25272527
25282528 <subsection|Buffers>
25292529
2530- A buffer is defined as a bounded list. \ We recursively define a buffer
2531- up to (but excluding) <math|2<rsup|n>> as
2530+ A buffer is defined as a bounded list. \ We recursively define a buffer up
2531+ to (but excluding) <math|2<rsup|n>> as
25322532
25332533 <\eqnarray*>
25342534 <tformat|<table|<row|<cell|A<rsup|\<less\>2>>|<cell|\<assign\>>|<cell|<maybe>A>>|<row|<cell|A<rsup|\<less\>4>>|<cell|\<assign\>>|<cell|<maybe><around*|(|A<rsup|2>|)>\<times\>A<rsup|\<less\>2>>>|<row|<cell|>|<cell|\<vdots\>>|<cell|>>|<row|<cell|A<rsup|\<less\>2<rsup|1+n>>>|<cell|\<assign\>>|<cell|<maybe><around*|(|A<rsup|2<rsup|n>>|)>\<times\>A<rsup|\<less\>2<rsup|n>>>>|<row|<cell|>|<cell|\<vdots\>>|<cell|>>>>
35583558 The SHA-256 hash function is composed from two components, a padding
35593559 function <math|SHA256<rsub|Pad>\<of\><2><rsup|\<ast\>>\<rightarrow\><around*|(|<2><rsup|512>|)><rsup|+>>,
35603560 which appends padding and length data to produce a (non-empty) sequence of
3561- blocks of 512 bits, and the Merkle\UDamgård construction
3561+ blocks of 512 bits, and the Merkle\UDamg�rd construction
35623562 <math|SHA256<rsub|MD>\<of\><2><rsup|256>\<times\><around*|(|<2><rsup|512>|)><rsup|\<ast\>>\<rightarrow\><2><rsup|256>>.
35633563
35643564 <\equation*>
73967396 <subsection|Full Simplicity>
73977397
73987398 The <verbatim|FullSimplicity> algebra, found in the
7399- <verbatim|PrimitiveModule> in <verbatim|Simplicity/Primitive.v>, is the meet
7400- of the <verbatim|Jet> and the <verbatim|Witness> algebras (equiv. the meet
7401- of the <verbatim|Jet> and <verbatim|AssertionWitness> algebras) with no
7402- additional combinators. It defines the full Simplicity language. The
7399+ <verbatim|PrimitiveModule> in <verbatim|Simplicity/Primitive.v>, is the
7400+ meet of the <verbatim|Jet> and the <verbatim|Witness> algebras (equiv. the
7401+ meet of the <verbatim|Jet> and <verbatim|AssertionWitness> algebras) with
7402+ no additional combinators. It defines the full Simplicity language. The
74037403 <verbatim|SimplicityPrimSem> canonical structure provides the functional
74047404 semantics of the full Simplicity language as the <verbatim|primSem M> type
74057405 family when <verbatim|M> is a monad zero.
95009500
95019501 <math|<text|<samp|right-extend>><rsub|2<rsup|n>,2<rsup|m>>
95029502 :<2><rsup|2<rsup|n>>\<vdash\><2><rsup|2<rsup|m>>> for
9503- <math|1\<leq\>n\<less\>m>\
9504-
9505- \;
9503+ <math|1\<leq\>n\<less\>m>\
95069504
95079505 Properties:
95089506
96149612
96159613 (CAUTION: Not defined when <math|n=0> or <math|m=0>.)
96169614
9617- (Note: Support only recommended up to <math|2<rsup|n>\<cdot\>2<rsup|m>\<leq\>256>.)
9615+ (Note: Support only recommended up to
9616+ <math|2<rsup|n>\<cdot\>2<rsup|m>\<leq\>256>.)
96189617
96199618 <\math>
96209619 <rep|<text|<samp|'transpose'>><rsub|2<rsup|n>,2<rsup|m>>|>\<assign\><verbatim|<around*|[|110|]>><rsub|<2>>\<cdummy\><rep|<value|subsection-nr>|>\<cdummy\><rep|<value|subsubsection-nr>|>\<cdummy\><rep|n|>\<cdummy\><rep|m|>
1042810427
1042910428 <paragraph|<samp|sha3-absorb>>
1043010429
10431- (Note: we should probably byte-stwap the input before xoring it into place
10430+ (Note: we should probably byte-stwap the input before xoring it into
10431+ place
1043210432
1043310433 <\math>
1043410434 <rep|<text|<samp|'sha3-absorb'>><rsub|n,m>|>\<assign\><verbatim|<around*|[|110|]>><rsub|<2>>\<cdummy\><rep|<value|subsection-nr>|>\<cdummy\><rep|<value|subsubsection-nr>|>\<cdummy\><rep|<value|paragraph-nr>|>\<cdummy\><rep|n|>\<cdummy\><rep|m|>
1617416174 <no-break><pageref|auto-506><vspace|0.5fn>
1617516175 </associate>
1617616176 </collection>
16177- </auxiliary>
16177+ </auxiliary>
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