Removed compat tests.
--- a/Nominal/Test_compat.thy Tue Mar 23 08:11:39 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,653 +0,0 @@
-theory Test_compat
-imports "Parser" "../Attic/Prove"
-begin
-
-text {*
- example 1
-
- single let binding
-*}
-
-nominal_datatype lam =
- VAR "name"
-| APP "lam" "lam"
-| LET bp::"bp" t::"lam" bind "bi bp" in t
-and bp =
- BP "name" "lam"
-binder
- bi::"bp \<Rightarrow> atom set"
-where
- "bi (BP x t) = {atom x}"
-
-thm alpha_lam_raw_alpha_bp_raw.intros[no_vars]
-thm fv_lam_raw_fv_bp_raw.simps[no_vars]
-
-abbreviation "VAR \<equiv> VAR_raw"
-abbreviation "APP \<equiv> APP_raw"
-abbreviation "LET \<equiv> LET_raw"
-abbreviation "BP \<equiv> BP_raw"
-abbreviation "bi \<equiv> bi_raw"
-
-(* non-recursive case *)
-primrec
- fv_lam :: "lam_raw \<Rightarrow> atom set"
-and fv_compat :: "bp_raw \<Rightarrow> atom set"
-where
- "fv_lam (VAR name) = {atom name}"
-| "fv_lam (APP lam1 lam2) = fv_lam lam1 \<union> fv_lam lam2"
-| "fv_lam (LET bp lam) = (fv_compat bp) \<union> (fv_lam lam - bi bp)"
-| "fv_compat (BP name lam) = fv_lam lam"
-
-primrec
- fv_bp :: "bp_raw \<Rightarrow> atom set"
-where
- "fv_bp (BP name lam) = {atom name} \<union> fv_lam lam"
-
-
-inductive
- alpha_lam :: "lam_raw \<Rightarrow> lam_raw \<Rightarrow> bool" and
- alpha_bp :: "bp_raw \<Rightarrow> bp_raw \<Rightarrow> bool" and
- compat_bp :: "bp_raw \<Rightarrow> perm \<Rightarrow> bp_raw \<Rightarrow> bool"
-where
- "x = y \<Longrightarrow> alpha_lam (VAR x) (VAR y)"
-| "alpha_lam l1 s1 \<and> alpha_lam l2 s2 \<Longrightarrow> alpha_lam (APP l1 l2) (APP s1 s2)"
-| "\<exists>pi. (bi bp, lam) \<approx>gen alpha_lam fv_lam_raw pi (bi bp', lam') \<and> compat_bp bp pi bp'
- \<Longrightarrow> alpha_lam (LET bp lam) (LET bp' lam')"
-| "alpha_lam lam lam' \<and> name = name' \<Longrightarrow> alpha_bp (BP name lam) (BP name' lam')"
-| "alpha_lam t t' \<and> pi \<bullet> x = x' \<Longrightarrow> compat_bp (BP x t) pi (BP x' t')"
-
-lemma test1:
- shows "alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR x)) (VAR y))"
-apply(rule alpha_lam_alpha_bp_compat_bp.intros)
-apply(rule_tac x="(x \<leftrightarrow> y)" in exI)
-apply(simp add: alpha_gen fresh_star_def)
-apply(simp add: alpha_lam_alpha_bp_compat_bp.intros(1))
-apply(rule alpha_lam_alpha_bp_compat_bp.intros)
-apply(simp add: alpha_lam_alpha_bp_compat_bp.intros(1))
-done
-
-lemma test2:
- assumes asm: "distinct [x, y]"
- shows "\<not> alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR y)) (VAR y))"
-using asm
-apply(clarify)
-apply(erule alpha_lam.cases)
-apply(simp_all)
-apply(erule exE)
-apply(clarify)
-apply(simp add: alpha_gen fresh_star_def)
-apply(erule alpha_lam.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule compat_bp.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule alpha_lam.cases)
-apply(simp_all)
-done
-
-(* recursive case where we have also bind "bi bp" in bp *)
-
-inductive
- Alpha_lam :: "lam_raw \<Rightarrow> lam_raw \<Rightarrow> bool" and
- Alpha_bp :: "bp_raw \<Rightarrow> bp_raw \<Rightarrow> bool" and
- Compat_bp :: "bp_raw \<Rightarrow> perm \<Rightarrow> bp_raw \<Rightarrow> bool"
-where
- "x = y \<Longrightarrow> Alpha_lam (VAR x) (VAR y)"
-| "Alpha_lam l1 s1 \<and> Alpha_lam l2 s2 \<Longrightarrow> Alpha_lam (APP l1 l2) (APP s1 s2)"
-| "\<exists>pi. (bi bp, lam) \<approx>gen Alpha_lam fv_lam_raw pi (bi bp', lam') \<and> Compat_bp bp pi bp'
- \<Longrightarrow> Alpha_lam (LET bp lam) (LET bp' lam')"
-| "Alpha_lam lam lam' \<and> name = name' \<Longrightarrow> Alpha_bp (BP name lam) (BP name' lam')"
-| "Alpha_lam (pi \<bullet> t) t' \<and> pi \<bullet> x = x' \<Longrightarrow> Compat_bp (BP x t) pi (BP x' t')"
-
-lemma Test1:
- assumes "distinct [x, y]"
- shows "Alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR y)) (VAR y))"
-apply(rule Alpha_lam_Alpha_bp_Compat_bp.intros)
-apply(rule_tac x="(x \<leftrightarrow> y)" in exI)
-apply(simp add: alpha_gen fresh_star_def)
-apply(simp add: Alpha_lam_Alpha_bp_Compat_bp.intros(1))
-apply(rule Alpha_lam_Alpha_bp_Compat_bp.intros)
-apply(simp add: Alpha_lam_Alpha_bp_Compat_bp.intros(1))
-done
-
-lemma Test2:
- assumes asm: "distinct [x, y]"
- shows "\<not> Alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR x)) (VAR y))"
-using asm
-apply(clarify)
-apply(erule Alpha_lam.cases)
-apply(simp_all)
-apply(erule exE)
-apply(clarify)
-apply(simp add: alpha_gen fresh_star_def)
-apply(erule Alpha_lam.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule Compat_bp.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule Alpha_lam.cases)
-apply(simp_all)
-done
-
-
