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<h3>
Sebastian Graf pushed to branch wip/refactor-demand
at <a href="https://gitlab.haskell.org/ghc/ghc">Glasgow Haskell Compiler / GHC</a>
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<h4>
Commits:
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<ul>
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<strong><a href="https://gitlab.haskell.org/ghc/ghc/-/commit/c70b5613a4ac59e4046feed23e7d99f388cdd958">c70b5613</a></strong>
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<span>by Sebastian Graf</span>
<i>at 2020-11-10T13:20:04+01:00</i>
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<pre class="commit-message" style="white-space: pre-wrap; margin: 0;">Update user's guide entry on demand analysis and worker/wrapper
The demand signature notation has been undocumented for a long time.
The only source to understand it, apart from reading the `Outputable`
instance, has been an outdated wiki page.
Since the previous commits have reworked the demand lattice, I took
it as an opportunity to also write some documentation about notation.
</pre>
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<h4>4 changed files:</h4>
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<a href="#d87dfc77856eeaef6134e28336290ddcbcf18d7d">
docs/users_guide/9.2.1-notes.rst
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<li class="file-stats">
<a href="#36435f993774454b5956f3a38a9276ed176c61cc">
docs/users_guide/debugging.rst
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<li class="file-stats">
<a href="#ed75822e0b6142f196a6abeb623c7669d31b4711">
docs/users_guide/exts/instances.rst
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<li class="file-stats">
<a href="#2e45f2cd303dd998950a7c8042e796a5b2abd64f">
docs/users_guide/using-optimisation.rst
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<h4>Changes:</h4>
<li id="d87dfc77856eeaef6134e28336290ddcbcf18d7d">
<a href="https://gitlab.haskell.org/ghc/ghc/-/commit/c70b5613a4ac59e4046feed23e7d99f388cdd958#d87dfc77856eeaef6134e28336290ddcbcf18d7d"><strong>docs/users_guide/9.2.1-notes.rst</strong></a>
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<td class="diff-line-num unfold js-unfold new_line" data-linenumber="44" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -44,7 +44,7 @@ Compiler</td>
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<pre style="margin: 0;"> <span id="LC44" class="line" lang="plaintext"> Code using ``Void#`` now has to enable :extension:`UnboxedTuples`.</span>
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<pre style="margin: 0;"> <span id="LC45" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC46" class="line" lang="plaintext">``ghc`` library</span>
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<pre style="margin: 0;">-<span id="LC47" class="line" lang="plaintext">~~~~~~~~~~~~~</span>
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<pre style="margin: 0;">+<span id="LC47" class="line" lang="plaintext">~~~~~~~~~~~~~<span class="idiff left right">~~</span></span>
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<pre style="margin: 0;"> <span id="LC48" class="line" lang="plaintext"></span>
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<td class="diff-line-num old_line" data-linenumber="49" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
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<pre style="margin: 0;"> <span id="LC49" class="line" lang="plaintext">- The ``con_args`` field of ``ConDeclGADT`` has been renamed to ``con_g_args``.</span>
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<pre style="margin: 0;"> <span id="LC50" class="line" lang="plaintext"> This is because the type of ``con_g_args`` is now different from the type of</span>
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<li id="36435f993774454b5956f3a38a9276ed176c61cc">
<a href="https://gitlab.haskell.org/ghc/ghc/-/commit/c70b5613a4ac59e4046feed23e7d99f388cdd958#36435f993774454b5956f3a38a9276ed176c61cc"><strong>docs/users_guide/debugging.rst</strong></a>
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<td class="diff-line-num unfold js-unfold new_line" data-linenumber="334" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -334,16 +334,22 @@ subexpression elimination pass.</td>
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<pre style="margin: 0;"> <span id="LC334" class="line" lang="plaintext"> its rationale.</span>
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<pre style="margin: 0;"> <span id="LC335" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC336" class="line" lang="plaintext">.. ghc-flag:: -ddump-stranal</span>
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<pre style="margin: 0;">-<span id="LC337" class="line" lang="plaintext"> :shortdesc: Dump <span class="idiff left right">strictness analyser</span> output</span>
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<pre style="margin: 0;">+<span id="LC337" class="line" lang="plaintext"> :shortdesc: Dump <span class="idiff left right">demand analysis</span> output</span>
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<pre style="margin: 0;"> <span id="LC338" class="line" lang="plaintext"> :type: dynamic</span>
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<pre style="margin: 0;"> <span id="LC339" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">-<span id="LC340" class="line" lang="plaintext"> Dump strictness analyser output</span>
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<pre style="margin: 0;">+<span id="LC340" class="line" lang="plaintext"> Dump demand analysis output.</span>
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<pre style="margin: 0;">+<span id="LC341" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC342" class="line" lang="plaintext"> See :ghc-flag:`-fstrictness` for the syntax and semantics of demand</span>
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<pre style="margin: 0;">+<span id="LC343" class="line" lang="plaintext"> annotations.</span>
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<pre style="margin: 0;"> <span id="LC344" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC345" class="line" lang="plaintext">.. ghc-flag:: -ddump-str-signatures</span>
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<pre style="margin: 0;">-<span id="LC343" class="line" lang="plaintext"> :shortdesc: Dump <span class="idiff left right">strictness</span> signatures</span>
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<pre style="margin: 0;">+<span id="LC346" class="line" lang="plaintext"> :shortdesc: Dump <span class="idiff left right">top-level demand</span> signatures</span>
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<pre style="margin: 0;"> <span id="LC347" class="line" lang="plaintext"> :type: dynamic</span>
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<pre style="margin: 0;"> <span id="LC348" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">-<span id="LC346" class="line" lang="plaintext"> Dump strictness signatures</span>
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<pre style="margin: 0;">+<span id="LC349" class="line" lang="plaintext"> Dump top-level demand signatures as produced by demand analysis.</span>
