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Simplicity-TR.tm
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<TeXmacs|2.1>
<style|<tuple|book|old-spacing|old-dots|old-lengths>>
<\body>
<\doc-data|<\doc-title>
Simplicity
</doc-title>|<doc-author|<author-data|<author-name|Russell
O'Connor>|<\author-affiliation>
Blockstream
</author-affiliation>|<author-email|[email protected]>>>|<doc-misc|DRAFT>|<doc-date|<date>>>
\;
</doc-data>
<\table-of-contents|toc>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|1<space|2spc>Introduction>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-1><vspace|0.5fn>
1.1<space|2spc>Bitcoin Script <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-2>
1.2<space|2spc>Simplicity's Design Goals
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-3>
<with|par-left|1tab|1.2.1<space|2spc>Static Analysis
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-4>>
<with|par-left|1tab|1.2.2<space|2spc>Pruning and Sharing
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-5>>
<with|par-left|1tab|1.2.3<space|2spc>Formal Semantics
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-6>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|2<space|2spc>Type
Theory Preliminaries> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-7><vspace|0.5fn>
2.1<space|2spc>Algebraic Types <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-8>
<with|par-left|1tab|2.1.1<space|2spc>Records
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-9>>
2.2<space|2spc>Functors <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-10>
<with|par-left|1tab|2.2.1<space|2spc>Option Functor
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-11>>
<with|par-left|1tab|2.2.2<space|2spc>List Functors
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-12>>
<with|par-left|1tab|2.2.3<space|2spc>Buffers
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-13>>
2.3<space|2spc>Monads <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-14>
<with|par-left|1tab|2.3.1<space|2spc>Kleisli Morphisms
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-15>>
<with|par-left|1tab|2.3.2<space|2spc>Cartesian Strength
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-16>>
<with|par-left|1tab|2.3.3<space|2spc>Identity Monad
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-17>>
<with|par-left|1tab|2.3.4<space|2spc>Monad Zero
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-18>>
<with|par-left|2tab|2.3.4.1<space|2spc>Option Monad
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-19>>
2.4<space|2spc>Multi-bit Words <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-20>
<with|par-left|1tab|2.4.1<space|2spc>Byte Strings
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-21>>
<with|par-left|1tab|2.4.2<space|2spc>Bit Strings
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-22>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|3<space|2spc>Core
Simplicity> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-23><vspace|0.5fn>
3.1<space|2spc>Types <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-24>
<with|par-left|1tab|3.1.1<space|2spc>Abstract Syntax
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-25>>
<with|par-left|1tab|3.1.2<space|2spc>Formal Syntax
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-26>>
<with|par-left|1tab|3.1.3<space|2spc>Formal Semantics
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-27>>
3.2<space|2spc>Terms <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-28>
<with|par-left|1tab|3.2.1<space|2spc>Identity
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-29>>
<with|par-left|1tab|3.2.2<space|2spc>Composition
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-30>>
<with|par-left|1tab|3.2.3<space|2spc>Constant Unit
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-31>>
<with|par-left|1tab|3.2.4<space|2spc>Left Injection
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-32>>
<with|par-left|1tab|3.2.5<space|2spc>Right Injection
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-33>>
<with|par-left|1tab|3.2.6<space|2spc>Case
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-34>>
<with|par-left|1tab|3.2.7<space|2spc>Pair
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-35>>
<with|par-left|1tab|3.2.8<space|2spc>Take
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-36>>
<with|par-left|1tab|3.2.9<space|2spc>Drop
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-37>>
<with|par-left|1tab|3.2.10<space|2spc>Formal Syntax
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-38>>
<with|par-left|1tab|3.2.11<space|2spc>Formal Semantics
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-39>>
3.3<space|2spc>Example Simplicity <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-40>
<with|par-left|1tab|3.3.1<space|2spc>Bit Operations
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-41>>
<with|par-left|1tab|3.3.2<space|2spc>Simplicity Notation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-42>>
<with|par-left|1tab|3.3.3<space|2spc>Generic Equality
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-43>>
<with|par-left|1tab|3.3.4<space|2spc>Arithmetic
