a1 0 def
+/r1 0 def
+/r2 0 def
+/dx 0 def
+/Nsteps 0 def
+/sh3tp 0 def
+/ymax 0 def
+/ymin 0 def
+/xmax 0 def
+/xmin 0 def
+
+/setupFunEval % funDict -- % this calculates and sets up a function dict for evaulation.
+{
+ begin
+ /nRange Range length 2 idiv store
+ /mulRange % precompute the range data needed to map a sample value from the table to a range value
+ % this data looks like [ range0mul range0min range1mul range1min ... rangeN-1mul rangeN-1min ]
+ [
+ 0 1 nRange 1 sub
+ { % index
+ 2 mul/nDim2 xd % 2*dimension# we are dealing with
+ Range nDim2 get % ymin
+ Range nDim2 1 add get % ymin ymax
+ 1 index sub % ymin (ymax-ymin)
+ % xmin = 0, xmax = 255 (2^bitspersample - 1)
+ 255 div % ymin (ymax-ymin)/(xmax - xmin)
+ exch % (ymax-ymin)/(xmax - xmin) ymin
+ }for
+ ]store
+ end
+}bd
+
+/FunEval % val1 fundict -> comp1 comp2 ... compN
+{
+ begin
+ % the value passed in is the base index into the table
+ nRange mul /val xd % compute the actual index to the table
+ % since there are nRange entries per base index
+ 0 1 nRange 1 sub
+ {
+ dup 2 mul/nDim2 xd % dim
+ val % base value to use to do our lookup
+ add DataSource exch get % lookedupval
+ mulRange nDim2 get mul % lookedupval*(ymax-ymin)/(xmax-xmin)
+ mulRange nDim2 1 add get % lookedupval*(ymax-ymin)/(xmax-xmin) ymin
+ add % interpolated result
+ }for % comp1 comp2 ... compN
+ end
+}bd
+
+/max % a b -> max(a, b)
+{
+ 2 copy lt
+ {exch pop}{pop}ifelse
+}bd
+
+/sh2
+{ % emulation of shading type 2. Assumes shading dictionary is top dictionary on the dict stack
+ /Coords load aload pop % x0 y0 x1 y1
+ 3 index 3 index translate % origin is now at beginning point of shading
+ % x0 y0 x1 y1
+ 3 -1 roll sub % x0 x1 y1-y0
+ 3 1 roll exch % y1-y0 x1 x0
+ sub % y1-y0 x1-x0
+ 2 copy
+ dup mul exch dup mul add sqrt % length of segment between two points
+ dup
+ scale
+ atan % atan (dy/dx)
+ %dup (rotation angle = )print ==
+ rotate % now line between 0,0 and 1,0 is the line perpendicular to which the axial lines are drawn
+
+ /Function load setupFunEval % may need to setup function dictionary by calling setupFunEval
+
+ % this is now specific to axial shadings. Compute the maximum bounds to fill
+ clippath {pathbbox}stopped {0 0 0 0}if newpath % x0 y0 x1 y1
+ /ymax xs
+ /xmax xs
+ /ymin xs
+ /xmin xs
+ currentdict/Extend known
+ {
+ /Extend load 0 get
+ {
+ 0/Function load FunEval sc % evaluate the function to get a color and set it
+ xmin ymin xmin abs ymax ymin sub rectfill
+ }if
+ }if
+ % paint the rects. The sampling frequency is that of our table
+ /Nsteps/Function load/Size get 0 get 1 sub store
+ /dx 1 Nsteps div store
+ gsave
+ /di ymax ymin sub store
+ /Function load
+ % loop Nsteps + 1 times, incrementing the index by 1 each time
+ 0 1 Nsteps
+ {
+ 1 index FunEval sc
+ 0 ymin dx di rectfill
+ dx 0 translate
+ }for
+ pop % pop our function
+ grestore % origin is back to start point
+ currentdict/Extend known
+ {
+ /Extend load 1 get
+ {
+ Nsteps/Function load FunEval sc % last element
+ 1 ymin xmax 1 sub abs ymax ymin sub rectfill
+ }if
+ }if
+}bd
+
+/shp % this paints our shape for shading type 3
+{ % x1 r1 x0 r0 -
+ 4 copy
+
+ % fill interior arc
+ dup 0 gt{
+ 0 exch a1 a0 arc
+ }{
+ pop 0 moveto
+ }ifelse
+
+ dup 0 gt{
+ 0 exch a0 a1 arcn
+ }{
+ pop 0 lineto
+ }ifelse
+
+ fill
+
+ % fill exterior arc
+ dup 0 gt{
+ 0 exch a0 a1 arc
+ }{
+ pop 0 moveto
+ }ifelse
+
+ dup 0 gt{
+ 0 exch a1 a0 arcn
+ }{
+ pop 0 lineto
+ }ifelse
+
+ fill
+}bd
+
+/calcmaxs
+{ % calculate maximum distance vector from origin to corner points
+ % of bbox
+ xmin dup mul ymin dup mul add sqrt % (xmin2 + ymin2)
+ xmax dup mul ymin dup mul add sqrt % (xmax2 + ymin2)
+ xmin dup mul ymax dup mul add sqrt % (xmin2 + ymax2)
+ xmax dup mul ymax dup mul add sqrt % (xmax2 + ymax2)
+ max max max % maximum value
+}bd
+
+/sh3
+{ % emulation of shading type 3. Assumes shading dictionary is top dictionary on the dict stack
+ /Coords load aload pop % x0 y0 r1 x1 y1 r2
+ 5 index 5 index translate % origin is now at first circle origin
+ 3 -1 roll 6 -1 roll sub % y0 r1 y1 r2 dx
+ 3 -1 roll 5 -1 roll sub % r1 r2 dx dy
+ 2 copy dup mul exch dup mul add sqrt
+ /dx xs % r1 r2 dx dy
+ 2 copy 0 ne exch 0 ne or
+ {
+ % r1 r2 dx dy