-text {* example 2 *}
-
-nominal_datatype trm' =
- Var "name"
-| App "trm'" "trm'"
-| Lam x::"name" t::"trm'" bind x in t
-| Let p::"pat'" "trm'" t::"trm'" bind "f p" in t
-and pat' =
- PN
-| PS "name"
-| PD "name" "name"
-binder
- f::"pat' \<Rightarrow> atom set"
-where
- "f PN = {}"
-| "f (PS x) = {atom x}"
-| "f (PD x y) = {atom x} \<union> {atom y}"
-
-thm alpha_trm'_raw_alpha_pat'_raw.intros[no_vars]
-
-abbreviation "Var \<equiv> Var_raw"
-abbreviation "App \<equiv> App_raw"
-abbreviation "Lam \<equiv> Lam_raw"
-abbreviation "Lett \<equiv> Let_raw"
-abbreviation "PN \<equiv> PN_raw"
-abbreviation "PS \<equiv> PS_raw"
-abbreviation "PD \<equiv> PD_raw"
-abbreviation "f \<equiv> f_raw"
-
-(* not_yet_done *)
-inductive
- alpha_trm' :: "trm'_raw \<Rightarrow> trm'_raw \<Rightarrow> bool" and
- alpha_pat' :: "pat'_raw \<Rightarrow> pat'_raw \<Rightarrow> bool" and
- compat_pat' :: "pat'_raw \<Rightarrow> perm \<Rightarrow> pat'_raw \<Rightarrow> bool"
-where
- "name = name' \<Longrightarrow> alpha_trm' (Var name) (Var name')"
-| "alpha_trm' t2 t2' \<and> alpha_trm' t1 t1' \<Longrightarrow> alpha_trm' (App t1 t2) (App t1' t2')"
-| "\<exists>pi. ({atom x}, t) \<approx>gen alpha_trm' fv_trm'_raw pi ({atom x'}, t') \<Longrightarrow> alpha_trm' (Lam x t) (Lam x' t')"
-| "\<exists>pi. (f p, t) \<approx>gen alpha_trm' fv_trm'_raw pi (f p', t') \<and> alpha_trm' s s' \<and>
- compat_pat' p pi p' \<Longrightarrow> alpha_trm' (Lett p s t) (Lett p' s' t')"
-| "alpha_pat' PN PN"
-| "name = name' \<Longrightarrow> alpha_pat' (PS name) (PS name')"
-| "name2 = name2' \<and> name1 = name1' \<Longrightarrow> alpha_pat' (PD name1 name2) (PD name1' name2')"
-| "compat_pat' PN pi PN"
-| "pi \<bullet> x = x' \<Longrightarrow> compat_pat' (PS x) pi (PS x')"
-| "pi \<bullet> p1 = p1' \<and> pi \<bullet> p2 = p2' \<Longrightarrow> compat_pat' (PD p1 p2) pi (PD p1' p2')"
-
-lemma
- assumes a: "distinct [x, y, z, u]"
- shows "alpha_trm' (Lett (PD x u) t (App (Var x) (Var y)))
- (Lett (PD z u) t (App (Var z) (Var y)))"
-using a
-apply -
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(auto simp add: alpha_gen)
-apply(rule_tac x="(x \<leftrightarrow> z)" in exI)
-apply(auto simp add: fresh_star_def)
-defer
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(simp add: alpha_trm'_alpha_pat'_compat_pat'.intros)
-defer
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(simp)
-(* they can be proved *)
-oops
-
-lemma
- assumes a: "distinct [x, y, z, u]"
- shows "\<not> alpha_trm' (Lett (PD x u) t (App (Var x) (Var y)))
- (Lett (PD z z) t (App (Var z) (Var y)))"
-using a
-apply(clarify)
-apply(erule alpha_trm'.cases)
-apply(simp_all)
-apply(auto simp add: alpha_gen)
-apply(erule alpha_trm'.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule compat_pat'.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule alpha_trm'.cases)
-apply(simp_all)
-done
-
-nominal_datatype trm0 =
- Var0 "name"
-| App0 "trm0" "trm0"
-| Lam0 x::"name" t::"trm0" bind x in t
-| Let0 p::"pat0" "trm0" t::"trm0" bind "f0 p" in t
-and pat0 =
- PN0
-| PS0 "name"
-| PD0 "pat0" "pat0"
-binder
- f0::"pat0 \<Rightarrow> atom set"
-where
- "f0 PN0 = {}"
-| "f0 (PS0 x) = {atom x}"
-| "f0 (PD0 p1 p2) = (f0 p1) \<union> (f0 p2)"
-
-thm f0_raw.simps
-(*thm trm0_pat0_induct
-thm trm0_pat0_perm
-thm trm0_pat0_fv
-thm trm0_pat0_bn*)
-
-text {* example type schemes *}
-
-(* does not work yet
-nominal_datatype t =
- Var "name"
-| Fun "t" "t"
-
-nominal_datatype tyS =
- All xs::"name list" ty::"t_raw" bind xs in ty
-*)
-
-
-nominal_datatype t =
- Var "name"
-| Fun "t" "t"
-and tyS =
- All xs::"name set" ty::"t" bind xs in ty
-
-(* example 1 from Terms.thy *)
-
-nominal_datatype trm1 =
- Vr1 "name"
-| Ap1 "trm1" "trm1"
-| Lm1 x::"name" t::"trm1" bind x in t
-| Lt1 p::"bp1" "trm1" t::"trm1" bind "bv1 p" in t
-and bp1 =
- BUnit1
-| BV1 "name"
-| BP1 "bp1" "bp1"
-binder
- bv1
-where
- "bv1 (BUnit1) = {}"
-| "bv1 (BV1 x) = {atom x}"
-| "bv1 (BP1 bp1 bp2) = (bv1 bp1) \<union> (bv1 bp2)"
-
-thm bv1_raw.simps
-
-(* example 2 from Terms.thy *)
-
-nominal_datatype trm2 =
- Vr2 "name"
-| Ap2 "trm2" "trm2"
-| Lm2 x::"name" t::"trm2" bind x in t
-| Lt2 r::"assign" t::"trm2" bind "bv2 r" in t
-and assign =
- As "name" "trm2"
-binder
- bv2
-where
- "bv2 (As x t) = {atom x}"
-
-(* compat should be
-compat (As x t) pi (As x' t') == pi o x = x' & alpha t t'
-*)
-
-
-thm fv_trm2_raw_fv_assign_raw.simps[no_vars]
-thm alpha_trm2_raw_alpha_assign_raw.intros[no_vars]
-
-
-
-text {* example 3 from Terms.thy *}
-
-nominal_datatype trm3 =
- Vr3 "name"
-| Ap3 "trm3" "trm3"
-| Lm3 x::"name" t::"trm3" bind x in t