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<pre style="margin: 0;">+<span id="LC350" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC351" class="line" lang="plaintext"> See :ghc-flag:`-fstrictness` for the syntax and semantics of demand</span>
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<pre style="margin: 0;">+<span id="LC352" class="line" lang="plaintext"> annotations.</span>
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<pre style="margin: 0;"> <span id="LC353" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC354" class="line" lang="plaintext">.. ghc-flag:: -ddump-cpranal</span>
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<pre style="margin: 0;"> <span id="LC355" class="line" lang="plaintext"> :shortdesc: Dump CPR analysis output</span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -381,7 +387,6 @@ subexpression elimination pass.</td>
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<pre style="margin: 0;"> <span id="LC387" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC388" class="line" lang="plaintext"> Dump output of Core preparation pass</span>
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<pre style="margin: 0;"> <span id="LC389" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">-<span id="LC384" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC390" class="line" lang="plaintext">STG representation</span>
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<pre style="margin: 0;"> <span id="LC391" class="line" lang="plaintext">~~~~~~~~~~~~~~~~~~</span>
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<pre style="margin: 0;"> <span id="LC392" class="line" lang="plaintext"></span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/commit/c70b5613a4ac59e4046feed23e7d99f388cdd958#ed75822e0b6142f196a6abeb623c7669d31b4711"><strong>docs/users_guide/exts/instances.rst</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -147,7 +147,7 @@ Where:</td>
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<pre style="margin: 0;"> <span id="LC147" class="line" lang="plaintext"> ``(forall a. a)`` and ``(Eq a => a)`` are legal.</span>
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<pre style="margin: 0;"> <span id="LC148" class="line" lang="plaintext">- ``ctype`` is a ``btype`` that has no restrictions on an outermost</span>
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<pre style="margin: 0;"> <span id="LC149" class="line" lang="plaintext"> ``forall``/``=>``, so ``forall a. a`` and ``Eq a => a`` are legal ``ctype``\s.</span>
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<pre style="margin: 0;">-<span id="LC150" class="line" lang="plaintext">- ``arg_type`` is a type that is not allowed to have ``forall``s or ``=>``\s</span>
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<pre style="margin: 0;">+<span id="LC150" class="line" lang="plaintext">- ``arg_type`` is a type that is not allowed to have ``forall``<span class="idiff left right">\</span>s or ``=>``\s</span>
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<pre style="margin: 0;"> <span id="LC151" class="line" lang="plaintext">- ``prefix_cls_tycon`` is a class type constructor written prefix (e.g.,</span>
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<pre style="margin: 0;"> <span id="LC152" class="line" lang="plaintext"> ``Show`` or ``(&&&)``), while ``infix_cls_tycon`` is a class type constructor</span>
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<pre style="margin: 0;"> <span id="LC153" class="line" lang="plaintext"> written infix (e.g., ``\`Show\``` or ``&&&``).</span>
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<a href="https://gitlab.haskell.org/ghc/ghc/-/commit/c70b5613a4ac59e4046feed23e7d99f388cdd958#2e45f2cd303dd998950a7c8042e796a5b2abd64f"><strong>docs/users_guide/using-optimisation.rst</strong></a>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1125,7 +1125,7 @@ by saying ``-fno-wombat``.</td>
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<pre style="margin: 0;"> <span id="LC1125" class="line" lang="plaintext"> available parameter registers on x86_64.</span>
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<pre style="margin: 0;"> <span id="LC1126" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC1127" class="line" lang="plaintext">.. ghc-flag:: -fstrictness</span>
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<pre style="margin: 0;">-<span id="LC1128" class="line" lang="plaintext"> :shortdesc: Turn on <span class="idiff left right">strictness</span> analysis.</span>
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<pre style="margin: 0;">+<span id="LC1128" class="line" lang="plaintext"> :shortdesc: Turn on <span class="idiff left right">demand</span> analysis.</span>
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<pre style="margin: 0;"> <span id="LC1129" class="line" lang="plaintext"> Implied by :ghc-flag:`-O`. Implies :ghc-flag:`-fworker-wrapper`</span>
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<pre style="margin: 0;"> <span id="LC1130" class="line" lang="plaintext"> :type: dynamic</span>
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<pre style="margin: 0;"> <span id="LC1131" class="line" lang="plaintext"> :reverse: -fno-strictness</span>
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<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1133,23 +1133,147 @@ by saying ``-fno-wombat``.</td>
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<pre style="margin: 0;"> <span id="LC1133" class="line" lang="plaintext"></span>
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<pre style="margin: 0;"> <span id="LC1134" class="line" lang="plaintext"> :default: on</span>
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<pre style="margin: 0;"> <span id="LC1135" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">-<span id="LC1136" class="line" lang="plaintext"> Switch on the strictness analyser. The implementation is described in the</span>
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1137
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<pre style="margin: 0;">-<span id="LC1137" class="line" lang="plaintext"> paper `Theory and Practice of Demand Analysis in Haskell</span>
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<pre style="margin: 0;">-<span id="LC1138" class="line" lang="plaintext"> <https://www.microsoft.com/en-us/research/wp-content/uploads/2017/03/demand-jfp-draft.pdf>`__.</span>
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1139
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<pre style="margin: 0;">-<span id="LC1139" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">-<span id="LC1140" class="line" lang="plaintext"> The strictness analyser figures out when arguments and variables in</span>
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<pre style="margin: 0;">-<span id="LC1141" class="line" lang="plaintext"> a function can be treated 'strictly' (that is they are always</span>
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1142
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<pre style="margin: 0;">-<span id="LC1142" class="line" lang="plaintext"> evaluated in the function at some point). This allow GHC to apply</span>
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<pre style="margin: 0;">-<span id="LC1143" class="line" lang="plaintext"> certain optimisations such as unboxing that otherwise don't apply as</span>