+ exch atan rotate % we are now rotated so dy is zero and positive values of dx move us as expected
+ }{
+ pop pop
+ }ifelse
+ % r1 r2
+ /r2 xs
+ /r1 xs
+ /Function load
+ dup/Size get 0 get 1 sub % this is the size of our table minus 1
+ /Nsteps xs % at some point we should optimize this better so NSteps is based on needed steps for the device
+ setupFunEval % may need to setup function dictionary by calling setupFunEval
+ % determine the case:
+ % case 0: circle1 inside circle2
+ % case 1: circle 2 inside circle 1
+ % case 2: r1 = r2
+ % case 3: r1 != r2
+ dx r2 add r1 lt{
+ % circle 2 inside of circle 1
+ 0
+ }{
+ dx r1 add r2 le
+ { % circle 1 inside of circle 2
+ 1
+ }{ % circles don't contain each other
+ r1 r2 eq
+ { % equal
+ 2
+ }{ % r1 != r2
+ 3
+ }ifelse
+ }ifelse
+ }ifelse
+ /sh3tp xs % sh3tp has the number of our different cases
+ clippath {pathbbox}stopped {0 0 0 0}if
+ newpath % x0 y0 x1 y1
+ /ymax xs
+ /xmax xs
+ /ymin xs
+ /xmin xs
+
+ % Arc angle atan( sqrt((dx*dx + dy*dy) - dr*dr), dr)
+ dx dup mul r2 r1 sub dup mul sub dup 0 gt
+ {
+ sqrt r2 r1 sub atan
+ /a0 exch 180 exch sub store
+ /a1 a0 neg store
+ }{
+ pop
+ /a0 0 store
+ /a1 360 store
+ }ifelse
+
+ currentdict/Extend known
+ {
+ /Extend load 0 get r1 0 gt and % no need to extend if the radius of the first end is 0
+ {
+ 0/Function load FunEval sc % evaluate the function to get a color and set it
+ % case 0: circle1 inside circle2
+ % case 1: circle 2 inside circle 1
+ % case 2: circles don't contain each other and r1 == r2
+ % case 3: circles don't contain each other and r1 != r2
+ {
+ { % case 0
+ dx 0 r1 360 0 arcn
+ xmin ymin moveto
+ xmax ymin lineto
+ xmax ymax lineto
+ xmin ymax lineto
+ xmin ymin lineto
+ eofill % for the bigger radius we fill everything except our circle
+ }
+ { % case 1
+ r1 0 gt{0 0 r1 0 360 arc fill}if
+ }
+ { % case 2
+ % r1 == r2, extend 0
+ % r3 = r, x3 = -(abs(minx) + r), x1 = 0
+
+ % x(i+1) r(i+1) x(i) r(i) shp
+ 0 r1 xmin abs r1 add neg r1 shp
+ }
+ { % case 3
+ % no containment, r1 != r2
+
+ r2 r1 gt{ % the endpoint we are drawing is that with a circle of zero radius
+ % x(i+1) r(i+1) x(i) r(i) shp
+ 0 r1
+ r1 neg r2 r1 sub div dx mul % this is point of beginning circle
+ 0 % point of ending circle
+ shp % takes x(i+1) r(i+1) x(i) r(i)
+ }{ % the first circle is the bigger of the two
+ % we find a circle on our line which is outside the bbox in the
+ % negative direction
+ % x(i+1) r(i+1) x(i) r(i) shp
+ 0 r1 calcmaxs % 0 r1 maxs
+ dup
+ % calculating xs: (-(maxs+r2)*x2)/(x2-(r1-r2))
+ r2 add dx mul dx r1 r2 sub sub div
+ neg % maxs xs'
+ exch 1 index % xs' maxs xs'
+ abs exch sub
+ shp
+ }ifelse
+ }
+ }sh3tp get exec % execute the extend at beginning proc for our shading type
+ }if
+ }if
+
+ % now do the shading
+ /d0 0 store
+ /r0 r1 store
+ /di dx Nsteps div store
+ /ri r2 r1 sub Nsteps div store
+ /Function load
+ 0 1 Nsteps
+ { % function t(i)
+ 1 index FunEval sc
+ d0 di add r0 ri add d0 r0 shp
+ {
+ % fill interior arc
+ d0 0 r0 a1 a0 arc
+ d0 di add 0 r0 ri add a0 a1 arcn
+ fill
+
+ % fill exterior arc
+ d0 0 r0 a0 a1 arc
+ d0 di add 0 r0 ri add a1 a0 arcn
+ fill
+ }pop
+
+ % advance to next
+ /d0 d0 di add store
+ /r0 r0 ri add store
+ }for
+ pop % pop our function dict
+
+ % handle Extend
+ currentdict/Extend known
+ {
+ /Extend load 1 get r2 0 gt and % no need to extend if the radius of the last end is 0
+ {
+ Nsteps/Function load FunEval sc % last element
+ % case 0: circle1 inside circle2
+ % case 1: circle 2 inside circle 1
+ % case 2: circles don't contain each other and r1 == r2
+ % case 3: circles don't contain each other and r1 != r2
+ {
+ {
+ dx 0 r2 0 360 arc fill
+ }
+ {
+ dx 0 r2 360 0 arcn
+ xmin ymin moveto
+ xmax ymin lineto
+ xmax ymax lineto
+ xmin ymax lineto
+ xmin ymin lineto
+ eofill % for the bigger radius we fill everything except our circle
+ }
+ { % r1 == r2, extend 1
+ % r3 = r, x3 = (abs(xmax) + r), x1 = dx
+ % x(i+1) r(i+1) x(i) r(i) shp
+ xmax abs r1 add r1 dx r1 shp
+ }
+ { % no containment, r1 != r2
+
+ r2 r1 gt{
+ % we find a circle on our line which is outside the bbox in the
+ % positive direction
+ % x(i+1) r(i+1) x(i) r(i) shp
+ calcmaxs dup % maxs maxs
+ % calculating xs: ((maxs+r1)*x2)/(x2-(r2-r1))