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-44>>
<with|par-left|1tab|3.3.5<space|2spc>Bitwise Operations
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-45>>
<with|par-left|1tab|3.3.6<space|2spc>SHA-256
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-46>>
<with|par-left|2tab|3.3.6.1<space|2spc>Tagged Hashes
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-47>>
<with|par-left|1tab|3.3.7<space|2spc>Elliptic Curve Operations on
secp256k1 <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-48>>
<with|par-left|2tab|3.3.7.1<space|2spc>libsecp256k1
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-49>>
<with|par-left|2tab|3.3.7.2<space|2spc>libsecp256k1 in Simplicity
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-50>>
<with|par-left|2tab|3.3.7.3<space|2spc>Schnorr Signature Validation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-51>>
3.4<space|2spc>Completeness Theorem <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-52>
3.5<space|2spc>Operational Semantics <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-53>
<with|par-left|1tab|3.5.1<space|2spc>Representing Values as Cell Arrays
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-54>>
<with|par-left|1tab|3.5.2<space|2spc>Bit Machine
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-55>>
<with|par-left|2tab|3.5.2.1<space|2spc>Frame Instructions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-57>>
<with|par-left|2tab|3.5.2.2<space|2spc>Active Write Frame Instructions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-58>>
<with|par-left|2tab|3.5.2.3<space|2spc>Active Read Frame Instructions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-59>>
<with|par-left|2tab|3.5.2.4<space|2spc>Abort Instruction
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-60>>
<with|par-left|2tab|3.5.2.5<space|2spc>Bit Machine Programs
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-61>>
<with|par-left|2tab|3.5.2.6<space|2spc>Crashing the Bit Machine
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-62>>
<with|par-left|1tab|3.5.3<space|2spc>Executing Simplicity
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-63>>
<with|par-left|2tab|3.5.3.1<space|2spc>Tail Composition Optimisation
(TCO) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-64>>
3.6<space|2spc>Static Analysis <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-65>
<with|par-left|1tab|3.6.1<space|2spc>Space Resources
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-66>>
<with|par-left|2tab|3.6.1.1<space|2spc>Maximum Cell Count Bound
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-67>>
<with|par-left|2tab|3.6.1.2<space|2spc>Maximum Frame Count Bound
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-68>>
<with|par-left|1tab|3.6.2<space|2spc>Time Resources
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-69>>
3.7<space|2spc>Commitment Merkle Root
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-70>
3.8<space|2spc>Type Merkle Root <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-71>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|4<space|2spc>Simplicity
Extensions> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-72><vspace|0.5fn>
4.1<space|2spc>Monadic Semantics <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-73>
4.2<space|2spc>Witness <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-74>
<with|par-left|1tab|4.2.1<space|2spc>Elided Computation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-75>>
<with|par-left|1tab|4.2.2<space|2spc>Type Inference with Witness
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-76>>
4.3<space|2spc>Assertions and Failure
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-77>
<with|par-left|1tab|4.3.1<space|2spc>Denotational Semantics
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-78>>
<with|par-left|1tab|4.3.2<space|2spc>Merkle Roots
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-79>>
<with|par-left|2tab|4.3.2.1<space|2spc>Pruning Unused
<with|font-family|ss|case> Branches <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-80>>
<with|par-left|2tab|4.3.2.2<space|2spc>Salted Expressions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-81>>
4.4<space|2spc>Blockchain Primitives <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-82>
<with|par-left|1tab|4.4.1<space|2spc>Bitcoin Transactions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-83>>
<with|par-left|2tab|4.4.1.1<space|2spc>Denotational Semantics
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-84>>
<with|par-left|2tab|4.4.1.2<space|2spc>Merkle Roots
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-85>>
4.5<space|2spc>Simplicity Programs <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-86>
<with|par-left|1tab|4.5.1<space|2spc>Example:
<rigid|<with|mode|text|<with|font-family|ss|font-shape|right|checkSigHashAll>>>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-87>>
4.6<space|2spc>Schnorr Signature Aggregation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-88>
4.7<space|2spc>Malleability <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-89>
<with|par-left|1tab|4.7.1<space|2spc>Transaction Weight