-| Lt3 r::"rassigns3" t::"trm3" bind "bv3 r" in t
-and rassigns3 =
- ANil
-| ACons "name" "trm3" "rassigns3"
-binder
- bv3
-where
- "bv3 ANil = {}"
-| "bv3 (ACons x t as) = {atom x} \<union> (bv3 as)"
-
-
-(* compat should be
-compat (ANil) pi (PNil) \<equiv> TRue
-compat (ACons x t ts) pi (ACons x' t' ts') \<equiv> pi o x = x' \<and> alpha t t' \<and> compat ts pi ts'
-*)
-
-(* example 4 from Terms.thy *)
-
-(* fv_eqvt does not work, we need to repaire defined permute functions
- defined fv and defined alpha... *)
-nominal_datatype trm4 =
- Vr4 "name"
-| Ap4 "trm4" "trm4 list"
-| Lm4 x::"name" t::"trm4" bind x in t
-
-thm alpha_trm4_raw_alpha_trm4_raw_list.intros[no_vars]
-thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]
-
-(* example 5 from Terms.thy *)
-
-nominal_datatype trm5 =
- Vr5 "name"
-| Ap5 "trm5" "trm5"
-| Lt5 l::"lts" t::"trm5" bind "bv5 l" in t
-and lts =
- Lnil
-| Lcons "name" "trm5" "lts"
-binder
- bv5
-where
- "bv5 Lnil = {}"
-| "bv5 (Lcons n t ltl) = {atom n} \<union> (bv5 ltl)"
-
-(* example 6 from Terms.thy *)
-
-(* BV is not respectful, needs to fail*)
-nominal_datatype trm6 =
- Vr6 "name"
-| Lm6 x::"name" t::"trm6" bind x in t
-| Lt6 left::"trm6" right::"trm6" bind "bv6 left" in right
-binder
- bv6
-where
- "bv6 (Vr6 n) = {}"
-| "bv6 (Lm6 n t) = {atom n} \<union> bv6 t"
-| "bv6 (Lt6 l r) = bv6 l \<union> bv6 r"
-(* example 7 from Terms.thy *)
-
-(* BV is not respectful, needs to fail*)
-nominal_datatype trm7 =
- Vr7 "name"
-| Lm7 l::"name" r::"trm7" bind l in r
-| Lt7 l::"trm7" r::"trm7" bind "bv7 l" in r
-binder
- bv7
-where
- "bv7 (Vr7 n) = {atom n}"
-| "bv7 (Lm7 n t) = bv7 t - {atom n}"
-| "bv7 (Lt7 l r) = bv7 l \<union> bv7 r"
-
-(* example 8 from Terms.thy *)
-
-nominal_datatype foo8 =
- Foo0 "name"
-| Foo1 b::"bar8" f::"foo8" bind "bv8 b" in f --"check fo error if this is called foo"
-and bar8 =
- Bar0 "name"
-| Bar1 "name" s::"name" b::"bar8" bind s in b
-binder
- bv8
-where
- "bv8 (Bar0 x) = {}"
-| "bv8 (Bar1 v x b) = {atom v}"
-
-(* example 9 from Terms.thy *)
-
-(* BV is not respectful, needs to fail*)
-nominal_datatype lam9 =
- Var9 "name"
-| Lam9 n::"name" l::"lam9" bind n in l
-and bla9 =
- Bla9 f::"lam9" s::"lam9" bind "bv9 f" in s
-binder
- bv9
-where
- "bv9 (Var9 x) = {}"
-| "bv9 (Lam9 x b) = {atom x}"
-
-(* example from my PHD *)
-
-atom_decl coname
-
-nominal_datatype phd =
- Ax "name" "coname"
-| Cut n::"coname" t1::"phd" c::"coname" t2::"phd" bind n in t1, bind c in t2
-| AndR c1::"coname" t1::"phd" c2::"coname" t2::"phd" "coname" bind c1 in t1, bind c2 in t2
-| AndL1 n::"name" t::"phd" "name" bind n in t
-| AndL2 n::"name" t::"phd" "name" bind n in t
-| ImpL c::"coname" t1::"phd" n::"name" t2::"phd" "name" bind c in t1, bind n in t2
-| ImpR c::"coname" n::"name" t::"phd" "coname" bind n in t, bind c in t
-
-thm alpha_phd_raw.intros[no_vars]
-thm fv_phd_raw.simps[no_vars]
-
-
-(* example form Leroy 96 about modules; OTT *)
-
-nominal_datatype mexp =
- Acc "path"
-| Stru "body"
-| Funct x::"name" "sexp" m::"mexp" bind x in m
-| FApp "mexp" "path"
-| Ascr "mexp" "sexp"
-and body =
- Empty
-| Seq c::defn d::"body" bind "cbinders c" in d
-and defn =
- Type "name" "tyty"
-| Dty "name"
-| DStru "name" "mexp"
-| Val "name" "trmtrm"
-and sexp =
- Sig sbody
-| SFunc "name" "sexp" "sexp"
-and sbody =
- SEmpty
-| SSeq C::spec D::sbody bind "Cbinders C" in D
-and spec =
- Type1 "name"
-| Type2 "name" "tyty"
-| SStru "name" "sexp"
-| SVal "name" "tyty"
-and tyty =
- Tyref1 "name"
-| Tyref2 "path" "tyty"
-| Fun "tyty" "tyty"
-and path =
- Sref1 "name"
-| Sref2 "path" "name"
-and trmtrm =
- Tref1 "name"
-| Tref2 "path" "name"
-| Lam' v::"name" "tyty" M::"trmtrm" bind v in M
-| App' "trmtrm" "trmtrm"
-| Let' "body" "trmtrm"
-binder
- cbinders :: "defn \<Rightarrow> atom set"
-and Cbinders :: "spec \<Rightarrow> atom set"
-where
- "cbinders (Type t T) = {atom t}"
-| "cbinders (Dty t) = {atom t}"
-| "cbinders (DStru x s) = {atom x}"
-| "cbinders (Val v M) = {atom v}"
-| "Cbinders (Type1 t) = {atom t}"
-| "Cbinders (Type2 t T) = {atom t}"
-| "Cbinders (SStru x S) = {atom x}"
-| "Cbinders (SVal v T) = {atom v}"
-
-(* core haskell *)
-print_theorems
-
-atom_decl var
-atom_decl tvar
-
-
-(* there are types, coercion types and regular types *)
-nominal_datatype tkind =
- KStar
-| KFun "tkind" "tkind"
-and ckind =
- CKEq "ty" "ty"
-and ty =
- TVar "tvar"
-| TC "string"
-| TApp "ty" "ty"
-| TFun "string" "ty list"
-| TAll tv::"tvar" "tkind" T::"ty" bind tv in T
-| TEq "ty" "ty" "ty"
-and co =
- CC "string"
-| CApp "co" "co"
-| CFun "string" "co list"
