Add Coq realization for map.Map.

Makefile.in

@@ -815,13 +815,16 @@ COQLIBS_NUMBER = $(addprefix lib/coq/number/, $(COQLIBS_NUMBER_FILES))
 COQLIBS_SET_FILES = Set
 COQLIBS_SET = $(addprefix lib/coq/set/, $(COQLIBS_SET_FILES))
 
+COQLIBS_MAP_FILES = Map
+COQLIBS_MAP = $(addprefix lib/coq/map/, $(COQLIBS_MAP_FILES))
+
 ifeq (@enable_coq_fp_libs@,yes)
 COQLIBS_FP_FILES = Rounding SingleFormat Single DoubleFormat Double
 COQLIBS_FP_ALL_FILES = GenFloat $(COQLIBS_FP_FILES)
 COQLIBS_FP = $(addprefix lib/coq/floating_point/, $(COQLIBS_FP_ALL_FILES))
 endif
 
-COQLIBS_FILES = lib/coq/BuiltIn $(COQLIBS_INT) $(COQLIBS_REAL) $(COQLIBS_NUMBER) $(COQLIBS_SET) $(COQLIBS_FP)
+COQLIBS_FILES = lib/coq/BuiltIn $(COQLIBS_INT) $(COQLIBS_REAL) $(COQLIBS_NUMBER) $(COQLIBS_SET) $(COQLIBS_MAP) $(COQLIBS_FP)
 
 COQV  = $(addsuffix .v,  $(COQLIBS_FILES))
 COQVO = $(addsuffix .vo, $(COQLIBS_FILES))
@@ -847,6 +850,8 @@ drivers/coq-realizations.aux: Makefile
 	echo 'theory number.'"$$f"' meta "realized_theory" "number.'"$$f"'", "" end'; done; \
 	for f in $(COQLIBS_SET_FILES); do \
 	echo 'theory set.'"$$f"' meta "realized_theory" "set.'"$$f"'", "" end'; done; \
+	for f in $(COQLIBS_MAP_FILES); do \
+	echo 'theory map.'"$$f"' meta "realized_theory" "map.'"$$f"'", "" end'; done; \
 	for f in $(COQLIBS_FP_FILES); do \
 	echo 'theory floating_point.'"$$f"' meta "realized_theory" "floating_point.'"$$f"'", "" end'; done; \
 	) > $@
@@ -855,8 +860,8 @@ opt byte: $(COQVO)
 
 install_no_local::
 	mkdir -p $(LIBDIR)/why3/coq
-	mkdir -p $(LIBDIR)/why3/coq/int
 	cp lib/coq/BuiltIn.vo $(LIBDIR)/why3/coq/
+	mkdir -p $(LIBDIR)/why3/coq/int
 	cp $(addsuffix .vo, $(COQLIBS_INT)) $(LIBDIR)/why3/coq/int/
 	mkdir -p $(LIBDIR)/why3/coq/real
 	cp $(addsuffix .vo, $(COQLIBS_REAL)) $(LIBDIR)/why3/coq/real/
@@ -864,6 +869,8 @@ install_no_local::
 	cp $(addsuffix .vo, $(COQLIBS_NUMBER)) $(LIBDIR)/why3/coq/number/
 	mkdir -p $(LIBDIR)/why3/coq/set
 	cp $(addsuffix .vo, $(COQLIBS_SET)) $(LIBDIR)/why3/coq/set/
+	mkdir -p $(LIBDIR)/why3/coq/map
+	cp $(addsuffix .vo, $(COQLIBS_MAP)) $(LIBDIR)/why3/coq/map/
 ifeq (@enable_coq_fp_libs@,yes)
 	mkdir -p $(LIBDIR)/why3/coq/floating_point
 	cp $(addsuffix .vo, $(COQLIBS_FP)) $(LIBDIR)/why3/coq/floating_point/
@@ -883,7 +890,7 @@ depend: $(COQVD)
 clean::
 	rm -f $(COQVO) $(COQVD) $(addsuffix .glob, $(COQLIBS_FILES))
 