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-90>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|5<space|2spc>Jets>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-91><vspace|0.5fn>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|6<space|2spc>Delegation>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-92><vspace|0.5fn>
6.1<space|2spc>Implementing <with|font-family|ss|disconnect> on the Bit
Machine <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-93>
<with|par-left|1tab|6.1.1<space|2spc>Static Analysis of
<with|font-family|ss|disconnect> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-94>>
<with|par-left|2tab|6.1.1.1<space|2spc>Space Resources
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-95>>
6.2<space|2spc>Unbounded Loops <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-96>
<with|par-left|1tab|6.2.1<space|2spc>Adding a <with|font-family|ss|loop>
primitive to Simplicity? <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-97>>
6.3<space|2spc>Universal Signature Hash Modes
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-98>
<with|par-left|1tab|6.3.1<space|2spc>Side-Effects and Delegation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-99>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|7<space|2spc>Type
Inference and Serialization> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-100><vspace|0.5fn>
7.1<space|2spc>Explicit Simplicity DAGs
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-101>
<with|par-left|1tab|7.1.1<space|2spc>Type Inference
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-102>>
<with|par-left|1tab|7.1.2<space|2spc>Reconstructing Simplicity
Expressions <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-103>>
<with|par-left|2tab|7.1.2.1<space|2spc>syncase
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-104>>
<with|par-left|2tab|7.1.2.2<space|2spc>inflate
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-105>>
7.2<space|2spc>Serialization <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-106>
<with|par-left|1tab|7.2.1<space|2spc>Serialization of Bit Strings and
Positive Numbers <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-107>>
<with|par-left|1tab|7.2.2<space|2spc>Serialization of Simplicity
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-108>>
<with|par-left|2tab|7.2.2.1<space|2spc>Serialization of Word Jets
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-109>>
<with|par-left|1tab|7.2.3<space|2spc>Identity Merkle Root
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-110>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|8<space|2spc>Coq
Library Guide> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-111><vspace|0.5fn>
8.1<space|2spc>Simplicity Types <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-112>
8.2<space|2spc>Simplicity Terms <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-113>
<with|par-left|1tab|8.2.1<space|2spc>The \PInitial\Q Representation of
Terms <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-114>>
<with|par-left|1tab|8.2.2<space|2spc>The \PFinal\Q Representation of
Terms <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-115>>
<with|par-left|2tab|8.2.2.1<space|2spc>Simplicity Algebras
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-116>>
<with|par-left|2tab|8.2.2.2<space|2spc>The \PFinal\Q Representation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-117>>
<with|par-left|2tab|8.2.2.3<space|2spc>Constructing \PFinal\Q Terms
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-118>>
<with|par-left|1tab|8.2.3<space|2spc>Why two representations of Terms?
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-119>>
8.3<space|2spc>Example Simplicity Expressions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-120>
<with|par-left|1tab|8.3.1<space|2spc>Bits
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-121>>
<with|par-left|1tab|8.3.2<space|2spc>Arithmetic
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-122>>
<with|par-left|1tab|8.3.3<space|2spc>SHA256
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-123>>
8.4<space|2spc>The Hierarchy of Simplicity Language Extensions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-124>
<with|par-left|1tab|8.4.1<space|2spc>Witness
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-126>>
<with|par-left|1tab|8.4.2<space|2spc>Assertion
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-127>>
<with|par-left|1tab|8.4.3<space|2spc>Delegation
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-128>>
<with|par-left|1tab|8.4.4<space|2spc>Primitives
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-129>>
<with|par-left|2tab|8.4.4.1<space|2spc>Bitcoin
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-130>>
<with|par-left|1tab|8.4.5<space|2spc>Jets
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-131>>
<with|par-left|1tab|8.4.6<space|2spc>Full Simplicity
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-132>>
8.5<space|2spc>Merkle Roots <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-133>
8.6<space|2spc>The Bit Machine <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-134>