-| CAll tv::"tvar" "ckind" C::"co" bind tv in C
-| CEq "co" "co" "co"
-| CSym "co"
-| CCir "co" "co"
-| CLeft "co"
-| CRight "co"
-| CSim "co"
-| CRightc "co"
-| CLeftc "co"
-| CCoe "co" "co"
-
-
-typedecl ty --"hack since ty is not yet defined"
-
-abbreviation
- "atoms A \<equiv> atom ` A"
-
-nominal_datatype trm =
- Var "var"
-| C "string"
-| LAM tv::"tvar" "kind" t::"trm" bind tv in t
-| APP "trm" "ty"
-| Lam v::"var" "ty" t::"trm" bind v in t
-| App "trm" "trm"
-| Let x::"var" "ty" "trm" t::"trm" bind x in t
-| Case "trm" "assoc list"
-| Cast "trm" "ty" --"ty is supposed to be a coercion type only"
-and assoc =
- A p::"pat" t::"trm" bind "bv p" in t
-and pat =
- K "string" "(tvar \<times> kind) list" "(var \<times> ty) list"
-binder
- bv :: "pat \<Rightarrow> atom set"
-where
- "bv (K s ts vs) = (atoms (set (map fst ts))) \<union> (atoms (set (map fst vs)))"
-
-(*
-compat (K s ts vs) pi (K s' ts' vs') ==
- s = s' &
-
-*)
-
-
-(*thm bv_raw.simps*)
-
-(* example 3 from Peter Sewell's bestiary *)
-nominal_datatype exp =
- VarP "name"
-| AppP "exp" "exp"
-| LamP x::"name" e::"exp" bind x in e
-| LetP x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1
-and pat =
- PVar "name"
-| PUnit
-| PPair "pat" "pat"
-binder
- bp :: "pat \<Rightarrow> atom set"
-where
- "bp (PVar x) = {atom x}"
-| "bp (PUnit) = {}"
-| "bp (PPair p1 p2) = bp p1 \<union> bp p2"
-thm alpha_exp_raw_alpha_pat_raw.intros
-
-(* example 6 from Peter Sewell's bestiary *)
-nominal_datatype exp6 =
- EVar name
-| EPair exp6 exp6
-| ELetRec x::name p::pat6 e1::exp6 e2::exp6 bind x in e1, bind x in e2, bind "bp6 p" in e1
-and pat6 =
- PVar' name
-| PUnit'
-| PPair' pat6 pat6
-binder
- bp6 :: "pat6 \<Rightarrow> atom set"
-where
- "bp6 (PVar' x) = {atom x}"
-| "bp6 (PUnit') = {}"
-| "bp6 (PPair' p1 p2) = bp6 p1 \<union> bp6 p2"
-thm alpha_exp6_raw_alpha_pat6_raw.intros
-
-(* example 7 from Peter Sewell's bestiary *)
-nominal_datatype exp7 =
- EVar name
-| EUnit
-| EPair exp7 exp7
-| ELetRec l::lrbs e::exp7 bind "b7s l" in e, bind "b7s l" in l
-and lrb =
- Assign name exp7
-and lrbs =
- Single lrb
-| More lrb lrbs
-binder
- b7 :: "lrb \<Rightarrow> atom set" and
- b7s :: "lrbs \<Rightarrow> atom set"
-where
- "b7 (Assign x e) = {atom x}"
-| "b7s (Single a) = b7 a"
-| "b7s (More a as) = (b7 a) \<union> (b7s as)"
-thm alpha_exp7_raw_alpha_lrb_raw_alpha_lrbs_raw.intros
-
-(* example 8 from Peter Sewell's bestiary *)
-nominal_datatype exp8 =
- EVar name
-| EUnit
-| EPair exp8 exp8
-| ELetRec l::lrbs8 e::exp8 bind "b_lrbs8 l" in e, bind "b_lrbs8 l" in l
-and fnclause =
- K x::name p::pat8 e::exp8 bind "b_pat p" in e
-and fnclauses =
- S fnclause
-| ORs fnclause fnclauses
-and lrb8 =
- Clause fnclauses
-and lrbs8 =
- Single lrb8
-| More lrb8 lrbs8
-and pat8 =
- PVar name
-| PUnit
-| PPair pat8 pat8
-binder
- b_lrbs8 :: "lrbs8 \<Rightarrow> atom set" and
- b_pat :: "pat8 \<Rightarrow> atom set" and
- b_fnclauses :: "fnclauses \<Rightarrow> atom set" and
- b_fnclause :: "fnclause \<Rightarrow> atom set" and
- b_lrb8 :: "lrb8 \<Rightarrow> atom set"
-where
- "b_lrbs8 (Single l) = b_lrb8 l"
-| "b_lrbs8 (More l ls) = b_lrb8 l \<union> b_lrbs8 ls"
-| "b_pat (PVar x) = {atom x}"
-| "b_pat (PUnit) = {}"
-| "b_pat (PPair p1 p2) = b_pat p1 \<union> b_pat p2"
-| "b_fnclauses (S fc) = (b_fnclause fc)"
-| "b_fnclauses (ORs fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"
-| "b_lrb8 (Clause fcs) = (b_fnclauses fcs)"
-| "b_fnclause (K x pat exp8) = {atom x}"
-thm alpha_exp8_raw_alpha_fnclause_raw_alpha_fnclauses_raw_alpha_lrb8_raw_alpha_lrbs8_raw_alpha_pat8_raw.intros
-
-
-
-
-(* example 9 from Peter Sewell's bestiary *)
-(* run out of steam at the moment *)
-
-end
-
-
-
--- a/Nominal/Test_compat1.thy Tue Mar 23 08:11:39 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,692 +0,0 @@
-theory Test_compat
-imports "Parser" "../Attic/Prove"
-begin
-
-text {*
- example 1
-
- single let binding
-*}
-
-nominal_datatype lam =
- VAR "name"
-| APP "lam" "lam"
-| LET bp::"bp" t::"lam" bind "bi bp" in t
-and bp =
- BP "name" "lam"
-binder
- bi::"bp \<Rightarrow> atom set"
-where
- "bi (BP x t) = {atom x}"
-
-thm alpha_lam_raw_alpha_bp_raw.intros[no_vars]
-
-abbreviation "VAR \<equiv> VAR_raw"
-abbreviation "APP \<equiv> APP_raw"
-abbreviation "LET \<equiv> LET_raw"
-abbreviation "BP \<equiv> BP_raw"
-abbreviation "bi \<equiv> bi_raw"
-
-(* non-recursive case *)
-
-fun
- fv_lam
-and fv_bi
-and fv_bp
-where
- "fv_lam (VAR name) = {atom name}"
-| "fv_lam (APP lam1 lam2) = fv_lam lam1 \<union> fv_lam lam2"
-| "fv_lam (LET bp lam) = (fv_bi bp) \<union> (fv_lam lam - bi bp)"