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<pre style="margin: 0;">-<span id="LC1144" class="line" lang="plaintext"> they change the semantics of the program when applied to lazy</span>
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1145
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<pre style="margin: 0;">-<span id="LC1145" class="line" lang="plaintext"> arguments.</span>
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1136
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<pre style="margin: 0;">+<span id="LC1136" class="line" lang="plaintext"> Turn on demand analysis.</span>
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1137
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<pre style="margin: 0;">+<span id="LC1137" class="line" lang="plaintext"></span>
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1138
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<pre style="margin: 0;">+<span id="LC1138" class="line" lang="plaintext"> A *Demand* describes an evaluation context of an expression. *Demand</span>
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1139
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<pre style="margin: 0;">+<span id="LC1139" class="line" lang="plaintext"> analysis* tries to find out what demands a function puts on its arguments</span>
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1140
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<pre style="margin: 0;">+<span id="LC1140" class="line" lang="plaintext"> when called: If an argument is scrutinised on every code path, the function</span>
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1141
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<pre style="margin: 0;">+<span id="LC1141" class="line" lang="plaintext"> is strict in that argument and GHC is free to use the more efficient</span>
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1142
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<pre style="margin: 0;">+<span id="LC1142" class="line" lang="plaintext"> call-by-value calling convention, as well as pass parameters unboxed.</span>
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1143
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<pre style="margin: 0;">+<span id="LC1143" class="line" lang="plaintext"></span>
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1144
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<pre style="margin: 0;">+<span id="LC1144" class="line" lang="plaintext"> Apart from *strictness analysis*, demand analysis also performs *usage</span>
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1145
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<pre style="margin: 0;">+<span id="LC1145" class="line" lang="plaintext"> analysis*: Where *strict* translates to "evaluated at least once", usage</span>
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1146
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<pre style="margin: 0;">+<span id="LC1146" class="line" lang="plaintext"> analysis asks whether arguments and bindings are "evaluated at most once"</span>
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1147
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<pre style="margin: 0;">+<span id="LC1147" class="line" lang="plaintext"> or not at all ("evaluated at most zero times"), e.g. *absent*. For the</span>
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1148
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<pre style="margin: 0;">+<span id="LC1148" class="line" lang="plaintext"> former, GHC may use call-by-name instead of call-by-need, effectively</span>
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1149
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<pre style="margin: 0;">+<span id="LC1149" class="line" lang="plaintext"> turning thunks into non-memoised functions. For the latter, no code needs</span>
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1150
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<pre style="margin: 0;">+<span id="LC1150" class="line" lang="plaintext"> to be generated at all: An absent argument can simply be replaced by a</span>
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1151
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<pre style="margin: 0;">+<span id="LC1151" class="line" lang="plaintext"> dummy value at the call site or omitted altogether.</span>
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1152
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<pre style="margin: 0;">+<span id="LC1152" class="line" lang="plaintext"></span>
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1153
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<pre style="margin: 0;">+<span id="LC1153" class="line" lang="plaintext"> The worker/wrapper transformation (:ghc-flag:`-fworker-wrapper`) is</span>
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1154
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<pre style="margin: 0;">+<span id="LC1154" class="line" lang="plaintext"> reponsible for exploiting unboxing opportunities and replacing absent</span>
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1155
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<pre style="margin: 0;">+<span id="LC1155" class="line" lang="plaintext"> arguments by dummies. For arugments that can't be unboxed, opportunities</span>
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1156
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<pre style="margin: 0;">+<span id="LC1156" class="line" lang="plaintext"> for call-by-value and call-by-name are exploited in CorePrep when</span>
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1157
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<pre style="margin: 0;">+<span id="LC1157" class="line" lang="plaintext"> translating to STG.</span>
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1158
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<pre style="margin: 0;">+<span id="LC1158" class="line" lang="plaintext"></span>
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1159
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<pre style="margin: 0;">+<span id="LC1159" class="line" lang="plaintext"> It's not only interesting to look at how often a binding is *evaluated*,</span>
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1160
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<pre style="margin: 0;">+<span id="LC1160" class="line" lang="plaintext"> but also how often a function *is called*. If a function is called at most</span>
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1161
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<pre style="margin: 0;">+<span id="LC1161" class="line" lang="plaintext"> once, we may freely eta-expand it, even if doing so destroys shared work</span>
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1162
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<pre style="margin: 0;">+<span id="LC1162" class="line" lang="plaintext"> if the function was called multiple times. This information translates</span>
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1163
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<pre style="margin: 0;">+<span id="LC1163" class="line" lang="plaintext"> into ``OneShotInfo`` annotations that the Simplifier acts on.</span>
