+++ /dev/null
-(*
- ||M|| This file is part of HELM, an Hypertextual, Electronic
- ||A|| Library of Mathematics, developed at the Computer Science
- ||T|| Department of the University of Bologna, Italy.
- ||I||
- ||T||
- ||A|| This file is distributed under the terms of the
- \ / GNU General Public License Version 2
- \ /
- V_______________________________________________________________ *)
-
-(* THE FORMAL SYSTEM λδ - MATITA SOURCE SCRIPTS
- * Specification started: 2011 April 17
- * - Patience on me so that I gain peace and perfection! -
- * [ suggested invocation to start formal specifications with ]
- *)
-
-include "lambda-delta/ground.ma".
-
-(* BINARY ITEMS *************************************************************)
-
-(* binary binding items *)
-inductive bind2: Type[0] ≝
-| Abbr: bind2 (* abbreviation *)
-| Abst: bind2 (* abstraction *)
-.
-
-(* binary non-binding items *)
-inductive flat2: Type[0] ≝
-| Appl: flat2 (* application *)
-| Cast: flat2 (* explicit type annotation *)
-.
-
-(* binary items *)
-inductive item2: Type[0] ≝
-| Bind: bind2 → item2 (* binding item *)
-| Flat: flat2 → item2 (* non-binding item *)
-.
-
-coercion item2_of_bind2: ∀I:bind2.item2 ≝ Bind on _I:bind2 to item2.
-
-coercion item2_of_flat2: ∀I:flat2.item2 ≝ Flat on _I:flat2 to item2.
-
-(* reduction-related categorization *****************************************)
-
-(* binding items entitled for zeta-reduction *)
-definition zable ≝ λI. I = Abbr.
-
-interpretation "is entitled for zeta-reduction" 'Zeta I = (zable I).
-
-(* non-binding items entitled for zeta-reduction *)
-definition table ≝ λI. I = Cast.
-
-interpretation "is entitled for tau-reduction" 'Tau I = (table I).
-
-(* binding items entitled for theta-reduction *)
-definition thable ≝ λI. I = Abbr.
-
-interpretation "is entitled for theta-reduction" 'Theta I = (thable I).
+++ /dev/null
-(*
- ||M|| This file is part of HELM, an Hypertextual, Electronic
- ||A|| Library of Mathematics, developed at the Computer Science
- ||T|| Department of the University of Bologna, Italy.
- ||I||
- ||T||
- ||A|| This file is distributed under the terms of the
- \ / GNU General Public License Version 2
- \ /
- V_______________________________________________________________ *)
-
-include "lambda-delta/language/term.ma".
-
-(* LOCAL ENVIRONMENTS *******************************************************)
-
-(* local environments *)
-inductive lenv: Type[0] ≝
-| LSort: lenv (* empty *)
-| LPair: lenv → bind2 → term → lenv (* binary binding construction *)
-.
-
-interpretation "sort (local environment)" 'Star = LSort.
-
-interpretation "environment binding construction (binary)" 'DBind L I T = (LPair L I T).
+++ /dev/null
-(*
- ||M|| This file is part of HELM, an Hypertextual, Electronic
- ||A|| Library of Mathematics, developed at the Computer Science
- ||T|| Department of the University of Bologna, Italy.
- ||I||
- ||T||
- ||A|| This file is distributed under the terms of the
- \ / GNU General Public License Version 2
- \ /
- V_______________________________________________________________ *)
-
-include "lambda-delta/ground.ma".
-
-(* SORT HIERARCHY ***********************************************************)
-
-(* sort hierarchy specifications *)
-record sh: Type[0] ≝ {
- next: nat → nat; (* next sort in the hierarchy *)
- next_lt: ∀k. k < next k (* strict monotonicity condition *)
-}.
+++ /dev/null
-(*
- ||M|| This file is part of HELM, an Hypertextual, Electronic
- ||A|| Library of Mathematics, developed at the Computer Science
- ||T|| Department of the University of Bologna, Italy.
- ||I||
- ||T||
- ||A|| This file is distributed under the terms of the
- \ / GNU General Public License Version 2
- \ /
- V_______________________________________________________________ *)
-
-include "lambda-delta/language/item.ma".
-
-(* TERMS ********************************************************************)
-
-(* terms *)
-inductive term: Type[0] ≝
-| TSort: nat → term (* sort: starting at 0 *)
-| TLRef: nat → term (* reference by index: starting at 0 *)
-| TPair: item2 → term → term → term (* binary item construction *)
-.
-
-interpretation "sort (term)" 'Star k = (TSort k).
-
-interpretation "local reference (term)" 'Weight i = (TLRef i).
-
-interpretation "term construction (binary)" 'SItem I T1 T2 = (TPair I T1 T2).
-
-interpretation "term binding construction (binary)" 'SBind I T1 T2 = (TPair (Bind I) T1 T2).
-
-interpretation "term flat construction (binary)" 'SFlat I T1 T2 = (TPair (Flat I) T1 T2).
+++ /dev/null
-(*
- ||M|| This file is part of HELM, an Hypertextual, Electronic
- ||A|| Library of Mathematics, developed at the Computer Science
- ||T|| Department of the University of Bologna, Italy.
- ||I||
- ||T||
- ||A|| This file is distributed under the terms of the
- \ / GNU General Public License Version 2
- \ /
- V_______________________________________________________________ *)
-
-include "lambda-delta/language/lenv.ma".
-
-(* WEIGHTS ******************************************************************)
-
-(* the weight of a term *)
-let rec tw T ≝ match T with
-[ TSort _ ⇒ 1
-| TLRef _ ⇒ 1
-| TPair _ V T ⇒ tw V + tw T + 1
-].