+ r1 add dx mul dx r2 r1 sub sub div % maxs xs
+ exch 1 index % xs maxs xs
+ exch sub
+ dx r2
+ shp
+ }{ % the endpoint we are drawing is that with a circle of zero radius
+ % x(i+1) r(i+1) x(i) r(i) shp
+ r1 neg r2 r1 sub div dx mul % this is point of ending circle
+ 0 % radius of ending circle
+ dx % point of starting circle
+ r2 % radius of starting circle
+ shp
+ }ifelse
+ }
+ }
+ sh3tp get exec % execute the extend at end proc for our shading type
+ }if
+ }if
+}bd
+/sh % emulation of shfill operator for type 2 and type 3 shadings based on type 0 functions
+{ % shadingDict --
+ begin
+ /ShadingType load dup dup 2 eq exch 3 eq or
+ { % shadingtype
+ gsave
+ newpath
+ /ColorSpace load scs
+ currentdict/BBox known
+ {
+ /BBox load aload pop % llx lly urx ury
+ 2 index sub % llx lly urx ury-lly
+ 3 index % llx lly urx ury-lly llx
+ 3 -1 roll exch sub
+ exch rectclip
+ }if
+ 2 eq
+ {sh2}{sh3}ifelse
+ grestore
+ }{
+ % shadingtype
+ pop
+ (DEBUG: shading type unimplemented\n)print flush
+ }ifelse
+ end
+}bd
+
+% end of language level 2 ONLY code
+
+{restore}if not dup{save exch}if
+% languagelevel3 ONLY code goes here
+ L3?{ % we do these loads conditionally or else they will fail on a level 2 printer
+ /sh/shfill ld
+ /csq/clipsave ld
+ /csQ/cliprestore ld
+ }if
+{restore}if
+
+%currentdict dup maxlength exch length sub (number of extra slots in md = )print == flush % *** how many entries are free
+end
+setpacking
+% count 0 ne { pstack(***extras on stack during prolog execution***\n)print flush}if % *** BARK if anything is left on stack
+%%EndFile
+%%EndProlog
+%%BeginSetup
+%%EndSetup
+%%Page: 1 1
+%%PageBoundingBox: 0 0 886 652
+%%BeginPageSetup
+cg_md begin
+bp
+sdmtx
+[ /CIEBasedABC 4 dict dup begin
+/WhitePoint [ 0.9505 1.0000 1.0891 ] def
+/DecodeABC [ { 1.8008 exp } bind { 1.8008 exp } bind { 1.8008 exp } bind ] def
+/MatrixABC [ 0.4295 0.2318 0.0204 0.3278 0.6722 0.1111 0.1933 0.0960 0.9578 ] def
+/RangeLMN [ 0.0 0.9505 0.0 1.0000 0.0 1.0891 ] def
+end ] /Cs1 exch/ColorSpace dr pop
+[ /CIEBasedABC 4 dict dup begin
+/WhitePoint [ 0.9505 1.0000 1.0891 ] def
+/DecodeABC [ { 1.8008 exp } bind { 1.8008 exp } bind { 1.8008 exp } bind ] def
+/MatrixABC [ 0.4295 0.2318 0.0204 0.3278 0.6722 0.1111 0.1933 0.0960 0.9578 ] def
+/RangeLMN [ 0.0 0.9505 0.0 1.0000 0.0 1.0891 ] def
+end ] /Cs2 exch/ColorSpace dr pop
+[ /CIEBasedABC 4 dict dup begin
+/WhitePoint [ 0.9505 1.0000 1.0891 ] def
+/DecodeABC [
+{ 1.0 0.0 3 -1 roll 1 index 1 index le { exch pop} { pop } ifelse
+ 1 index 1 index ge { exch pop } { pop } ifelse <
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diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaBasics.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaBasics.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,1 @@
+module AgdaBasics where
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaInterface.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaInterface.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,35 @@
+open import Level renaming (suc to succ ; zero to Zero )
+module AgdaInterface where
+
+data Maybe {n : Level } (a : Set n) : Set n where
+ Nothing : Maybe a
+ Just : a @$\rightarrow$@ Maybe a
+
+record StackMethods {n m : Level } (a : Set n ) {t : Set m }(stackImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ push : stackImpl @$\rightarrow$@ a @$\rightarrow$@ (stackImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ get : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ get2 : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ clear : stackImpl @$\rightarrow$@ (stackImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+open StackMethods
+
+record Stack {n m : Level } (a : Set n ) {t : Set m } (si : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ stack : si
+ stackMethods : StackMethods {n} {m} a {t} si
+ pushStack : a @$\rightarrow$@ (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
+ pushStack d next = push (stackMethods ) (stack ) d (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))