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1164
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<pre style="margin: 0;">+<span id="LC1164" class="line" lang="plaintext"></span>
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1165
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<pre style="margin: 0;">+<span id="LC1165" class="line" lang="plaintext"> **Notation**</span>
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1166
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<pre style="margin: 0;">+<span id="LC1166" class="line" lang="plaintext"></span>
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1167
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<pre style="margin: 0;">+<span id="LC1167" class="line" lang="plaintext"> So demand analysis is about conservatively inferring lower and upper</span>
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1168
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<pre style="margin: 0;">+<span id="LC1168" class="line" lang="plaintext"> bounds about how many times something is evaluated/called. We call the</span>
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1169
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<pre style="margin: 0;">+<span id="LC1169" class="line" lang="plaintext"> "how many times" part a *cardinality*. In the compiler and debug output</span>
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1170
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<pre style="margin: 0;">+<span id="LC1170" class="line" lang="plaintext"> we differentiate the following cardinality intervals as approximations</span>
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1171
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<pre style="margin: 0;">+<span id="LC1171" class="line" lang="plaintext"> to cardinality:</span>
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1172
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<pre style="margin: 0;">+<span id="LC1172" class="line" lang="plaintext"></span>
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1173
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<pre style="margin: 0;">+<span id="LC1173" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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1174
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<pre style="margin: 0;">+<span id="LC1174" class="line" lang="plaintext"> | Interval | Set of denoted cardinalities | Syntax | Explanation tying syntax to semantics |</span>
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1175
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<pre style="margin: 0;">+<span id="LC1175" class="line" lang="plaintext"> +==========+==============================+========+=======================================+</span>
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1176
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<pre style="margin: 0;">+<span id="LC1176" class="line" lang="plaintext"> | [1,0] | {} | ``B`` | bottom element |</span>
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1177
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<pre style="margin: 0;">+<span id="LC1177" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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1178
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<pre style="margin: 0;">+<span id="LC1178" class="line" lang="plaintext"> | [0,0] | {0} | ``A`` | absent |</span>
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1179
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<pre style="margin: 0;">+<span id="LC1179" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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<td class="diff-line-num new new_line" data-linenumber="1180" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1180
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<pre style="margin: 0;">+<span id="LC1180" class="line" lang="plaintext"> | [0,1] | {0,1} | ``1`` | used at most once |</span>
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1181
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<pre style="margin: 0;">+<span id="LC1181" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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1182
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<pre style="margin: 0;">+<span id="LC1182" class="line" lang="plaintext"> | [0,ω] | {0,1,ω} | ``U`` | top element, no information, |</span>
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1183
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<pre style="margin: 0;">+<span id="LC1183" class="line" lang="plaintext"> | | | | used at least 0, at most many times |</span>
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1184
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<pre style="margin: 0;">+<span id="LC1184" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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1185
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<pre style="margin: 0;">+<span id="LC1185" class="line" lang="plaintext"> | [1,1] | {1} | ``S`` | strict, used exactly once |</span>
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1186
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<pre style="margin: 0;">+<span id="LC1186" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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1187
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<pre style="margin: 0;">+<span id="LC1187" class="line" lang="plaintext"> | [1,ω] | {1,ω} | ``M`` | strict, used possibly many times |</span>
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1188
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<pre style="margin: 0;">+<span id="LC1188" class="line" lang="plaintext"> +----------+------------------------------+--------+---------------------------------------+</span>
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1189
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<pre style="margin: 0;">+<span id="LC1189" class="line" lang="plaintext"></span>
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1190
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<pre style="margin: 0;">+<span id="LC1190" class="line" lang="plaintext"> Note that it's never interesting to differentiate between a cardinality</span>
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1191
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<pre style="margin: 0;">+<span id="LC1191" class="line" lang="plaintext"> of 2 and 3, or even 4232123. We just approximate the >1 case with ω,</span>
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1192
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<pre style="margin: 0;">+<span id="LC1192" class="line" lang="plaintext"> standing for "many times".</span>
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1193
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<pre style="margin: 0;">+<span id="LC1193" class="line" lang="plaintext"></span>
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1194
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<pre style="margin: 0;">+<span id="LC1194" class="line" lang="plaintext"> Apart from the cardinality describing *how often* an argument is evaluated,</span>
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1195