-| "fv_bi (BP name lam) = fv_lam lam"
-| "fv_bp (BP name lam) = {atom name} \<union> fv_lam lam"
-
-inductive
- alpha_lam :: "lam_raw \<Rightarrow> lam_raw \<Rightarrow> bool" and
- alpha_bp :: "bp_raw \<Rightarrow> bp_raw \<Rightarrow> bool" and
- alpha_bi :: "bp_raw \<Rightarrow> perm \<Rightarrow> bp_raw \<Rightarrow> bool"
-where
- "x = y \<Longrightarrow> alpha_lam (VAR x) (VAR y)"
-| "alpha_lam l1 s1 \<and> alpha_lam l2 s2 \<Longrightarrow> alpha_lam (APP l1 l2) (APP s1 s2)"
-| "\<exists>pi. (bi bp, lam) \<approx>gen alpha_lam fv_lam_raw pi (bi bp', lam') \<and> (pi \<bullet> (bi bp)) = bi bp'
- \<and> alpha_bi bp pi bp'
- \<Longrightarrow> alpha_lam (LET bp lam) (LET bp' lam')"
-| "alpha_lam lam lam' \<and> name = name' \<Longrightarrow> alpha_bp (BP name lam) (BP name' lam')"
-| "alpha_lam t t' \<Longrightarrow> alpha_bi (BP x t) pi (BP x' t')"
-
-lemma test1:
- assumes "distinct [x, y]"
- shows "alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR x)) (VAR y))"
-apply(rule alpha_lam_alpha_bp_alpha_bi.intros)
-apply(rule_tac x="(x \<leftrightarrow> y)" in exI)
-apply(simp add: alpha_gen fresh_star_def)
-apply(simp add: alpha_lam_alpha_bp_alpha_bi.intros(1))
-apply(rule conjI)
-defer
-apply(rule alpha_lam_alpha_bp_alpha_bi.intros)
-apply(simp add: alpha_lam_alpha_bp_alpha_bi.intros(1))
-apply(simp add: permute_set_eq atom_eqvt)
-done
-
-lemma test2:
- assumes asm: "distinct [x, y]"
- shows "\<not> alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR y)) (VAR y))"
-using asm
-apply(clarify)
-apply(erule alpha_lam.cases)
-apply(simp_all)
-apply(erule exE)
-apply(clarify)
-apply(simp add: alpha_gen fresh_star_def)
-apply(erule alpha_lam.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule alpha_bi.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule alpha_lam.cases)
-apply(simp_all)
-done
-
-(* recursive case where we have also bind "bi bp" in bp *)
-
-inductive
- Alpha_lam :: "lam_raw \<Rightarrow> lam_raw \<Rightarrow> bool" and
- Alpha_bp :: "bp_raw \<Rightarrow> bp_raw \<Rightarrow> bool" and
- Compat_bp :: "bp_raw \<Rightarrow> perm \<Rightarrow> bp_raw \<Rightarrow> bool"
-where
- "x = y \<Longrightarrow> Alpha_lam (VAR x) (VAR y)"
-| "Alpha_lam l1 s1 \<and> Alpha_lam l2 s2 \<Longrightarrow> Alpha_lam (APP l1 l2) (APP s1 s2)"
-| "\<exists>pi. (bi bp, lam) \<approx>gen Alpha_lam fv_lam_raw pi (bi bp', lam') \<and> Compat_bp bp pi bp'
- \<and> (pi \<bullet> (bi bp)) = bi bp'
- \<Longrightarrow> Alpha_lam (LET bp lam) (LET bp' lam')"
-| "Alpha_lam lam lam' \<and> name = name' \<Longrightarrow> Alpha_bp (BP name lam) (BP name' lam')"
-| "Alpha_lam (pi \<bullet> t) t' \<Longrightarrow> Compat_bp (BP x t) pi (BP x' t')"
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding Alpha_inj}, []), (build_alpha_inj @{thms Alpha_lam_Alpha_bp_Compat_bp.intros} @{thms lam_raw.distinct lam_raw.inject bp_raw.distinct bp_raw.inject} @{thms Alpha_lam.cases Alpha_bp.cases Compat_bp.cases} ctxt)) ctxt)) *}
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha_inj}, []), (build_alpha_inj @{thms alpha_lam_raw_alpha_bp_raw.intros} @{thms lam_raw.distinct lam_raw.inject bp_raw.distinct bp_raw.inject} @{thms alpha_lam_raw.cases alpha_bp_raw.cases} ctxt)) ctxt)) *}
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha_dis}, []), (flat (map (distinct_rel ctxt @{thms alpha_lam_raw.cases}) ([(@{thms lam_raw.distinct},@{term alpha_lam_raw})])))) ctxt)) *}
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding Alpha_dis}, []), (flat (map (distinct_rel ctxt @{thms Alpha_lam.cases}) ([(@{thms lam_raw.distinct},@{term Alpha_lam})])))) ctxt)) *}
-lemma "Alpha_lam x y = alpha_lam_raw x y"
-apply rule
-apply(induct x y rule: Alpha_lam_Alpha_bp_Compat_bp.inducts(1))
-apply(simp_all only: alpha_lam_raw_alpha_bp_raw.intros)
-apply(simp_all add: alpha_inj)
-apply(erule exE) apply(rule_tac x="pi" in exI)
-apply(simp add: alpha_gen)
-apply clarify
-apply simp
-defer
-apply(induct x y rule: alpha_lam_raw_alpha_bp_raw.inducts(1))
-apply(simp_all only: Alpha_lam_Alpha_bp_Compat_bp.intros)
-apply(simp_all add: Alpha_inj)
-apply(erule exE) apply(rule_tac x="pi" in exI)
-apply(simp add: alpha_gen)
-apply clarify
-apply simp
-oops
-
-lemma Test1:
- assumes "distinct [x, y]"
- shows "Alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR y)) (VAR y))"
-apply(rule Alpha_lam_Alpha_bp_Compat_bp.intros)
-apply(rule_tac x="(x \<leftrightarrow> y)" in exI)
-apply(simp add: alpha_gen fresh_star_def)
-apply(simp add: Alpha_lam_Alpha_bp_Compat_bp.intros(1))
-apply(rule conjI)
-apply(rule Alpha_lam_Alpha_bp_Compat_bp.intros)