+ popStack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ popStack next = pop (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ pop2Stack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop2Stack next = pop2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ getStack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ getStack next = get (stackMethods ) (stack ) (\s1 d1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 )
+ get2Stack : (Stack a si @$\rightarrow$@ Maybe a @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ get2Stack next = get2 (stackMethods ) (stack ) (\s1 d1 d2 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods }) d1 d2)
+ clearStack : (Stack a si @$\rightarrow$@ t) @$\rightarrow$@ t
+ clearStack next = clear (stackMethods ) (stack ) (\s1 @$\rightarrow$@ next (record {stack = s1 ; stackMethods = stackMethods } ))
+
+open Stack
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaSingleLinkedStack.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaSingleLinkedStack.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,63 @@
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+push = pushSingleLinkedStack
+; pop = popSingleLinkedStack
+; pop2 = pop2SingleLinkedStack
+; get = getSingleLinkedStack
+; get2 = get2SingleLinkedStack
+; clear = clearSingleLinkedStack
+}
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+stack = emptySingleLinkedStack ;
+stackMethods = singleLinkedStackSpec
+}
+
+-- Implementation
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} @$\rightarrow$@ SingleLinkedStack Data @$\rightarrow$@ Data @$\rightarrow$@ (Code : SingleLinkedStack Data @$\rightarrow$@ t) @$\rightarrow$@ t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+
+popSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+popSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack1 (Just data1)
+ where
+ data1 = datum d
+ stack1 = record { top = (next d) }
+
+pop2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+pop2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = pop2SingleLinkedStack' {n} {m} stack cs
+ where
+ pop2SingleLinkedStack' : {n m : Level } {t : Set m } @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+ pop2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs (record {top = (next d1)}) (Just (datum d)) (Just (datum d1))
+
+
+getSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+getSingleLinkedStack stack cs with (top stack)
+... | Nothing = cs stack Nothing
+... | Just d = cs stack (Just data1)
+ where
+ data1 = datum d
+
+get2SingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+get2SingleLinkedStack {n} {m} {t} {a} stack cs with (top stack)
+... | Nothing = cs stack Nothing Nothing
+... | Just d = get2SingleLinkedStack' {n} {m} stack cs
+ where
+ get2SingleLinkedStack' : {n m : Level} {t : Set m } @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (Code : SingleLinkedStack a @$\rightarrow$@ (Maybe a) @$\rightarrow$@ (Maybe a) @$\rightarrow$@ t) @$\rightarrow$@ t
+ get2SingleLinkedStack' stack cs with (next d)
+ ... | Nothing = cs stack Nothing Nothing
+ ... | Just d1 = cs stack (Just (datum d)) (Just (datum d1))
+
+clearSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ SingleLinkedStack a @$\rightarrow$@ (SingleLinkedStack a @$\rightarrow$@ t) @$\rightarrow$@ t
+clearSingleLinkedStack stack next = next (record {top = Nothing})
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaStackImpl.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaStackImpl.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,28 @@
+record SingleLinkedStack {n : Level } (a : Set n) : Set n where
+ field
+ top : Maybe (Element a)
+open SingleLinkedStack
+
+pushSingleLinkedStack : {n m : Level } {t : Set m } {Data : Set n} @$\rightarrow$@ SingleLinkedStack Data @$\rightarrow$@ Data @$\rightarrow$@ (Code : SingleLinkedStack Data @$\rightarrow$@ t) @$\rightarrow$@ t
+pushSingleLinkedStack stack datum next = next stack1
+ where
+ element = cons datum (top stack)
+ stack1 = record {top = Just element}
+
+-- Basic stack implementations are specifications of a Stack
+
+singleLinkedStackSpec : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ StackMethods {n} {m} a {t} (SingleLinkedStack a)
+singleLinkedStackSpec = record {
+ push = pushSingleLinkedStack
+ ; pop = popSingleLinkedStack
+ ; pop2 = pop2SingleLinkedStack