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<pre style="margin: 0;">+<span id="LC1195" class="line" lang="plaintext"> a demand also carries a *sub-demand*, describing *how deep* something</span>
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1196
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<pre style="margin: 0;">+<span id="LC1196" class="line" lang="plaintext"> is evaluated beyond a simple ``seq``-like evaluation.</span>
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1197
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<pre style="margin: 0;">+<span id="LC1197" class="line" lang="plaintext"></span>
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1198
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<pre style="margin: 0;">+<span id="LC1198" class="line" lang="plaintext"> For example, ``fst`` is strict in its argument, and also in the first</span>
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1199
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<pre style="margin: 0;">+<span id="LC1199" class="line" lang="plaintext"> component of the argument. It will not evaluate the argument's second</span>
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1200
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<pre style="margin: 0;">+<span id="LC1200" class="line" lang="plaintext"> component. That is expressed by the demand ``SP(SU,A)``. The ``P`` is for</span>
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1201
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<pre style="margin: 0;">+<span id="LC1201" class="line" lang="plaintext"> "product sub-demand", which has a *demand* for each product field. The</span>
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1202
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<pre style="margin: 0;">+<span id="LC1202" class="line" lang="plaintext"> notation ``SU`` just says "evaluated strictly (``S``), with everything</span>
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1203
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<pre style="margin: 0;">+<span id="LC1203" class="line" lang="plaintext"> nested inside evaluated according to ``U``" -- e.g., no information,</span>
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1204
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<pre style="margin: 0;">+<span id="LC1204" class="line" lang="plaintext"> because that would depend on the evaluation context of the call site of</span>
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1205
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<pre style="margin: 0;">+<span id="LC1205" class="line" lang="plaintext"> ``fst``. The role of ``U`` in ``SU`` is that of a *polymorphic* sub-demand,</span>
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1206
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<pre style="margin: 0;">+<span id="LC1206" class="line" lang="plaintext"> being semantically equivalent to the sub-demand ``P(UP(..))``, which we</span>
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1207
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<pre style="margin: 0;">+<span id="LC1207" class="line" lang="plaintext"> simply abbreviate by the (consequently overloaded) cardinality notation</span>
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1208
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<pre style="margin: 0;">+<span id="LC1208" class="line" lang="plaintext"> ``U``.</span>
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1209
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<pre style="margin: 0;">+<span id="LC1209" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1210" class="line" lang="plaintext"> For another example, the expression ``x + 1`` evaluates ``x`` according to</span>
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1211
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<pre style="margin: 0;">+<span id="LC1211" class="line" lang="plaintext"> demand ``SP(U)``. We have seen single letters stand for cardinalities and</span>
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1212
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<pre style="margin: 0;">+<span id="LC1212" class="line" lang="plaintext"> polymorphic sub-demands, but what does the single letter ``U`` mean for a</span>
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1213
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<pre style="margin: 0;">+<span id="LC1213" class="line" lang="plaintext"> *demand*? Such a single letter demand simply expands to a cardinality and</span>
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1214
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<pre style="margin: 0;">+<span id="LC1214" class="line" lang="plaintext"> a polymorphic sub-demand of the same letter: E.g. ``U`` is equivalent to</span>
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1215
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<pre style="margin: 0;">+<span id="LC1215" class="line" lang="plaintext"> ``UU`` by expansion of the single letter demand, which is equivalent to</span>
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1216
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<pre style="margin: 0;">+<span id="LC1216" class="line" lang="plaintext"> ``UP(UP(..))``, so ``U``\s all the way down.</span>
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1217
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<pre style="margin: 0;">+<span id="LC1217" class="line" lang="plaintext"></span>
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1218
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<pre style="margin: 0;">+<span id="LC1218" class="line" lang="plaintext"> **Demand signatures**</span>
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1219
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<pre style="margin: 0;">+<span id="LC1219" class="line" lang="plaintext"></span>
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1220
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<pre style="margin: 0;">+<span id="LC1220" class="line" lang="plaintext"> We summarise a function's demand properties in its *demand signature*.</span>
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1221
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<pre style="margin: 0;">+<span id="LC1221" class="line" lang="plaintext"> This is the general syntax:</span>
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1222
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<pre style="margin: 0;">+<span id="LC1222" class="line" lang="plaintext"></span>
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1223
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<pre style="margin: 0;">+<span id="LC1223" class="line" lang="plaintext"> .. code-block::</span>
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1224
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<pre style="margin: 0;">+<span id="LC1224" class="line" lang="plaintext"></span>
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1225
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<pre style="margin: 0;">+<span id="LC1225" class="line" lang="plaintext"> {x->dx,y->dy,z->dz...}<d1><d2><d3>...<dn>d</span>
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1226