<with|par-left|1tab|8.6.1<space|2spc>Bit Machine Code
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-135>>
<with|par-left|2tab|8.6.1.1<space|2spc>Bit Machine Programs
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-136>>
<with|par-left|1tab|8.6.2<space|2spc>Translating Simplicity to the Bit
Machine <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-137>>
<with|par-left|1tab|8.6.3<space|2spc>Static Analysis
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-138>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|9<space|2spc>Haskell
Library Guide> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-139><vspace|0.5fn>
9.1<space|2spc><with|font-family|tt|language|verbatim|Simplicity-Core>
library <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-140>
<with|par-left|1tab|9.1.1<space|2spc>Simplicity Types
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-141>>
<with|par-left|1tab|9.1.2<space|2spc>Simplicity Terms
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-142>>
<with|par-left|1tab|9.1.3<space|2spc>Merkle Roots
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-143>>
<with|par-left|1tab|9.1.4<space|2spc>Tensors
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-144>>
<with|par-left|1tab|9.1.5<space|2spc>Example Simplicity Expressions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-145>>
<with|par-left|2tab|9.1.5.1<space|2spc>Generic
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-146>>
<with|par-left|2tab|9.1.5.2<space|2spc>Bits
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-147>>
<with|par-left|2tab|9.1.5.3<space|2spc>Multi-bit Words
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-148>>
<with|par-left|2tab|9.1.5.4<space|2spc>Arithmetic
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-149>>
<with|par-left|2tab|9.1.5.5<space|2spc>Loop
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-150>>
<with|par-left|1tab|9.1.6<space|2spc>Libraries of Simplicity Expressions
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-151>>
<with|par-left|2tab|9.1.6.1<space|2spc>SHA-256
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-152>>
<with|par-left|2tab|9.1.6.2<space|2spc>LibSecp256k1
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-153>>
<with|par-left|2tab|9.1.6.3<space|2spc>CheckSigHash
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-154>>
<with|par-left|1tab|9.1.7<space|2spc>The Bit Machine
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-155>>
<with|par-left|2tab|9.1.7.1<space|2spc>Translating Simplicity to the Bit
Machine <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-156>>
<with|par-left|2tab|9.1.7.2<space|2spc>Static Analysis
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-157>>
<with|par-left|2tab|9.1.7.3<space|2spc>Fast Evaluation with FFI
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-158>>
9.2<space|2spc><with|font-family|tt|language|verbatim|Simplicity-Indef>
library <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-159>
<with|par-left|1tab|9.2.1<space|2spc>Primitive Signature
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-160>>
<with|par-left|1tab|9.2.2<space|2spc>Primitive Terms
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-161>>
<with|par-left|1tab|9.2.3<space|2spc><with|font-family|tt|language|verbatim|JetType>
class <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-162>>
<with|par-left|1tab|9.2.4<space|2spc>Denotational Semantics of Full
Simplicity <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-163>>
<with|par-left|1tab|9.2.5<space|2spc>Type Inference
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-164>>
<with|par-left|1tab|9.2.6<space|2spc>Serialization
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-165>>
<with|par-left|2tab|9.2.6.1<space|2spc>Free Monadic Deserializaiton
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-166>>
<with|par-left|2tab|9.2.6.2<space|2spc>Serialization of Simplicity DAGs
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-167>>
<with|par-left|1tab|9.2.7<space|2spc>Jet Substitution
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-168>>
9.3<space|2spc><with|font-family|tt|language|verbatim|Simplicity-Bitcoin>
Libary <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-169>
9.4<space|2spc><with|font-family|tt|language|verbatim|Simplicity> Library
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-170>
<with|par-left|1tab|9.4.1<space|2spc>CheckSigHashAll
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-171>>
<with|par-left|1tab|9.4.2<space|2spc>Known Discounted Jets
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-172>>
9.5<space|2spc>Simplicity <with|font-family|tt|language|verbatim|testsuite>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-173>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|10<space|2spc>C
Library Guide> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-174><vspace|0.5fn>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|Appendix
A<space|2spc>Elements Application> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-175><vspace|0.5fn>
A.1<space|2spc>Denotational Semantics
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-176>