-
-interpretation "weight (term)" 'Weight T = (tw T).
-
-(* the weight of a local environment *)
-let rec lw L ≝ match L with
-[ LSort ⇒ 0
-| LPair L _ V ⇒ lw L + #V
-].
-
-interpretation "weight (local environment)" 'Weight L = (lw L).
-
-(* the weight of a closure *)
-definition cw: lenv → term → ? ≝ λL,T. #L + #T.
-
-interpretation "weight (closure)" 'Weight L T = (cw L T).
-
-axiom cw_wf_ind: ∀P:lenv→term→Prop.
- (∀L2,T2. (∀L1,T1. #[L1,T1] < #[L2,T2] → P L1 T1) → P L2 T2) →
- ∀L,T. P L T.
(* language *****************************************************************)
-notation "hvbox( ζ I )"
- non associative with precedence 45
- for @{ 'Zeta $I }.
-
-notation "hvbox( τ I )"
- non associative with precedence 45
- for @{ 'Tau $I }.
-
-notation "hvbox( θ I )"
- non associative with precedence 45
- for @{ 'Theta $I }.
-
notation "hvbox( ⋆ )"
non associative with precedence 90
for @{ 'Star }.
\ /
V_______________________________________________________________ *)
-include "lambda-delta/language/term.ma".
+include "lambda-delta/syntax/term.ma".
(* RELOCATION ***************************************************************)
\ /
V_______________________________________________________________ *)
-include "lambda-delta/language/lenv.ma".
+include "lambda-delta/syntax/lenv.ma".
include "lambda-delta/substitution/lift.ma".
(* TELESCOPIC SUBSTITUTION **************************************************)
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+(* THE FORMAL SYSTEM λδ - MATITA SOURCE SCRIPTS
+ * Specification started: 2011 April 17
+ * - Patience on me so that I gain peace and perfection! -
+ * [ suggested invocation to start formal specifications with ]
+ *)
+
+include "lambda-delta/ground.ma".
+
+(* BINARY ITEMS *************************************************************)
+
+(* binary binding items *)
+inductive bind2: Type[0] ≝
+| Abbr: bind2 (* abbreviation *)
+| Abst: bind2 (* abstraction *)
+.
+
+(* binary non-binding items *)
+inductive flat2: Type[0] ≝
+| Appl: flat2 (* application *)
+| Cast: flat2 (* explicit type annotation *)
+.
+
+(* binary items *)
+inductive item2: Type[0] ≝
+| Bind: bind2 → item2 (* binding item *)
+| Flat: flat2 → item2 (* non-binding item *)
+.
+
+coercion item2_of_bind2: ∀I:bind2.item2 ≝ Bind on _I:bind2 to item2.
+
+coercion item2_of_flat2: ∀I:flat2.item2 ≝ Flat on _I:flat2 to item2.
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+include "lambda-delta/syntax/term.ma".
+
+(* LOCAL ENVIRONMENTS *******************************************************)
+
+(* local environments *)
+inductive lenv: Type[0] ≝
+| LSort: lenv (* empty *)
+| LPair: lenv → bind2 → term → lenv (* binary binding construction *)
+.
+
+interpretation "sort (local environment)" 'Star = LSort.
+
+interpretation "environment binding construction (binary)" 'DBind L I T = (LPair L I T).
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+include "lambda-delta/ground.ma".
+
+(* SORT HIERARCHY ***********************************************************)
+
+(* sort hierarchy specifications *)
+record sh: Type[0] ≝ {
+ next: nat → nat; (* next sort in the hierarchy *)
+ next_lt: ∀k. k < next k (* strict monotonicity condition *)
+}.
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+include "lambda-delta/syntax/item.ma".
+
+(* TERMS ********************************************************************)
+
+(* terms *)
+inductive term: Type[0] ≝
+| TSort: nat → term (* sort: starting at 0 *)
+| TLRef: nat → term (* reference by index: starting at 0 *)
+| TPair: item2 → term → term → term (* binary item construction *)
+.
+
+interpretation "sort (term)" 'Star k = (TSort k).
+
+interpretation "local reference (term)" 'Weight i = (TLRef i).
+
+interpretation "term construction (binary)" 'SItem I T1 T2 = (TPair I T1 T2).
+
+interpretation "term binding construction (binary)" 'SBind I T1 T2 = (TPair (Bind I) T1 T2).
+
+interpretation "term flat construction (binary)" 'SFlat I T1 T2 = (TPair (Flat I) T1 T2).
--- /dev/null
+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A|| This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ \ /
+ V_______________________________________________________________ *)
+
+include "lambda-delta/syntax/lenv.ma".
+
+(* WEIGHTS ******************************************************************)
+
+(* the weight of a term *)
+let rec tw T ≝ match T with
+[ TSort _ ⇒ 1
+| TLRef _ ⇒ 1
+| TPair _ V T ⇒ tw V + tw T + 1
+].
+
+interpretation "weight (term)" 'Weight T = (tw T).
+
+(* the weight of a local environment *)
+let rec lw L ≝ match L with
+[ LSort ⇒ 0
+| LPair L _ V ⇒ lw L + #V
+].
+
+interpretation "weight (local environment)" 'Weight L = (lw L).
+
+(* the weight of a closure *)
+definition cw: lenv → term → ? ≝ λL,T. #L + #T.
+
+interpretation "weight (closure)" 'Weight L T = (cw L T).
+
+axiom cw_wf_ind: ∀P:lenv→term→Prop.
+ (∀L2,T2. (∀L1,T1. #[L1,T1] < #[L2,T2] → P L1 T1) → P L2 T2) →
+ ∀L,T. P L T.
projects / helm.git / commitdiff