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<pre style="margin: 0;">+<span id="LC1226" class="line" lang="plaintext"> ^ ^ ^ ^ ^ ^</span>
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1227
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<pre style="margin: 0;">+<span id="LC1227" class="line" lang="plaintext"> | | | | | |</span>
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1228
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<pre style="margin: 0;">+<span id="LC1228" class="line" lang="plaintext"> | \---+---+------/ |</span>
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1229
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<pre style="margin: 0;">+<span id="LC1229" class="line" lang="plaintext"> | | |</span>
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1230
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<pre style="margin: 0;">+<span id="LC1230" class="line" lang="plaintext"> demand on free demand on divergence</span>
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1231
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<pre style="margin: 0;">+<span id="LC1231" class="line" lang="plaintext"> variables arguments information</span>
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1232
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<pre style="margin: 0;">+<span id="LC1232" class="line" lang="plaintext"> (omitted if empty) (omitted if</span>
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1233
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<pre style="margin: 0;">+<span id="LC1233" class="line" lang="plaintext"> no information)</span>
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1234
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<pre style="margin: 0;">+<span id="LC1234" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1235" class="line" lang="plaintext"> We summarise ``fst``'s demand properties in its *demand signature*</span>
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<pre style="margin: 0;">+<span id="LC1236" class="line" lang="plaintext"> ``<SP(SU,A)>``, which just says "If ``fst`` is applied to one argument,</span>
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<pre style="margin: 0;">+<span id="LC1237" class="line" lang="plaintext"> that argument is evaluated according to ``SP(SU,A)``". For another</span>
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<pre style="margin: 0;">+<span id="LC1238" class="line" lang="plaintext"> example, the demand signature of ``seq`` would be ``<SA>`` and that of</span>
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<pre style="margin: 0;">+<span id="LC1239" class="line" lang="plaintext"> ``+`` would be ``<SP(U)><SP(U)>``.</span>
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1240
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<pre style="margin: 0;">+<span id="LC1240" class="line" lang="plaintext"></span>
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1241
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<pre style="margin: 0;">+<span id="LC1241" class="line" lang="plaintext"> If not omitted, the divergence information can be ``b`` (surely diverges)</span>
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1242
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<pre style="margin: 0;">+<span id="LC1242" class="line" lang="plaintext"> or ``x`` (surely diverges or throws a precise exception). For example,</span>
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<pre style="margin: 0;">+<span id="LC1243" class="line" lang="plaintext"> ``error`` has demand signature ``<M>b`` and ``throwIO`` (which is the</span>
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<pre style="margin: 0;">+<span id="LC1244" class="line" lang="plaintext"> only way to throw precise exceptions) has demand signature ``<_><U><U>x``</span>
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<pre style="margin: 0;">+<span id="LC1245" class="line" lang="plaintext"> (leaving out the complicated demand on the ``Exception`` dictionary).</span>
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<pre style="margin: 0;">+<span id="LC1246" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1247" class="line" lang="plaintext"> **Call sub-demands**</span>
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<pre style="margin: 0;">+<span id="LC1248" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1249" class="line" lang="plaintext"> Consider ``maybe``:</span>
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<pre style="margin: 0;">+<span id="LC1250" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1251" class="line" lang="plaintext"> .. code-block::</span>
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<pre style="margin: 0;">+<span id="LC1252" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1253" class="line" lang="plaintext"> maybe :: b -> (a -> b) -> Maybe a -> b</span>
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<pre style="margin: 0;">+<span id="LC1254" class="line" lang="plaintext"> maybe n _ Nothing = n</span>
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<pre style="margin: 0;">+<span id="LC1255" class="line" lang="plaintext"> maybe _ s (Just a) = s a</span>
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<pre style="margin: 0;">+<span id="LC1256" class="line" lang="plaintext"></span>
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<pre style="margin: 0;">+<span id="LC1257" class="line" lang="plaintext"> We give it demand signature ``<U><C1(U)><SU>``. The ``C1(U)`` is a</span>
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<pre style="margin: 0;">+<span id="LC1258" class="line" lang="plaintext"> *call sub-demand* that says "called at most once, where the result is</span>
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<pre style="margin: 0;">+<span id="LC1259" class="line" lang="plaintext"> used according to ``U``". It's in a position where we expect a demand,</span>
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<pre style="margin: 0;">+<span id="LC1260" class="line" lang="plaintext"> and similarly to before, this notation is short for ``1C1(U)``, which also</span>
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1261
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<pre style="margin: 0;">+<span id="LC1261" class="line" lang="plaintext"> says that the argument was evaluated once. When the evaluation cardinality</span>
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1262
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<pre style="margin: 0;">+<span id="LC1262" class="line" lang="plaintext"> conincides with the outer call cardinality, it is omitted. The expression</span>
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1263
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<pre style="margin: 0;">+<span id="LC1263" class="line" lang="plaintext"> ``f `seq` f 1 2`` puts ``f`` under demand ``MCS(U)`` and serves as an example</span>
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1264
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<pre style="margin: 0;">+<span id="LC1264" class="line" lang="plaintext"> where evaluation cardinality doesn't conincide with call cardinality.</span>
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1265
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<pre style="margin: 0;">+<span id="LC1265" class="line" lang="plaintext"></span>