<with|par-left|1tab|A.1.1<space|2spc>Null Data
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-177>>
<with|par-left|1tab|A.1.2<space|2spc>Merkle Roots
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-178>>
<vspace*|1fn><with|font-series|bold|math-font-series|bold|Appendix
B<space|2spc>Catelogue of Jets> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-179><vspace|0.5fn>
B.1<space|2spc><with|font-family|tt|language|verbatim|110...: >Core Jets
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-180>
<with|par-left|1tab|B.1.1<space|2spc><with|font-family|tt|language|verbatim|1100...:
>Jets for multi-bit logic <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-181>>
<with|par-left|2tab|B.1.1.1<space|2spc>verify
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-182>>
<with|par-left|2tab|B.1.1.2<space|2spc><with|font-family|ss|low>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-183>>
<with|par-left|2tab|B.1.1.3<space|2spc><with|font-family|ss|high>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-184>>
<with|par-left|2tab|B.1.1.4<space|2spc><with|font-family|ss|complement>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-185>>
<with|par-left|2tab|B.1.1.5<space|2spc><with|font-family|ss|and>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-186>>
<with|par-left|2tab|B.1.1.6<space|2spc><with|font-family|ss|or>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-187>>
<with|par-left|2tab|B.1.1.7<space|2spc><with|font-family|ss|xor>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-188>>
<with|par-left|2tab|B.1.1.8<space|2spc><with|font-family|ss|maj>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-189>>
<with|par-left|2tab|B.1.1.9<space|2spc><with|font-family|ss|xor-xor>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-190>>
<with|par-left|2tab|B.1.1.10<space|2spc><with|font-family|ss|ch>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-191>>
<with|par-left|2tab|B.1.1.11<space|2spc><with|font-family|ss|some>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-192>>
<with|par-left|2tab|B.1.1.12<space|2spc><with|font-family|ss|all>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-193>>
<with|par-left|2tab|B.1.1.13<space|2spc><with|font-family|ss|eq>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-194>>
<with|par-left|2tab|B.1.1.14<space|2spc><with|font-family|ss|full-left-shift>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-195>>
<with|par-left|2tab|B.1.1.15<space|2spc><with|font-family|ss|full-right-shift>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-196>>
<with|par-left|2tab|B.1.1.16<space|2spc><with|font-family|ss|leftmost>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-197>>
<with|par-left|2tab|B.1.1.17<space|2spc><with|font-family|ss|rightmost>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-198>>
<with|par-left|2tab|B.1.1.18<space|2spc><with|font-family|ss|left-pad-low>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-199>>
<with|par-left|2tab|B.1.1.19<space|2spc><with|font-family|ss|left-pad-high>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-200>>
<with|par-left|2tab|B.1.1.20<space|2spc><with|font-family|ss|left-extend>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-201>>
<with|par-left|2tab|B.1.1.21<space|2spc><with|font-family|ss|right-pad-low>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-202>>
<with|par-left|2tab|B.1.1.22<space|2spc><with|font-family|ss|right-pad-high>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-203>>
<with|par-left|2tab|B.1.1.23<space|2spc><with|font-family|ss|right-extend>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-204>>
<with|par-left|2tab|B.1.1.24<space|2spc><with|font-family|ss|left-shift-with>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-205>>
<with|par-left|2tab|B.1.1.25<space|2spc><with|font-family|ss|right-shift-with>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-207>>
<with|par-left|2tab|B.1.1.26<space|2spc><with|font-family|ss|left-shift>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-208>>
<with|par-left|2tab|B.1.1.27<space|2spc><with|font-family|ss|right-shift>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-209>>
<with|par-left|2tab|B.1.1.28<space|2spc><with|font-family|ss|left-rotate>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-210>>
<with|par-left|2tab|B.1.1.29<space|2spc><with|font-family|ss|right-rotate>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-211>>
<with|par-left|2tab|B.1.1.30<space|2spc><with|font-family|ss|transpose>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-212>>
<with|par-left|2tab|B.1.1.31<space|2spc><with|font-family|ss|find-first-high>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-213>>
<with|par-left|2tab|B.1.1.32<space|2spc><with|font-family|ss|find-last-high>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-214>>
<with|par-left|2tab|B.1.1.33<space|2spc><with|font-family|ss|bit>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-215>>
<with|par-left|1tab|B.1.2<space|2spc><with|font-family|tt|language|verbatim|110100...:
>Jets for arithmetic <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-216>>