+ ; get = getSingleLinkedStack
+ ; get2 = get2SingleLinkedStack
+ ; clear = clearSingleLinkedStack
+ }
+
+createSingleLinkedStack : {n m : Level } {t : Set m } {a : Set n} @$\rightarrow$@ Stack {n} {m} a {t} (SingleLinkedStack a)
+createSingleLinkedStack = record {
+ stack = emptySingleLinkedStack ;
+ stackMethods = singleLinkedStackSpec
+ }
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaStackSomeState.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaStackSomeState.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,6 @@
+stackInSomeState : {l m : Level } {D : Set l} {t : Set m } (s : SingleLinkedStack D ) @$\rightarrow$@ Stack {l} {m} D {t} ( SingleLinkedStack D )
+stackInSomeState s = record { stack = s ; stackMethods = singleLinkedStackSpec }
+
+push@$\rightarrow$@push@$\rightarrow$@pop2 : {l : Level } {D : Set l} (x y : D ) (s : SingleLinkedStack D ) @$\rightarrow$@ pushStack (stackInSomeState s) x (\s1 @$\rightarrow$@ pushStack s1 y (\s2 @$\rightarrow$@ pop2Stack s2 (\s3 y1 x1 @$\rightarrow$@
+ (Just x @$\equiv$@ x1) ∧ (Just y @$\equiv$@ y1))))
+push@$\rightarrow$@push@$\rightarrow$@pop2 {l} {D} x y s = record { pi1 = refl ; pi2 = refl }
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaStackTest.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaStackTest.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,22 @@
+-- after push 1 and 2, pop2 get 1 and 2
+
+testStack02 : {m : Level } @$\rightarrow$@ ( Stack @$\mathbb{N}$@ (SingleLinkedStack @$\mathbb{N}$@) @$\rightarrow$@ Bool {m} ) @$\rightarrow$@ Bool {m}
+testStack02 cs = pushStack createSingleLinkedStack 1 (\s @$\rightarrow$@ pushStack s 2 cs)
+
+
+testStack031 : (d1 d2 : $\mathbb{N}$ ) @$\rightarrow$@ Bool {Zero}
+testStack031 2 1 = True
+testStack031 _ _ = False
+
+testStack032 : (d1 d2 : Maybe @$\mathbb{N}$@) @$\rightarrow$@ Bool {Zero}
+testStack032 (Just d1) (Just d2) = testStack031 d1 d2
+testStack032 _ _ = False
+
+testStack03 : {m : Level } @$\rightarrow$@ Stack @$\mathbb{N}$@ (SingleLinkedStack @$\mathbb{N}$@) @$\rightarrow$@ ((Maybe @$\mathbb{N}$@) @$\rightarrow$@ (Maybe @$\mathbb{N}$@) @$\rightarrow$@ Bool {m} ) @$\rightarrow$@ Bool {m}
+testStack03 s cs = pop2Stack s (\s d1 d2 @$\rightarrow$@ cs d1 d2 )
+
+testStack04 : Bool
+testStack04 = testStack02 (\s @$\rightarrow$@ testStack03 s testStack032)
+
+testStack05 : testStack04 @$\equiv$@ True
+testStack05 = refl
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaTree.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaTree.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,17 @@
+record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ putImpl : treeImpl @$\rightarrow$@ a @$\rightarrow$@ (treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ getImpl : treeImpl @$\rightarrow$@ (treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+open TreeMethods
+
+record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ tree : treeImpl
+ treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
+ putTree : a @$\rightarrow$@ (Tree treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ putTree d next = putImpl (treeMethods ) tree d (\t1 @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ))
+ getTree : (Tree treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ getTree next = getImpl (treeMethods ) tree (\t1 d @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ) d )
+
+open Tree
+
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaTreeDebug.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaTreeDebug.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,15 @@
+test31 = putTree1 {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} (createEmptyRedBlackTree@$\mathbb{N}$@ @$\mathbb{N}$@ ) 1 1
+ $ \t @$\rightarrow$@ putTree1 t 2 2
+ $ \t @$\rightarrow$@ putTree1 t 3 3
+ $ \t @$\rightarrow$@ putTree1 t 4 4
+ $ \t @$\rightarrow$@ getRedBlackTree t 4
+ $ \t x @$\rightarrow$@ x
+
+-- Just
+-- (record
+-- { key = 4
+-- ; value = 4
+-- ; right = Nothing
+-- ; left = Nothing
+-- ; color = Red
+-- })
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaTreeImpl.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaTreeImpl.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,47 @@
