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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Agda-TypeChecking-Telescope.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">Agda-2.3.2.1: A dependently typed functional programming language and proof assistant</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>None</td></tr></table><p class="caption">Agda.TypeChecking.Telescope</p></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><a href="#v:renameP">renameP</a> :: <a href="Agda-TypeChecking-Substitute.html#t:Subst">Subst</a> t => <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a> -> t -> t</li><li class="src short"><a href="#v:renaming">renaming</a> :: <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a> -> <a href="Agda-TypeChecking-Substitute.html#t:Substitution">Substitution</a></li><li class="src short"><a href="#v:renamingR">renamingR</a> :: <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a> -> <a href="Agda-TypeChecking-Substitute.html#t:Substitution">Substitution</a></li><li class="src short"><a href="#v:flattenTel">flattenTel</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>]</li><li class="src short"><a href="#v:reorderTel">reorderTel</a> :: [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>] -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a></li><li class="src short"><a href="#v:reorderTel_">reorderTel_</a> :: [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>] -> <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a></li><li class="src short"><a href="#v:unflattenTel">unflattenTel</a> :: [<a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-String.html#t:String">String</a>] -> [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>] -> <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a></li><li class="src short"><a href="#v:teleNames">teleNames</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> [<a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-String.html#t:String">String</a>]</li><li class="src short"><a href="#v:teleArgNames">teleArgNames</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> [<a href="Agda-Syntax-Common.html#t:Arg">Arg</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-String.html#t:String">String</a>]</li><li class="src short"><a href="#v:teleArgs">teleArgs</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> <a href="Agda-Syntax-Internal.html#t:Args">Args</a></li><li class="src short"><span class="keyword">data</span> <a href="#t:SplitTel">SplitTel</a> = <a href="#v:SplitTel">SplitTel</a> {<ul class="subs"><li><a href="#v:firstPart">firstPart</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a></li><li><a href="#v:secondPart">secondPart</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a></li><li><a href="#v:splitPerm">splitPerm</a> :: <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a></li></ul>}</li><li class="src short"><a href="#v:splitTelescope">splitTelescope</a> :: <a href="Agda-Utils-VarSet.html#t:VarSet">VarSet</a> -> <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> <a href="Agda-TypeChecking-Telescope.html#t:SplitTel">SplitTel</a></li><li class="src short"><a href="#v:telView">telView</a> :: <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-TypeChecking-Substitute.html#t:TelView">TelView</a></li><li class="src short"><a href="#v:telViewUpTo">telViewUpTo</a> :: <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Int.html#t:Int">Int</a> -> <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-TypeChecking-Substitute.html#t:TelView">TelView</a></li><li class="src short"><a href="#v:telViewUpTo-39-">telViewUpTo'</a> :: <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Int.html#t:Int">Int</a> -> (<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-TypeChecking-Substitute.html#t:TelView">TelView</a></li><li class="src short"><a href="#v:piApplyM">piApplyM</a> :: <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-Syntax-Internal.html#t:Args">Args</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><a name="v:renameP" class="def">renameP</a> :: <a href="Agda-TypeChecking-Substitute.html#t:Subst">Subst</a> t => <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a> -> t -> t<a href="src/Agda-TypeChecking-Telescope.html#renameP" class="link">Source</a></p><div class="doc"><p>The permutation should permute the corresponding telescope. (left-to-right list)
</p></div></div><div class="top"><p class="src"><a name="v:renaming" class="def">renaming</a> :: <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a> -> <a href="Agda-TypeChecking-Substitute.html#t:Substitution">Substitution</a><a href="src/Agda-TypeChecking-Telescope.html#renaming" class="link">Source</a></p><div class="doc"><p>If <code>permute π : [a]Γ -> [a]Δ</code>, then <code>applySubst (renaming π) : Term Γ -> Term Δ</code>
</p></div></div><div class="top"><p class="src"><a name="v:renamingR" class="def">renamingR</a> :: <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a> -> <a href="Agda-TypeChecking-Substitute.html#t:Substitution">Substitution</a><a href="src/Agda-TypeChecking-Telescope.html#renamingR" class="link">Source</a></p><div class="doc"><p>If <code>permute π : [a]Γ -> [a]Δ</code>, then <code>substs (renamingR π) : Term Δ -> Term Γ</code>
</p></div></div><div class="top"><p class="src"><a name="v:flattenTel" class="def">flattenTel</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>]<a href="src/Agda-TypeChecking-Telescope.html#flattenTel" class="link">Source</a></p><div class="doc"><p>Flatten telescope: (Γ : Tel) -> [Type Γ]
</p></div></div><div class="top"><p class="src"><a name="v:reorderTel" class="def">reorderTel</a> :: [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>] -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Maybe.html#t:Maybe">Maybe</a> <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a><a href="src/Agda-TypeChecking-Telescope.html#reorderTel" class="link">Source</a></p><div class="doc"><p>Order a flattened telescope in the correct dependeny order: Γ ->
Permutation (Γ -> Γ~)
</p></div></div><div class="top"><p class="src"><a name="v:reorderTel_" class="def">reorderTel_</a> :: [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>] -> <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a><a href="src/Agda-TypeChecking-Telescope.html#reorderTel_" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:unflattenTel" class="def">unflattenTel</a> :: [<a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-String.html#t:String">String</a>] -> [<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a>] -> <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a><a href="src/Agda-TypeChecking-Telescope.html#unflattenTel" class="link">Source</a></p><div class="doc"><p>Unflatten: turns a flattened telescope into a proper telescope. Must be
properly ordered.