-update-coq: update-coq-int update-coq-real update-coq-number update-coq-set update-coq-fp
+update-coq: update-coq-int update-coq-real update-coq-number update-coq-set update-coq-map update-coq-fp
 
 update-coq-int: bin/why3 drivers/coq-realizations.aux theories/int.why
 	for f in $(COQLIBS_INT_ALL_FILES); do WHY3CONFIG="" bin/why3.@OCAMLBEST@ --realize -L theories -D drivers/coq-realize.drv -T int.$$f -o lib/coq/int/; done
@@ -897,6 +904,9 @@ update-coq-number: bin/why3 drivers/coq-realizations.aux theories/number.why
 update-coq-set: bin/why3 drivers/coq-realizations.aux theories/set.why
 	for f in $(COQLIBS_SET_FILES); do WHY3CONFIG="" bin/why3.@OCAMLBEST@ --realize -L theories -D drivers/coq-realize.drv -T set.$$f -o lib/coq/set/; done
 
+update-coq-map: bin/why3 drivers/coq-realizations.aux theories/map.why
+	for f in $(COQLIBS_MAP_FILES); do WHY3CONFIG="" bin/why3.@OCAMLBEST@ --realize -L theories -D drivers/coq-realize.drv -T map.$$f -o lib/coq/map/; done
+
 update-coq-fp: bin/why3 drivers/coq-realizations.aux theories/floating_point.why
 	for f in $(COQLIBS_FP_FILES); do WHY3CONFIG="" bin/why3.@OCAMLBEST@ --realize -L theories -D drivers/coq-realize.drv -T floating_point.$$f -o lib/coq/floating_point/; done
 

lib/coq/map/Map.v

+(* This file is generated by Why3's Coq-realize driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import BuiltIn.
+Require BuiltIn.
+
+Require Import ClassicalEpsilon.
+
+Inductive _map (a b:Type) :=
+  | _map_constr : (a -> b) -> _map a b.
+
+(* Why3 goal *)
+Definition map : forall (a:Type) {a_WT:WhyType a} (b:Type) {b_WT:WhyType b},
+  Type.
+intros.
+exact (_map a b).
+Defined.
+
+Global Instance map_WhyType : forall (a:Type) {a_WT:WhyType a} (b:Type) {b_WT:WhyType b}, WhyType (map a b).
+Proof.
+intros.
+repeat split.
+exact (fun _ => why_inhabitant).
+intros x y.
+apply excluded_middle_informative.
+Qed.
+
+(* Why3 goal *)
+Definition get: forall {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b},
+  (map a b) -> a -> b.
+intros a a_WT b b_WT (m) x.
+exact (m x).
+Defined.
+
+(* Why3 goal *)
+Definition set: forall {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b},
+  (map a b) -> a -> b -> (map a b).
+intros a a_WT b b_WT (m) x y.
+split.
+intros x'.
+destruct (why_decidable_eq x x') as [H|H].
+exact y.
+exact (m x').
+Defined.
+
+(* Why3 goal *)
+Lemma Select_eq : forall {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b},
+  forall (m:(map a b)), forall (a1:a) (a2:a), forall (b1:b), (a1 = a2) ->
+  ((get (set m a1 b1) a2) = b1).
+Proof.
+intros a a_WT b b_WT (m) a1 a2 b1 h1.
+unfold get, set.
+now case why_decidable_eq.
+Qed.
+
+(* Why3 goal *)
+Lemma Select_neq : forall {a:Type} {a_WT:WhyType a}
+  {b:Type} {b_WT:WhyType b}, forall (m:(map a b)), forall (a1:a) (a2:a),
+  forall (b1:b), (~ (a1 = a2)) -> ((get (set m a1 b1) a2) = (get m a2)).
+Proof.
+intros a a_WT b b_WT (m) a1 a2 b1 h1.
+unfold get, set.
+now case why_decidable_eq.
+Qed.
+
+(* Why3 goal *)
+Definition const: forall {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b},
+  b -> (map a b).
+intros a a_WT b b_WT y.
+exact (_map_constr _ _ (fun _ => y)).
+Defined.
+
+(* Why3 goal *)
+Lemma Const : forall {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b},
+  forall (b1:b) (a1:a), ((get (const b1:(map a b)) a1) = b1).
+Proof.
+easy.
+Qed.
+
+