+record TreeMethods {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ putImpl : treeImpl @$\rightarrow$@ a @$\rightarrow$@ (treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ getImpl : treeImpl @$\rightarrow$@ (treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+open TreeMethods
+
+record Tree {n m : Level } {a : Set n } {t : Set m } (treeImpl : Set n ) : Set (m Level.@$\sqcup$@ n) where
+ field
+ tree : treeImpl
+ treeMethods : TreeMethods {n} {m} {a} {t} treeImpl
+ putTree : a @$\rightarrow$@ (Tree treeImpl @$\rightarrow$@ t) @$\rightarrow$@ t
+ putTree d next = putImpl (treeMethods ) tree d (\t1 @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ))
+ getTree : (Tree treeImpl @$\rightarrow$@ Maybe a @$\rightarrow$@ t) @$\rightarrow$@ t
+ getTree next = getImpl (treeMethods ) tree (\t1 d @$\rightarrow$@ next (record {tree = t1 ; treeMethods = treeMethods} ) d )
+open Tree
+
+record Node {n : Level } (a k : Set n) : Set n where
+ inductive
+ field
+ key : k
+ value : a
+ right : Maybe (Node a k)
+ left : Maybe (Node a k)
+ color : Color {n}
+open Node
+
+leafNode : {n : Level } {a k : Set n} @$\rightarrow$@ k @$\rightarrow$@ a @$\rightarrow$@ Node a k
+leafNode k1 value = record {
+ key = k1 ;
+ value = value ;
+ right = Nothing ;
+ left = Nothing ;
+ color = Red
+ }
+record RedBlackTree {n m : Level } {t : Set m} (a k : Set n) : Set (m Level.@$\sqcup$@ n) where
+ field
+ root : Maybe (Node a k)
+ nodeStack : SingleLinkedStack (Node a k)
+ compare : k @$\rightarrow$@ k @$\rightarrow$@ CompareResult {n}
+open RedBlackTree
+
+putRedBlackTree : {n m : Level } {a k : Set n} {t : Set m} @$\rightarrow$@ RedBlackTree {n} {m} {t} a k @$\rightarrow$@ k @$\rightarrow$@ a @$\rightarrow$@ (RedBlackTree {n} {m} {t} a k @$\rightarrow$@ t) @$\rightarrow$@ t
+putRedBlackTree {n} {m} {a} {k} {t} tree k1 value next with (root tree)
+... | Nothing = next (record tree {root = Just (leafNode k1 value) })
+... | Just n2 = clearSingleLinkedStack (nodeStack tree) (\ s @$\rightarrow$@ findNode tree s (leafNode k1 value) n2 (\ tree1 s n1 @$\rightarrow$@ insertNode tree1 s n1 next))
+
+-- 以下省略
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/AgdaTreeProof.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/AgdaTreeProof.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,34 @@
+redBlackInSomeState : { m : Level } (a : Set Level.zero) (n : Maybe (Node a @$\mathbb{N}$@)) {t : Set m} @$\rightarrow$@ RedBlackTree {Level.zero} {m} {t} a @$\mathbb{N}$@
+redBlackInSomeState {m} a n {t} = record { root = n ; nodeStack = emptySingleLinkedStack ; compare = compare2 }
+
+putTest1 :{ m : Level } (n : Maybe (Node @$\mathbb{N}$@ @$\mathbb{N}$@))
+ @$\rightarrow$@ (k : @$\mathbb{N}$@) (x : @$\mathbb{N}$@)
+ @$\rightarrow$@ putTree1 {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} (redBlackInSomeState {_} @$\mathbb{N}$@ n {Set Level.zero}) k x
+ (\ t @$\rightarrow$@ getRedBlackTree t k (\ t x1 @$\rightarrow$@ check2 x1 x @$\equiv$@ True))
+putTest1 n k x with n
+... | Just n1 = lemma2 ( record { top = Nothing } )
+ where
+ lemma2 : (s : SingleLinkedStack (Node @$\mathbb{N}$@ @$\mathbb{N}$@) ) @$\rightarrow$@ putTree1 (record { root = Just n1 ; nodeStack = s ; compare = compare2 }) k x (λ t →
+ GetRedBlackTree.checkNode t k (λ t@$\text{1}$@ x1 → check2 x1 x @$\equiv$@ True) (root t))
+ lemma2 s with compare2 k (key n1)
+ ... | EQ = lemma3 {!!}
+ where
+ lemma3 : compare2 k (key n1) @$\equiv$@ EQ @$\rightarrow$@ getRedBlackTree {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} {Set Level.zero} ( record { root = Just ( record {
+ key = key n1 ; value = x ; right = right n1 ; left = left n1 ; color = Black
+ } ) ; nodeStack = s ; compare = λ x@$\text{1}$@ y → compare2 x@$\text{1}$@ y } ) k ( \ t x1 @$\rightarrow$@ check2 x1 x @$\equiv$@ True)
+ lemma3 eq with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl with compare2 k (key n1) | eq
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
+ ... | GT = {!!}
+ ... | LT = {!!}
+
+... | Nothing = lemma1
+ where
+ lemma1 : getRedBlackTree {_} {_} {@$\mathbb{N}$@} {@$\mathbb{N}$@} {Set Level.zero} ( record { root = Just ( record {
+ key = k ; value = x ; right = Nothing ; left = Nothing ; color = Red