-apply(simp add: Alpha_lam_Alpha_bp_Compat_bp.intros(1))
-apply(simp add: permute_set_eq atom_eqvt)
-done
-
-lemma Test2:
- assumes asm: "distinct [x, y]"
- shows "\<not> Alpha_lam (LET (BP x (VAR x)) (VAR x))
- (LET (BP y (VAR x)) (VAR y))"
-using asm
-apply(clarify)
-apply(erule Alpha_lam.cases)
-apply(simp_all)
-apply(erule exE)
-apply(clarify)
-apply(simp add: alpha_gen fresh_star_def)
-apply(erule Alpha_lam.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule Compat_bp.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule Alpha_lam.cases)
-apply(simp_all)
-done
-
-
-text {* example 2 *}
-
-nominal_datatype trm' =
- Var "name"
-| App "trm'" "trm'"
-| Lam x::"name" t::"trm'" bind x in t
-| Let p::"pat'" "trm'" t::"trm'" bind "f p" in t
-and pat' =
- PN
-| PS "name"
-| PD "name" "name"
-binder
- f::"pat' \<Rightarrow> atom set"
-where
- "f PN = {}"
-| "f (PS x) = {atom x}"
-| "f (PD x y) = {atom x} \<union> {atom y}"
-
-thm alpha_trm'_raw_alpha_pat'_raw.intros[no_vars]
-
-abbreviation "Var \<equiv> Var_raw"
-abbreviation "App \<equiv> App_raw"
-abbreviation "Lam \<equiv> Lam_raw"
-abbreviation "Lett \<equiv> Let_raw"
-abbreviation "PN \<equiv> PN_raw"
-abbreviation "PS \<equiv> PS_raw"
-abbreviation "PD \<equiv> PD_raw"
-abbreviation "f \<equiv> f_raw"
-
-(* not_yet_done *)
-inductive
- alpha_trm' :: "trm'_raw \<Rightarrow> trm'_raw \<Rightarrow> bool" and
- alpha_pat' :: "pat'_raw \<Rightarrow> pat'_raw \<Rightarrow> bool" and
- compat_pat' :: "pat'_raw \<Rightarrow> perm \<Rightarrow> pat'_raw \<Rightarrow> bool"
-where
- "name = name' \<Longrightarrow> alpha_trm' (Var name) (Var name')"
-| "alpha_trm' t2 t2' \<and> alpha_trm' t1 t1' \<Longrightarrow> alpha_trm' (App t1 t2) (App t1' t2')"
-| "\<exists>pi. ({atom x}, t) \<approx>gen alpha_trm' fv_trm'_raw pi ({atom x'}, t') \<Longrightarrow> alpha_trm' (Lam x t) (Lam x' t')"
-| "\<exists>pi. (f p, t) \<approx>gen alpha_trm' fv_trm'_raw pi (f p', t') \<and> alpha_trm' s s' \<and> (pi \<bullet> f p) = f p' \<and>
- compat_pat' p pi p' \<Longrightarrow> alpha_trm' (Lett p s t) (Lett p' s' t')"
-| "alpha_pat' PN PN"
-| "name = name' \<Longrightarrow> alpha_pat' (PS name) (PS name')"
-| "name2 = name2' \<and> name1 = name1' \<Longrightarrow> alpha_pat' (PD name1 name2) (PD name1' name2')"
-| "compat_pat' PN pi PN"
-| "compat_pat' (PS x) pi (PS x')"
-| "compat_pat' (PD p1 p2) pi (PD p1' p2')"
-
-lemma
- assumes a: "distinct [x, y, z, u]"
- shows "alpha_trm' (Lett (PD x u) t (App (Var x) (Var y)))
- (Lett (PD z u) t (App (Var z) (Var y)))"
-using a
-apply -
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(auto simp add: alpha_gen)
-apply(rule_tac x="(x \<leftrightarrow> z)" in exI)
-apply(auto simp add: fresh_star_def permute_set_eq atom_eqvt)
-defer
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(simp add: alpha_trm'_alpha_pat'_compat_pat'.intros)
-prefer 4
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-(* they can be proved *)
-oops
-
-lemma
- assumes a: "distinct [x, y, z, u]"
- shows "alpha_trm' (Lett (PD x u) t (App (Var x) (Var y)))
- (Lett (PD z z) t (App (Var z) (Var y)))"
-using a
-apply -
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(auto simp add: alpha_gen)
-apply(rule_tac x="(x \<leftrightarrow> z)" in exI)
-apply(auto simp add: fresh_star_def permute_set_eq atom_eqvt)
-defer
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-apply(simp add: alpha_trm'_alpha_pat'_compat_pat'.intros)
-prefer 4
-apply(rule alpha_trm'_alpha_pat'_compat_pat'.intros)
-(* they can be proved *)
-oops
-
-using a
-apply(clarify)
-apply(erule alpha_trm'.cases)
-apply(simp_all)
-apply(auto simp add: alpha_gen)
-apply(erule alpha_trm'.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule compat_pat'.cases)
-apply(simp_all)
-apply(clarify)
-apply(erule alpha_trm'.cases)
-apply(simp_all)
-done
-
-nominal_datatype trm0 =
- Var0 "name"
-| App0 "trm0" "trm0"
-| Lam0 x::"name" t::"trm0" bind x in t
-| Let0 p::"pat0" "trm0" t::"trm0" bind "f0 p" in t
-and pat0 =
- PN0
-| PS0 "name"
-| PD0 "pat0" "pat0"
-binder
- f0::"pat0 \<Rightarrow> atom set"
-where
- "f0 PN0 = {}"
-| "f0 (PS0 x) = {atom x}"
-| "f0 (PD0 p1 p2) = (f0 p1) \<union> (f0 p2)"
-
-thm f0_raw.simps
-(*thm trm0_pat0_induct
-thm trm0_pat0_perm
-thm trm0_pat0_fv
-thm trm0_pat0_bn*)
-
-text {* example type schemes *}
-
-(* does not work yet
-nominal_datatype t =
- Var "name"
-| Fun "t" "t"
-
-nominal_datatype tyS =
- All xs::"name list" ty::"t_raw" bind xs in ty
-*)
-
-
-nominal_datatype t =
- Var "name"
-| Fun "t" "t"
-and tyS =
- All xs::"name set" ty::"t" bind xs in ty
-
-(* example 1 from Terms.thy *)
-
