diff --git a/Formula/ghc.rb b/Formula/ghc.rb
index ed3ff473d024..bbc72238b787 100644
--- a/Formula/ghc.rb
+++ b/Formula/ghc.rb
@@ -4,6 +4,7 @@ class Ghc < Formula
   url "https://downloads.haskell.org/~ghc/8.10.3/ghc-8.10.3-src.tar.xz"
   sha256 "ccdc8319549028a708d7163e2967382677b1a5a379ff94d948195b5cf46eb931"
   license "BSD-3-Clause"
+  revision 1
 
   livecheck do
     url "https://www.haskell.org/ghc/download.html"
@@ -20,10 +21,10 @@ class Ghc < Formula
   depends_on "sphinx-doc" => :build
 
   resource "gmp" do
-    url "https://ftp.gnu.org/gnu/gmp/gmp-6.2.1.tar.xz"
-    mirror "https://gmplib.org/download/gmp/gmp-6.2.1.tar.xz"
-    mirror "https://ftpmirror.gnu.org/gmp/gmp-6.2.1.tar.xz"
-    sha256 "fd4829912cddd12f84181c3451cc752be224643e87fac497b69edddadc49b4f2"
+    url "https://ftp.gnu.org/gnu/gmp/gmp-6.2.1.tar.bz2"
+    mirror "https://gmplib.org/download/gmp/gmp-6.2.1.tar.bz2"
+    mirror "https://ftpmirror.gnu.org/gmp/gmp-6.2.1.tar.bz2"
+    sha256 "eae9326beb4158c386e39a356818031bd28f3124cf915f8c5b1dc4c7a36b4d7c"
   end
 
   # https://www.haskell.org/ghc/download_ghc_8_10_1.html#macosx_x86_64
@@ -41,26 +42,19 @@ class Ghc < Formula
     end
   end
 
+  # Fixes for macOS ARM
+  # https://gitlab.haskell.org/ghc/ghc/-/merge_requests/4795
+  patch do
+    url "https://raw.githubusercontent.com/Homebrew/formula-patches/f6c5879312437dd58087e4885a86ac536a128ea9/ghc/ghc-8.10.3.patch"
+    sha256 "7aee4d6eeb37676450c84da6205e79b5ff8c9f2d4e5763f5bbf5b1c990d002b3"
+  end
+
   def install
     ENV["CC"] = ENV.cc
     ENV["LD"] = "ld"
     ENV["PYTHON"] = Formula["python@3.9"].opt_bin/"python3"
 
-    # Build a static gmp rather than in-tree gmp, otherwise all ghc-compiled
-    # executables link to Homebrew's GMP.
-    gmp = libexec/"integer-gmp"
-
-    # GMP *does not* use PIC by default without shared libs so --with-pic
-    # is mandatory or else you'll get "illegal text relocs" errors.
-    resource("gmp").stage do
-      system "./configure", "--prefix=#{gmp}", "--with-pic", "--disable-shared",
-                            "--build=#{Hardware.oldest_cpu}-apple-darwin#{OS.kernel_version.major}"
-      system "make"
-      system "make", "install"
-    end
-
-    args = ["--with-gmp-includes=#{gmp}/include",
-            "--with-gmp-libraries=#{gmp}/lib"]
+    args = []
 
     resource("binary").stage do
       binary = buildpath/"binary"
@@ -68,7 +62,69 @@ def install
       system "./configure", "--prefix=#{binary}", *args
       ENV.deparallelize { system "make", "install" }
 
-      ENV.prepend_path "PATH", binary/"bin"
+      ENV["GHC"] = binary/"bin/ghc"
+    end
+
+    cpu = if Hardware::CPU.arm?
+      "arm64"
+    else
+      Hardware.oldest_cpu
+    end
+
+    # Replace in-tree gmp with 6.2.1 which supports arm64.
+    rm "libraries/integer-gmp/gmp/gmp-tarballs/gmp-6.1.2-nodoc.tar.bz2", force: true
+    cp resource("gmp").cached_download, "libraries/integer-gmp/gmp/gmp-tarballs/gmp-6.2.1-nodoc.tar.bz2"
+
+    # There is no native codegen for ARM64 yet.
+    if Hardware::CPU.arm?
+      args << "--enable-unregisterised"
+
+      # The Xcode compiler is a cross compiler (ARM64/x86_64) but ghc's configure script will look for
+      # the standard tool names. Go ahead and create the required names. We can not just use symbolic
+      # links for gcc, nm, or ar as this confuses the command line tools.
+
+      tmp = buildpath/"binary-cross"
+
+      tmpbin = tmp/"bin"
+      mkdir_p tmpbin
+
+      make_contents = lambda { |command|
+        <<~EOF
+          #!/bin/bash
+          /usr/bin/#{command} $@
+        EOF
+      }
+
+      File.write(tmpbin/"#{cpu}-apple-darwin-nm", make_contents.call("nm"), { perm: 0755 })
+      File.write(tmpbin/"#{cpu}-apple-darwin-ar", make_contents.call("ar"), { perm: 0755 })
+      # This gcc forces ARM64 as the target. It may be invoked by an x86_64 binary (which would have
+      # selected x86_64 which is not what we want.
+      File.write(tmpbin/"#{cpu}-apple-darwin-gcc", make_contents.call("gcc -arch arm64"), { perm: 0755 })
+
+      ENV.prepend_path "PATH", tmpbin
+
+      # Basic build setup for the cross compile. This is based on the documentation for building a
+      # cross compiler for targetting iOS.
+      (buildpath/"mk/build.mk").write <<~EOS
+        BuildFlavour = perf-cross
+        HADDOCK_DOCS = NO
+      EOS
+
+      ENV["CC"] = "#{cpu}-apple-darwin-gcc"
+
+      # Run configure as x86_64 to ensure it correctly detects the build host as x86_64. Otherwise it might
+      # not cross-compile correctly.
+      system "arch", "-x86_64", "./configure", "--prefix=#{tmp}", "--target=#{cpu}-apple-darwin", *args
+      system "make"
+
+      ENV.deparallelize { system "make", "install" }
+
+      # clean up before rebuilding
+      system "make", "distclean"
+      rm "#{buildpath}/mk/build.mk", force: true
+
+      ENV["CC"] = ENV.cc
+      ENV["GHC"] = tmp/"bin/ghc"
     end
 
     system "./configure", "--prefix=#{prefix}", *args