+ } ) ; nodeStack = record { top = Nothing } ; compare = λ x@$\text{1}$@ y → compare2 x@$\text{1}$@ y } ) k
+ ( \ t x1 @$\rightarrow$@ check2 x1 x @$\equiv$@ True)
+ lemma1 with compare2 k k | putTest1Lemma2 k
+ ... | EQ | refl with compare2 x x | putTest1Lemma2 x
+ ... | EQ | refl = refl
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/CodeSegment.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/CodeSegment.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,2 @@
+data CodeSegment {l1 l2 : Level} (I : Set l1) (O : Set l2) : Set (l @$\sqcup$@ l1 @$\sqcup$@ l2) where
+ cs : (I @$\rightarrow$@ O) @$\rightarrow$@ CodeSegment I O
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/DataSegment.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/DataSegment.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,8 @@
+record ds0 : Set where
+ field
+ a : Int
+ b : Int
+
+record ds1 : Set where
+ field
+ c : Int
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/Goto.agda.replaced
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/Goto.agda.replaced Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,4 @@
+goto : {l1 l2 : Level} {I : Set l1} {O : Set l2}
+ @$\rightarrow$@ CodeSegment I O @$\rightarrow$@ I @$\rightarrow$@ O
+goto (cs b) i = b i
+
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/MetaGear.graffle
Binary file Paper/pic/MetaGear.graffle has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/MetaGear.pdf
Binary file Paper/pic/MetaGear.pdf has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/MetaGear.xbb
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/MetaGear.xbb Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,8 @@
+%%Title: ./MetaGear.pdf
+%%Creator: extractbb 20180217
+%%BoundingBox: 0 0 792 532
+%%HiResBoundingBox: 0.000000 0.000000 792.000000 532.000000
+%%PDFVersion: 1.3
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+
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/cbc-hoare.pdf
Binary file Paper/pic/cbc-hoare.pdf has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/cbc-hoare.xbb
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/cbc-hoare.xbb Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,8 @@
+%%Title: ./cbc-hoare.pdf
+%%Creator: extractbb 20180217
+%%BoundingBox: 0 0 580 175
+%%HiResBoundingBox: 0.000000 0.000000 580.000000 175.000000
+%%PDFVersion: 1.3
+%%Pages: 1
+%%CreationDate: Wed Dec 12 18:19:49 2018
+
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/cbc-subtype.pdf
Binary file Paper/pic/cbc-subtype.pdf has changed
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/cbc-subtype.xbb
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Paper/pic/cbc-subtype.xbb Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,8 @@
+%%Title: ./cbc-subtype.pdf
+%%Creator: extractbb 20180217
+%%BoundingBox: 0 0 1084 281
+%%HiResBoundingBox: 0.000000 0.000000 1084.000000 281.000000
+%%PDFVersion: 1.3
+%%Pages: 1
+%%CreationDate: Wed Dec 12 18:19:49 2018
+
diff -r 6e03fff298c5 -r df1552e4ac7a Paper/pic/cbc_goto.graffle
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
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@@ -0,0 +1,1037 @@
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+
+
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diff -r 6e03fff298c5 -r df1552e4ac7a Paper/tecrep.tex
--- a/Paper/tecrep.tex Tue Nov 13 22:53:20 2018 +0900
+++ b/Paper/tecrep.tex Wed Dec 12 18:44:19 2018 +0900
@@ -1,7 +1,9 @@
%% v3.1 [2018/04/18]
%\documentclass[Proof,technicalreport]{ieicej}
\documentclass[technicalreport]{ieicej}
-%\usepackage{graphicx}
+
+\usepackage[dvipdfmx]{graphicx}
+\usepackage{graphicx}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{textcomp}
@@ -9,6 +11,35 @@
%\usepackage[fleqn]{amsmath}
%\usepackage{amssymb}
+\usepackage{listings}
+\lstset{
+ frame=single,
+ keepspaces=true,
+ stringstyle={\ttfamily},
+ commentstyle={\ttfamily},
+ identifierstyle={\ttfamily},
+ keywordstyle={\ttfamily},
+ basicstyle={\ttfamily},
+ breaklines=true,
+ xleftmargin=0zw,
+ xrightmargin=0zw,
+ framerule=.2pt,
+ columns=[l]{fullflexible},
+ numbers=left,
+ stepnumber=1,
+ numberstyle={\scriptsize},
+ numbersep=1em,
+ language={},
+ tabsize=4,
+ lineskip=-0.5zw,