-nominal_datatype trm1 =
- Vr1 "name"
-| Ap1 "trm1" "trm1"
-| Lm1 x::"name" t::"trm1" bind x in t
-| Lt1 p::"bp1" "trm1" t::"trm1" bind "bv1 p" in t
-and bp1 =
- BUnit1
-| BV1 "name"
-| BP1 "bp1" "bp1"
-binder
- bv1
-where
- "bv1 (BUnit1) = {}"
-| "bv1 (BV1 x) = {atom x}"
-| "bv1 (BP1 bp1 bp2) = (bv1 bp1) \<union> (bv1 bp2)"
-
-thm bv1_raw.simps
-
-(* example 2 from Terms.thy *)
-
-nominal_datatype trm2 =
- Vr2 "name"
-| Ap2 "trm2" "trm2"
-| Lm2 x::"name" t::"trm2" bind x in t
-| Lt2 r::"assign" t::"trm2" bind "bv2 r" in t
-and assign =
- As "name" "trm2"
-binder
- bv2
-where
- "bv2 (As x t) = {atom x}"
-
-(* compat should be
-compat (As x t) pi (As x' t') == pi o x = x' & alpha t t'
-*)
-
-
-thm fv_trm2_raw_fv_assign_raw.simps[no_vars]
-thm alpha_trm2_raw_alpha_assign_raw.intros[no_vars]
-
-
-
-text {* example 3 from Terms.thy *}
-
-nominal_datatype trm3 =
- Vr3 "name"
-| Ap3 "trm3" "trm3"
-| Lm3 x::"name" t::"trm3" bind x in t
-| Lt3 r::"rassigns3" t::"trm3" bind "bv3 r" in t
-and rassigns3 =
- ANil
-| ACons "name" "trm3" "rassigns3"
-binder
- bv3
-where
- "bv3 ANil = {}"
-| "bv3 (ACons x t as) = {atom x} \<union> (bv3 as)"
-
-
-(* compat should be
-compat (ANil) pi (PNil) \<equiv> TRue
-compat (ACons x t ts) pi (ACons x' t' ts') \<equiv> pi o x = x' \<and> alpha t t' \<and> compat ts pi ts'
-*)
-
-(* example 4 from Terms.thy *)
-
-(* fv_eqvt does not work, we need to repaire defined permute functions
- defined fv and defined alpha... *)
-nominal_datatype trm4 =
- Vr4 "name"
-| Ap4 "trm4" "trm4 list"
-| Lm4 x::"name" t::"trm4" bind x in t
-
-thm alpha_trm4_raw_alpha_trm4_raw_list.intros[no_vars]
-thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]
-
-(* example 5 from Terms.thy *)
-
-nominal_datatype trm5 =
- Vr5 "name"
-| Ap5 "trm5" "trm5"
-| Lt5 l::"lts" t::"trm5" bind "bv5 l" in t
-and lts =
- Lnil
-| Lcons "name" "trm5" "lts"
-binder
- bv5
-where
- "bv5 Lnil = {}"
-| "bv5 (Lcons n t ltl) = {atom n} \<union> (bv5 ltl)"
-
-(* example 6 from Terms.thy *)
-
-(* BV is not respectful, needs to fail*)
-nominal_datatype trm6 =
- Vr6 "name"
-| Lm6 x::"name" t::"trm6" bind x in t
-| Lt6 left::"trm6" right::"trm6" bind "bv6 left" in right
-binder
- bv6
-where
- "bv6 (Vr6 n) = {}"
-| "bv6 (Lm6 n t) = {atom n} \<union> bv6 t"
-| "bv6 (Lt6 l r) = bv6 l \<union> bv6 r"
-(* example 7 from Terms.thy *)
-
-(* BV is not respectful, needs to fail*)
-nominal_datatype trm7 =
- Vr7 "name"
-| Lm7 l::"name" r::"trm7" bind l in r
-| Lt7 l::"trm7" r::"trm7" bind "bv7 l" in r
-binder
- bv7
-where
- "bv7 (Vr7 n) = {atom n}"
-| "bv7 (Lm7 n t) = bv7 t - {atom n}"
-| "bv7 (Lt7 l r) = bv7 l \<union> bv7 r"
-
-(* example 8 from Terms.thy *)
-
-nominal_datatype foo8 =
- Foo0 "name"
-| Foo1 b::"bar8" f::"foo8" bind "bv8 b" in f --"check fo error if this is called foo"
-and bar8 =
- Bar0 "name"
-| Bar1 "name" s::"name" b::"bar8" bind s in b
-binder
- bv8
-where
- "bv8 (Bar0 x) = {}"
-| "bv8 (Bar1 v x b) = {atom v}"
-
-(* example 9 from Terms.thy *)
-
-(* BV is not respectful, needs to fail*)
-nominal_datatype lam9 =
- Var9 "name"
-| Lam9 n::"name" l::"lam9" bind n in l
-and bla9 =
- Bla9 f::"lam9" s::"lam9" bind "bv9 f" in s
-binder
- bv9
-where
- "bv9 (Var9 x) = {}"
-| "bv9 (Lam9 x b) = {atom x}"
-
-(* example from my PHD *)
-
-atom_decl coname
-
-nominal_datatype phd =
- Ax "name" "coname"
-| Cut n::"coname" t1::"phd" c::"coname" t2::"phd" bind n in t1, bind c in t2
-| AndR c1::"coname" t1::"phd" c2::"coname" t2::"phd" "coname" bind c1 in t1, bind c2 in t2
-| AndL1 n::"name" t::"phd" "name" bind n in t
-| AndL2 n::"name" t::"phd" "name" bind n in t
-| ImpL c::"coname" t1::"phd" n::"name" t2::"phd" "name" bind c in t1, bind n in t2
-| ImpR c::"coname" n::"name" t::"phd" "coname" bind n in t, bind c in t
-
-thm alpha_phd_raw.intros[no_vars]
-thm fv_phd_raw.simps[no_vars]
-
-
-(* example form Leroy 96 about modules; OTT *)
-
-nominal_datatype mexp =
- Acc "path"
-| Stru "body"
-| Funct x::"name" "sexp" m::"mexp" bind x in m
-| FApp "mexp" "path"
-| Ascr "mexp" "sexp"
-and body =
- Empty
-| Seq c::defn d::"body" bind "cbinders c" in d
-and defn =
- Type "name" "tyty"
-| Dty "name"
-| DStru "name" "mexp"
-| Val "name" "trmtrm"
-and sexp =
- Sig sbody
-| SFunc "name" "sexp" "sexp"
-and sbody =
- SEmpty
-| SSeq C::spec D::sbody bind "Cbinders C" in D
-and spec =
- Type1 "name"
-| Type2 "name" "tyty"
-| SStru "name" "sexp"
-| SVal "name" "tyty"
-and tyty =
- Tyref1 "name"
-| Tyref2 "path" "tyty"
-| Fun "tyty" "tyty"
-and path =
- Sref1 "name"
-| Sref2 "path" "name"
-and trmtrm =
- Tref1 "name"
-| Tref2 "path" "name"
-| Lam' v::"name" "tyty" M::"trmtrm" bind v in M