</p></div></div><div class="top"><p class="src"><a name="v:teleNames" class="def">teleNames</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> [<a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-String.html#t:String">String</a>]<a href="src/Agda-TypeChecking-Telescope.html#teleNames" class="link">Source</a></p><div class="doc"><p>Get the suggested names from a telescope
</p></div></div><div class="top"><p class="src"><a name="v:teleArgNames" class="def">teleArgNames</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> [<a href="Agda-Syntax-Common.html#t:Arg">Arg</a> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-String.html#t:String">String</a>]<a href="src/Agda-TypeChecking-Telescope.html#teleArgNames" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:teleArgs" class="def">teleArgs</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> <a href="Agda-Syntax-Internal.html#t:Args">Args</a><a href="src/Agda-TypeChecking-Telescope.html#teleArgs" class="link">Source</a></p></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:SplitTel" class="def">SplitTel</a> <a href="src/Agda-TypeChecking-Telescope.html#SplitTel" class="link">Source</a></p><div class="doc"><p>A telescope split in two.
</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:SplitTel" class="def">SplitTel</a></td><td class="doc empty"> </td></tr><tr><td colspan="2"><div class="subs fields"><p class="caption">Fields</p><dl><dt class="src"><a name="v:firstPart" class="def">firstPart</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a></dt><dd class="doc empty"> </dd><dt class="src"><a name="v:secondPart" class="def">secondPart</a> :: <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a></dt><dd class="doc empty"> </dd><dt class="src"><a name="v:splitPerm" class="def">splitPerm</a> :: <a href="Agda-Utils-Permutation.html#t:Permutation">Permutation</a></dt><dd class="doc empty"> </dd></dl><div class="clear"></div></div></td></tr></table></div></div><div class="top"><p class="src"><a name="v:splitTelescope" class="def">splitTelescope</a> :: <a href="Agda-Utils-VarSet.html#t:VarSet">VarSet</a> -> <a href="Agda-Syntax-Internal.html#t:Telescope">Telescope</a> -> <a href="Agda-TypeChecking-Telescope.html#t:SplitTel">SplitTel</a><a href="src/Agda-TypeChecking-Telescope.html#splitTelescope" class="link">Source</a></p><div class="doc"><p>Split a telescope into the part that defines the given variables and the
part that doesn't.
</p></div></div><div class="top"><p class="src"><a name="v:telView" class="def">telView</a> :: <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-TypeChecking-Substitute.html#t:TelView">TelView</a><a href="src/Agda-TypeChecking-Telescope.html#telView" class="link">Source</a></p></div><div class="top"><p class="src"><a name="v:telViewUpTo" class="def">telViewUpTo</a> :: <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Int.html#t:Int">Int</a> -> <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-TypeChecking-Substitute.html#t:TelView">TelView</a><a href="src/Agda-TypeChecking-Telescope.html#telViewUpTo" class="link">Source</a></p><div class="doc"><p><code>telViewUpTo n t</code> takes off the first <code>n</code> function types of <code>t</code>.
Takes off all if <code>n < 0</code>.
</p></div></div><div class="top"><p class="src"><a name="v:telViewUpTo-39-" class="def">telViewUpTo'</a> :: <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Int.html#t:Int">Int</a> -> (<a href="Agda-Syntax-Common.html#t:Dom">Dom</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="/usr/share/doc/ghc/html/libraries/base-4.5.1.0/Data-Bool.html#t:Bool">Bool</a>) -> <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-TypeChecking-Substitute.html#t:TelView">TelView</a><a href="src/Agda-TypeChecking-Telescope.html#telViewUpTo%27" class="link">Source</a></p><div class="doc"><p><code>telViewUpTo' n p t</code> takes off $t$
the first <code>n</code> (or arbitrary many if <code>n < 0</code>) function domains
as long as they satify <code>p</code>.
</p></div></div><div class="top"><p class="src"><a name="v:piApplyM" class="def">piApplyM</a> :: <a href="Agda-Syntax-Internal.html#t:Type">Type</a> -> <a href="Agda-Syntax-Internal.html#t:Args">Args</a> -> <a href="Agda-TypeChecking-Monad-Base.html#t:TCM">TCM</a> <a href="Agda-Syntax-Internal.html#t:Type">Type</a><a href="src/Agda-TypeChecking-Telescope.html#piApplyM" class="link">Source</a></p><div class="doc"><p>A safe variant of piApply.
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