add simpl.v

.gitattributes

+*.v gitlab-language=coq
+
+# Convert to native line endings on checkout.
+*.ref text
+# Shell scripts need Linux line endings.
+*.sh eol=lf

.gitignore

+*.vo
+*.vos
+*.vok
+*.vio
+*.v.d
+.coqdeps.d
+*.glob
+*.cache
+*.aux
+\#*\#
+.\#*
+*~
+*.bak
+.coqdeps.d
+.coq-native/
+*.crashcoqide
+.env
+builddep/
+_CoqProject.*
+Makefile.coq
+Makefile.coq.conf
+.Makefile.coq.d
+Makefile.package.*
+.Makefile.package.*

Makefile

+# Default target
+all: Makefile.coq
+	+@$(MAKE) -f Makefile.coq all
+.PHONY: all
+
+# Permit local customization
+-include Makefile.local
+
+# Forward most targets to Coq makefile (with some trick to make this phony)
+%: Makefile.coq phony
+	@#echo "Forwarding $@"
+	+@$(MAKE) -f Makefile.coq $@
+phony: ;
+.PHONY: phony
+
+clean: Makefile.coq
+	+@$(MAKE) -f Makefile.coq clean
+	@# Make sure not to enter the `_opam` folder.
+	find [a-z]*/ \( -name "*.d" -o -name "*.vo" -o -name "*.vo[sk]" -o -name "*.aux" -o -name "*.cache" -o -name "*.glob" -o -name "*.vio" \) -print -delete || true
+	rm -f Makefile.coq .lia.cache builddep/*
+.PHONY: clean
+
+# Create Coq Makefile.
+Makefile.coq: _CoqProject Makefile
+	"$(COQBIN)coq_makefile" -f _CoqProject -o Makefile.coq $(EXTRA_COQFILES)
+
+# Install build-dependencies
+OPAMFILES=$(wildcard *.opam)
+BUILDDEPFILES=$(addsuffix -builddep.opam, $(addprefix builddep/,$(basename $(OPAMFILES))))
+
+builddep/%-builddep.opam: %.opam Makefile
+	@echo "# Creating builddep package for $<."
+	@mkdir -p builddep
+	@sed <$< -E 's/^(build|install|remove):.*/\1: []/; s/"(.*)"(.*= *version.*)$$/"\1-builddep"\2/;' >$@
+
+builddep-opamfiles: $(BUILDDEPFILES)
+.PHONY: builddep-opamfiles
+
+builddep: builddep-opamfiles
+	@# We want opam to not just install the build-deps now, but to also keep satisfying these
+	@# constraints.  Otherwise, `opam upgrade` may well update some packages to versions
+	@# that are incompatible with our build requirements.
+	@# To achieve this, we create a fake opam package that has our build-dependencies as
+	@# dependencies, but does not actually install anything itself.
+	@echo "# Installing builddep packages."
+	@opam install $(OPAMFLAGS) $(BUILDDEPFILES)
+.PHONY: builddep
+
+# Backwards compatibility target
+build-dep: builddep
+.PHONY: build-dep
+
+# Some files that do *not* need to be forwarded to Makefile.coq.
+# ("::" lets Makefile.local overwrite this.)
+Makefile Makefile.local _CoqProject $(OPAMFILES):: ;

README.md

 # Coq Tricks
 
+This repository contain a collection of interesting tricks and facts about Coq that were useful during the development of Iris.
+
+- [simpl.v](theories/simpl.v): `simpl` and similar reduction insert casts even if they do not change the goal which can slow down Qed.

_CoqProject

+# We sometimes want to locally override notation, and there is no good way to do that with scopes.
+-arg -w -arg -notation-overridden
+# Cannot use non-canonical projections as it causes massive unification failures
+# (https://github.com/coq/coq/issues/6294).
+-arg -w -arg -redundant-canonical-projection
+# Search paths for all packages. They must all match the regex
+
+-Q theories tricks
+
+theories/simpl.v
\ No newline at end of file

theories/simpl.v

+(** [simpl] and other reduction tactics inserts casts in the goal even
+if they don't change the goal. This can lead to a slower Coq. To avoid
+this behaviour, one can use [try progress simpl] instead of [simpl].
+
+See also the discussion at
+https://coq.zulipchat.com/#narrow/stream/237656-Coq-devs.20.26.20plugin.20devs/topic/exact_no_check.2C.20repeated.20casts.20in.20proof.20terms
+and https://github.com/coq/coq/pull/15104 *)
+
+Goal 1 = 1.
+  Set Printing All.
+  Show Proof.
+  (** => ?Goal *)
+  simpl.
+  Show Proof.
+  (** => (?Goal : @eq nat (S O) (S O))
+   Notice the cast. *)
+  Undo.
+  Show Proof.
+  (** => ?Goal *)
+  try progress simpl.
+  Show Proof.
+  (** => ?Goal.
+    Notice that there is no cast *)
+Abort.