-| App' "trmtrm" "trmtrm"
-| Let' "body" "trmtrm"
-binder
- cbinders :: "defn \<Rightarrow> atom set"
-and Cbinders :: "spec \<Rightarrow> atom set"
-where
- "cbinders (Type t T) = {atom t}"
-| "cbinders (Dty t) = {atom t}"
-| "cbinders (DStru x s) = {atom x}"
-| "cbinders (Val v M) = {atom v}"
-| "Cbinders (Type1 t) = {atom t}"
-| "Cbinders (Type2 t T) = {atom t}"
-| "Cbinders (SStru x S) = {atom x}"
-| "Cbinders (SVal v T) = {atom v}"
-
-(* core haskell *)
-print_theorems
-
-atom_decl var
-atom_decl tvar
-
-
-(* there are types, coercion types and regular types *)
-nominal_datatype tkind =
- KStar
-| KFun "tkind" "tkind"
-and ckind =
- CKEq "ty" "ty"
-and ty =
- TVar "tvar"
-| TC "string"
-| TApp "ty" "ty"
-| TFun "string" "ty list"
-| TAll tv::"tvar" "tkind" T::"ty" bind tv in T
-| TEq "ty" "ty" "ty"
-and co =
- CC "string"
-| CApp "co" "co"
-| CFun "string" "co list"
-| CAll tv::"tvar" "ckind" C::"co" bind tv in C
-| CEq "co" "co" "co"
-| CSym "co"
-| CCir "co" "co"
-| CLeft "co"
-| CRight "co"
-| CSim "co"
-| CRightc "co"
-| CLeftc "co"
-| CCoe "co" "co"
-
-
-typedecl ty --"hack since ty is not yet defined"
-
-abbreviation
- "atoms A \<equiv> atom ` A"
-
-nominal_datatype trm =
- Var "var"
-| C "string"
-| LAM tv::"tvar" "kind" t::"trm" bind tv in t
-| APP "trm" "ty"
-| Lam v::"var" "ty" t::"trm" bind v in t
-| App "trm" "trm"
-| Let x::"var" "ty" "trm" t::"trm" bind x in t
-| Case "trm" "assoc list"
-| Cast "trm" "ty" --"ty is supposed to be a coercion type only"
-and assoc =
- A p::"pat" t::"trm" bind "bv p" in t
-and pat =
- K "string" "(tvar \<times> kind) list" "(var \<times> ty) list"
-binder
- bv :: "pat \<Rightarrow> atom set"
-where
- "bv (K s ts vs) = (atoms (set (map fst ts))) \<union> (atoms (set (map fst vs)))"
-
-(*
-compat (K s ts vs) pi (K s' ts' vs') ==
- s = s' &
-
-*)
-
-
-(*thm bv_raw.simps*)
-
-(* example 3 from Peter Sewell's bestiary *)
-nominal_datatype exp =
- VarP "name"
-| AppP "exp" "exp"
-| LamP x::"name" e::"exp" bind x in e
-| LetP x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1
-and pat =
- PVar "name"
-| PUnit
-| PPair "pat" "pat"
-binder
- bp :: "pat \<Rightarrow> atom set"
-where
- "bp (PVar x) = {atom x}"
-| "bp (PUnit) = {}"
-| "bp (PPair p1 p2) = bp p1 \<union> bp p2"
-thm alpha_exp_raw_alpha_pat_raw.intros
-
-(* example 6 from Peter Sewell's bestiary *)
-nominal_datatype exp6 =
- EVar name
-| EPair exp6 exp6
-| ELetRec x::name p::pat6 e1::exp6 e2::exp6 bind x in e1, bind x in e2, bind "bp6 p" in e1
-and pat6 =
- PVar' name
-| PUnit'
-| PPair' pat6 pat6
-binder
- bp6 :: "pat6 \<Rightarrow> atom set"
-where
- "bp6 (PVar' x) = {atom x}"
-| "bp6 (PUnit') = {}"
-| "bp6 (PPair' p1 p2) = bp6 p1 \<union> bp6 p2"
-thm alpha_exp6_raw_alpha_pat6_raw.intros
-
-(* example 7 from Peter Sewell's bestiary *)
-nominal_datatype exp7 =
- EVar name
-| EUnit
-| EPair exp7 exp7
-| ELetRec l::lrbs e::exp7 bind "b7s l" in e, bind "b7s l" in l
-and lrb =
- Assign name exp7
-and lrbs =
- Single lrb
-| More lrb lrbs
-binder
- b7 :: "lrb \<Rightarrow> atom set" and
- b7s :: "lrbs \<Rightarrow> atom set"
-where
- "b7 (Assign x e) = {atom x}"
-| "b7s (Single a) = b7 a"
-| "b7s (More a as) = (b7 a) \<union> (b7s as)"
-thm alpha_exp7_raw_alpha_lrb_raw_alpha_lrbs_raw.intros
-
-(* example 8 from Peter Sewell's bestiary *)
-nominal_datatype exp8 =
- EVar name
-| EUnit
-| EPair exp8 exp8
-| ELetRec l::lrbs8 e::exp8 bind "b_lrbs8 l" in e, bind "b_lrbs8 l" in l
-and fnclause =
- K x::name p::pat8 e::exp8 bind "b_pat p" in e
-and fnclauses =
- S fnclause
-| ORs fnclause fnclauses
-and lrb8 =
- Clause fnclauses
-and lrbs8 =
- Single lrb8
-| More lrb8 lrbs8
-and pat8 =
- PVar name
-| PUnit
-| PPair pat8 pat8
-binder
- b_lrbs8 :: "lrbs8 \<Rightarrow> atom set" and
- b_pat :: "pat8 \<Rightarrow> atom set" and
- b_fnclauses :: "fnclauses \<Rightarrow> atom set" and
- b_fnclause :: "fnclause \<Rightarrow> atom set" and
- b_lrb8 :: "lrb8 \<Rightarrow> atom set"
-where
- "b_lrbs8 (Single l) = b_lrb8 l"
-| "b_lrbs8 (More l ls) = b_lrb8 l \<union> b_lrbs8 ls"
-| "b_pat (PVar x) = {atom x}"
-| "b_pat (PUnit) = {}"
-| "b_pat (PPair p1 p2) = b_pat p1 \<union> b_pat p2"
-| "b_fnclauses (S fc) = (b_fnclause fc)"
-| "b_fnclauses (ORs fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"
-| "b_lrb8 (Clause fcs) = (b_fnclauses fcs)"
-| "b_fnclause (K x pat exp8) = {atom x}"
-thm alpha_exp8_raw_alpha_fnclause_raw_alpha_fnclauses_raw_alpha_lrb8_raw_alpha_lrbs8_raw_alpha_pat8_raw.intros
-
-
-
-
-(* example 9 from Peter Sewell's bestiary *)
-(* run out of steam at the moment *)
-
-end
-
-
-