<with|par-left|2tab|B.1.2.1<space|2spc><with|font-family|ss|one>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-217>>
<with|par-left|2tab|B.1.2.2<space|2spc><with|font-family|ss|full-add>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-218>>
<with|par-left|2tab|B.1.2.3<space|2spc><with|font-family|ss|add>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-219>>
<with|par-left|2tab|B.1.2.4<space|2spc><with|font-family|ss|full-increment>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-220>>
<with|par-left|2tab|B.1.2.5<space|2spc><with|font-family|ss|increment>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-221>>
<with|par-left|2tab|B.1.2.6<space|2spc><with|font-family|ss|popcount>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-222>>
<with|par-left|2tab|B.1.2.7<space|2spc><with|font-family|ss|full-subtract>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-224>>
<with|par-left|2tab|B.1.2.8<space|2spc><with|font-family|ss|subtract>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-225>>
<with|par-left|2tab|B.1.2.9<space|2spc><with|font-family|ss|negate>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-226>>
<with|par-left|2tab|B.1.2.10<space|2spc><with|font-family|ss|full-decrement>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-227>>
<with|par-left|2tab|B.1.2.11<space|2spc><with|font-family|ss|decrement>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-228>>
<with|par-left|2tab|B.1.2.12<space|2spc><with|font-family|ss|full-multiply>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-229>>
<with|par-left|2tab|B.1.2.13<space|2spc><with|font-family|ss|multiply>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-230>>
<with|par-left|2tab|B.1.2.14<space|2spc><with|font-family|tt|language|verbatim|><with|font-family|ss|is-zero>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-231>>
<with|par-left|2tab|B.1.2.15<space|2spc><with|font-family|tt|language|verbatim|><with|font-family|ss|is-one>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-232>>
<with|par-left|2tab|B.1.2.16<space|2spc><with|font-family|ss|le>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-233>>
<with|par-left|2tab|B.1.2.17<space|2spc><with|font-family|ss|lt>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-234>>
<with|par-left|2tab|B.1.2.18<space|2spc><with|font-family|ss|min>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-235>>
<with|par-left|2tab|B.1.2.19<space|2spc><with|font-family|ss|max>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-236>>
<with|par-left|2tab|B.1.2.20<space|2spc><with|font-family|ss|median>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-237>>
<with|par-left|2tab|B.1.2.21<space|2spc><with|font-family|ss|div2n1n>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-238>>
<with|par-left|2tab|B.1.2.22<space|2spc><with|font-family|ss|div-mod>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-239>>
<with|par-left|2tab|B.1.2.23<space|2spc><with|font-family|ss|divide>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-240>>
<with|par-left|2tab|B.1.2.24<space|2spc><with|font-family|ss|modulo>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-241>>
<with|par-left|2tab|B.1.2.25<space|2spc><with|font-family|ss|divides>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-242>>
<with|par-left|2tab|B.1.2.26<space|2spc><with|font-family|ss|eea>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-243>>
<with|par-left|2tab|B.1.2.27<space|2spc><with|font-family|ss|bezout>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-244>>
<with|par-left|2tab|B.1.2.28<space|2spc><with|font-family|ss|gcd>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-245>>
<with|par-left|2tab|B.1.2.29<space|2spc><with|font-family|ss|cofactors>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-246>>
<with|par-left|2tab|B.1.2.30<space|2spc><with|font-family|ss|lcm>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-247>>
<with|par-left|2tab|B.1.2.31<space|2spc><with|font-family|ss|jacobi>
(unsigned) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-248>>
<with|par-left|2tab|B.1.2.32<space|2spc><with|font-family|ss|absolute-value>
(signed input/unsigned output) <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-249>>
<with|par-left|2tab|B.1.2.33<space|2spc><with|font-family|tt|language|verbatim|><with|font-family|ss|sign>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-250>>
<with|par-left|2tab|B.1.2.34<space|2spc><with|font-family|ss|signed-le>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-251>>
<with|par-left|2tab|B.1.2.35<space|2spc><with|font-family|ss|signed-lt>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-252>>
<with|par-left|2tab|B.1.2.36<space|2spc><with|font-family|ss|signed-min>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-253>>
<with|par-left|2tab|B.1.2.37<space|2spc><with|font-family|ss|signed-max>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-254>>
<with|par-left|2tab|B.1.2.38<space|2spc><with|font-family|ss|signed-median>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-255>>
<with|par-left|2tab|B.1.2.39<space|2spc><with|font-family|ss|signed-right-shift>
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-256>>