+ inputencoding=utf8,
+ extendedchars=true,
+ escapechar={@}
+}
+\renewcommand{\lstlistingname}{Code}
+\usepackage{caption}
+\captionsetup[lstlisting]{font={small,tt}}
+
\def\IEICEJcls{\texttt{ieicej.cls}}
\def\IEICEJver{3.1}
\newcommand{\AmSLaTeX}{%
@@ -24,11 +55,11 @@
%% and Communication Engineers}
%% \esubtitle{Guide to the Technical Report and Template}
\authorlist{
- \authorentry[@cr.ie.u-ryukyu.ac.jp]{外間 政尊}{Masataka Hokama}{1}%
- \authorentry[@cr.ie.u-ryukyu.ac.jp]{河野 真治}{Shinji Kono}{2}%
+ \authorentry[masataka@cr.ie.u-ryukyu.ac.jp]{外間 政尊}{Masataka Hokama}{1}%
+ \authorentry[kono@cr.ie.u-ryukyu.ac.jp]{河野 真治}{Shinji Kono}{2}%
}
\affiliate[1]{琉球大学大学院理工学研究科情報工学専攻}
- {Interdisciplinary Information Engineering, Graduate Sc k533 hool of Engineering and Science, University of the Ryukyus.}
+ {Interdisciplinary Information Engineering, Graduate School of Engineering and Science, University of the Ryukyus.}
\affiliate[2]{琉球大学工学部情報工学科}
{Information Engineering, University of the Ryukyus.}
%\MailAddress{$\dagger$hanako@denshi.ac.jp,
@@ -39,7 +70,7 @@
\end{jabstract}
\begin{jkeyword}
プログラミング言語,
- 検証
+ CbC, Gears OS, Agda
%% あと他…？
\end{jkeyword}
%% \begin{eabstract}
@@ -73,10 +104,88 @@
した証明を導入し、今まで行っていた証明との比較を
行う。
\section{GearsOS}
-GearsOSについて
+Gears OS は信頼性をノーマルレベルの計算に対して保証し、拡張性をメタレベルの計算で実現することを目標に開発している OSである。
+
+Gears OS は処理の単位を Code Gear、データの単位を Data Gear と呼ばれる単位でプログラムを構成する。
+信頼性や拡張性はメタ計算として、通常の計算とは区別して記述する。
+
\section{CodeGearとDataGear}
-CodeGearとDataGearについて
+
+Gears OS ではプログラムとデータの単位として CodeGear、 DataGear を用いる。 Gear
+ は並列実行の単位、データ分割、 Gear 間の接続等になる。
+CodeGear はプログラムの処理そのもので、図\ref{fig:cgdg}で示しているように任意の数の
+Input DataGear を参照し、処理が完了すると任意の数の Output DataGear に書き込む。
+
+CodeGear 間の移動は継続を用いて行われる。継続は関数呼び出しとは異なり、呼び出し
+た後に元のコードに戻らず、次の CodeGear へ継続を行う。これは、関数型プログラミングでは末尾関数呼び出しを行うことに相当する。
+
+Gear では処理やデータ構造が CodeGear、 DataGear に閉じている。したがって、
+DataGear は Agda のデータ構造(data と record)で表現できる。
+CodeGear は Agda の CPS (Continuation Passing Style) で関数として表現することができる。
+
+\begin{figure}[htpb]
+ \begin{center}
+ \scalebox{0.3}{\includegraphics{pic/codeGear_dataGear.pdf}}
+ \end{center}
+ \caption{CodeGear と DataGear の関係}
+ \label{fig:cgdg}
+\end{figure}
+
+また Gears OS 自体もこの Code Gear、Data Gear を用いた CbC(Continuation based C) で実装される。
+そのため、Gears OS の実装は Code Gear、Data Gear を用いたプログラミングスタイルの指標となる。
+
+CodeGear は Agda では継続渡しで書かれた関数と等価である。
+継続は不定の型 (\verb+t+) を返す関数で表される。
+CodeGear 自体も同じ型 \verb+t+ を返す関数となる。
+例えば、 Stack への push を行う関数 pushStack は以下のような型を持つ。
+
+\begin{lstlisting}[caption=pushStack の型,label=push-stack]
+ pushStack : a -> (Stack a si -> t) -> t
+\end{lstlisting}
+
+\verb+pushStack+ が関数名で、コロンの後ろに型を記述する。
+最初の引数は Stack に格納される型\verb+a+ を持つ。
+二つ目の引数は継続であり、\verb+Stack a si+ (\verb+si+という実装を持つ\verb+a+を格納するStack)を受け取り不定の型\verb+t+を返す関数である。
+この CodeGear 自体は不定の型\verb+t+を返す。
+
+GearsOS で CodeGear の性質を証明するには、 Agda で記述された CodeGear と
+DataGear に対してメタ計算として証明を行う。証明すべき性質は、不定の型を持つ継続
+\verb+t+ に記述することができる。例えば、 Stack にある値\verb+x+をpushして、pop
+すると \verb+ x'+ が取れてくる。\verb+Just x+ と\verb+Just x'+ は等しい必要があ
+る。これは Agda では \verb+(Just x ≡ x' )+ と記述される。
+ここで Just とは Agda の以下のデータ構造である。
+
+% \begin{verbatim}
+\begin{lstlisting}[caption=data型の例:Maybe,label=maybe]
+data Maybe {n : Level } (a : Set n) : Set n where
+ Nothing : Maybe a
+ Just : a -> Maybe a
+\end{lstlisting}
+% \end{verbatim}
+
+これは DataGear に相当し、\verb+Nothing+ と \verb+Just+ の二つの状態を保つ。
+pop した時に、 Stack が空であれば\verb+Nothing+ を返し、そうでなければ\verb+Just+ のついた返り値を返す。
+
+この性質を Agda で表すと、以下のような型になる。
+Agda では証明すべき論理式は型で表される。
+継続部分に直接証明すべき性質を型として記述できる。
+Agda ではこの型に対応する$\lambda$項を与えると証明が完了したことになる。
+
+\begin{lstlisting}[caption=pushとpop,label=push-pop]
+push->pop : {l : Level} {D : Set l} (x : D )
+ (s : SingleLinkedStack D) ->
+ pushStack (stackInSomeState s)
+ x (\s -> popStack s
+ ( \s3 x1 -> (Just x ≡ x1)))
+\end{lstlisting}
+
+このように、CodeGear を Agda で記述し、継続部分に証明すべき性質を Agda で記述する。
+
+GearsOS での記述は interface によってモジュール化される。
+よって、このモジュール化もAgda により記述する必要がある。
+CbC で記述された任意の CodeGear と Meta CodeGear が Agda にそのまま変換されるわけではないが、変換可能なように記述されると仮定する。
+
\section{AgdaとGearsOS}
Agda と GearsOS
diff -r 6e03fff298c5 -r df1552e4ac7a ryokka-sigss.mm
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ryokka-sigss.mm Wed Dec 12 18:44:19 2018 +0900
@@ -0,0 +1,50 @@
+