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1266
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<pre style="margin: 0;">+<span id="LC1266" class="line" lang="plaintext"> Cardinality is always relative to the enclosing call cardinality, so</span>
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1267
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<pre style="margin: 0;">+<span id="LC1267" class="line" lang="plaintext"> ``g 1 2 + g 3 4`` puts ``g`` under demand ``CM(CS(U))``, which says "called</span>
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<td class="diff-line-num new new_line" data-linenumber="1268" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1268
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<pre style="margin: 0;">+<span id="LC1268" class="line" lang="plaintext"> multiple times (``M``), but every time it is called with one argument,</span>
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1269
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<pre style="margin: 0;">+<span id="LC1269" class="line" lang="plaintext"> it is applied exactly once to another argument (``S``)".</span>
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1146
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1270
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<pre style="margin: 0;"> <span id="LC1270" class="line" lang="plaintext"></span>
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1147
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1271
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<pre style="margin: 0;"> <span id="LC1271" class="line" lang="plaintext">.. ghc-flag:: -fstrictness-before=⟨n⟩</span>
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1148
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<pre style="margin: 0;">-<span id="LC1148" class="line" lang="plaintext"> :shortdesc: Run an additional <span class="idiff left right">strictness</span> analysis before simplifier phase ⟨n⟩</span>
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1272
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<pre style="margin: 0;">+<span id="LC1272" class="line" lang="plaintext"> :shortdesc: Run an additional <span class="idiff left right">demand</span> analysis before simplifier phase ⟨n⟩</span>
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1149
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1273
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<pre style="margin: 0;"> <span id="LC1273" class="line" lang="plaintext"> :type: dynamic</span>
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1150
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1274
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<pre style="margin: 0;"> <span id="LC1274" class="line" lang="plaintext"> :category:</span>
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1151
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1275
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<pre style="margin: 0;"> <span id="LC1275" class="line" lang="plaintext"></span>
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1152
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<pre style="margin: 0;">-<span id="LC1152" class="line" lang="plaintext"> Run an additional <span class="idiff left right">strictness</span> analysis before simplifier phase ⟨n⟩.</span>
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1276
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<pre style="margin: 0;">+<span id="LC1276" class="line" lang="plaintext"> Run an additional <span class="idiff left right">demand</span> analysis before simplifier phase ⟨n⟩.</span>
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1153
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1277
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<pre style="margin: 0;"> <span id="LC1277" class="line" lang="plaintext"></span>
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1154
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1278
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<pre style="margin: 0;"> <span id="LC1278" class="line" lang="plaintext">.. ghc-flag:: -funbox-small-strict-fields</span>
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1155
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1279
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<pre style="margin: 0;"> <span id="LC1279" class="line" lang="plaintext"> :shortdesc: Flatten strict constructor fields with a pointer-sized</span>
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<td class="diff-line-num unfold js-unfold old_line" data-linenumber="1308" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="diff-line-num unfold js-unfold new_line" data-linenumber="1432" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">...</td>
<td class="line_content match " style="padding-left: 0.5em; padding-right: 0.5em; color: rgba(0,0,0,0.3);" bgcolor="#fafafa">@@ -1308,14 +1432,20 @@ by saying ``-fno-wombat``.</td>
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1308
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1432
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<pre style="margin: 0;"> <span id="LC1432" class="line" lang="plaintext"> potential inlining.</span>
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1309
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1433
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<pre style="margin: 0;"> <span id="LC1433" class="line" lang="plaintext"></span>
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1310
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<pre style="margin: 0;"> <span id="LC1434" class="line" lang="plaintext">.. ghc-flag:: -fworker-wrapper</span>
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1311
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<pre style="margin: 0;">-<span id="LC1311" class="line" lang="plaintext"> :shortdesc: Enable the worker<span class="idiff left right">-</span>wrapper transformation.</span>
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<td class="diff-line-num new new_line" data-linenumber="1435" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1435
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<pre style="margin: 0;">+<span id="LC1435" class="line" lang="plaintext"> :shortdesc: Enable the worker<span class="idiff left right">/</span>wrapper transformation.</span>
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<td class="diff-line-num old_line" data-linenumber="1312" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1312
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<td class="diff-line-num new_line" data-linenumber="1436" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1436
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<pre style="margin: 0;"> <span id="LC1436" class="line" lang="plaintext"> :type: dynamic</span>
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<td class="diff-line-num old_line" data-linenumber="1313" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1313
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<td class="diff-line-num new_line" data-linenumber="1437" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1437
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<pre style="margin: 0;"> <span id="LC1437" class="line" lang="plaintext"> :category:</span>
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<td class="diff-line-num old_line" data-linenumber="1314" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1314
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<td class="diff-line-num new_line" data-linenumber="1438" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1438
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<pre style="margin: 0;"> <span id="LC1438" class="line" lang="plaintext"></span>
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<td class="diff-line-num old old_line" data-linenumber="1315" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1315
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<td class="diff-line-num new_line old" data-linenumber="1439" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1315" class="line" lang="plaintext"> Enable the worker-wrapper transformation after a strictness</span>
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<td class="diff-line-num old old_line" data-linenumber="1316" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1316
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<td class="diff-line-num new_line old" data-linenumber="1439" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
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<pre style="margin: 0;">-<span id="LC1316" class="line" lang="plaintext"> analysis pass. Implied by :ghc-flag:`-O`, and by :ghc-flag:`-fstrictness`.</span>
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<td class="diff-line-num new new_line" data-linenumber="1439" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1439
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<pre style="margin: 0;">+<span id="LC1439" class="line" lang="plaintext"> Enable the worker/wrapper transformation after a demand analysis pass.</span>
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<td class="diff-line-num new old_line" data-linenumber="1317" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
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<td class="diff-line-num new new_line" data-linenumber="1440" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1440
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<pre style="margin: 0;">+<span id="LC1440" class="line" lang="plaintext"></span>
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<td class="diff-line-num new old_line" data-linenumber="1317" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
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<td class="diff-line-num new new_line" data-linenumber="1441" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1441
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<pre style="margin: 0;">+<span id="LC1441" class="line" lang="plaintext"> Exploits strictness and absence information by unboxing strict arguments</span>
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<td class="diff-line-num new old_line" data-linenumber="1317" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
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<td class="diff-line-num new new_line" data-linenumber="1442" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1442
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<pre style="margin: 0;">+<span id="LC1442" class="line" lang="plaintext"> and replacing absent fields by dummy values in a wrapper function that</span>
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<td class="diff-line-num new new_line" data-linenumber="1443" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1443
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<pre style="margin: 0;">+<span id="LC1443" class="line" lang="plaintext"> will inline in all relevant scenarios and thus expose a specialised,</span>
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1444
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<pre style="margin: 0;">+<span id="LC1444" class="line" lang="plaintext"> unboxed calling convention of the worker function.</span>
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<td class="diff-line-num new new_line" data-linenumber="1445" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
1445
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<pre style="margin: 0;">+<span id="LC1445" class="line" lang="plaintext"></span>
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1446
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<pre style="margin: 0;">+<span id="LC1446" class="line" lang="plaintext"> Implied by :ghc-flag:`-O`, and by :ghc-flag:`-fstrictness`.</span>
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1317
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1447
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<pre style="margin: 0;"> <span id="LC1447" class="line" lang="plaintext"> Disabled by :ghc-flag:`-fno-strictness`. Enabling :ghc-flag:`-fworker-wrapper`</span>
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<td class="diff-line-num old old_line" data-linenumber="1318" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #fac5cd; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#f9d7dc">
1318
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<pre style="margin: 0;">-<span id="LC1318" class="line" lang="plaintext"> while <span class="idiff left right">strictness</span> analysis is disabled (by :ghc-flag:`-fno-strictness`)</span>
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<td class="diff-line-num new old_line" data-linenumber="1319" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #c7f0d2; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#ddfbe6">
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1448
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<pre style="margin: 0;">+<span id="LC1448" class="line" lang="plaintext"> while <span class="idiff left right">demand</span> analysis is disabled (by :ghc-flag:`-fno-strictness`)</span>
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<td class="diff-line-num old_line" data-linenumber="1319" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1319
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<td class="diff-line-num new_line" data-linenumber="1449" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1449
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<pre style="margin: 0;"> <span id="LC1449" class="line" lang="plaintext"> has no effect.</span>
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<td class="diff-line-num old_line" data-linenumber="1320" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1320
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1450
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<pre style="margin: 0;"> <span id="LC1450" class="line" lang="plaintext"></span>
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<td class="diff-line-num old_line" data-linenumber="1321" style="width: 35px; color: rgba(0,0,0,0.3); border-right-width: 1px; border-right-color: #f0f0f0; border-right-style: solid; padding: 0 5px;" align="right" bgcolor="#fafafa">
1321
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1451
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<pre style="margin: 0;"> <span id="LC1451" class="line" lang="plaintext">.. ghc-flag:: -fbinary-blob-threshold=⟨n⟩</span>
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