From 2feb56660700af107abb5a28a7120052ac405518 Mon Sep 17 00:00:00 2001 From: Josh Chen Date: Sun, 31 Jan 2021 02:54:51 +0000 Subject: rename things + some small changes --- spartan/core/Spartan.thy | 571 ----------------------------------- spartan/core/calc.ML | 87 ------ spartan/core/cases.ML | 42 --- spartan/core/comp.ML | 468 ---------------------------- spartan/core/context_facts.ML | 101 ------- spartan/core/context_tactical.ML | 256 ---------------- spartan/core/elaborated_statement.ML | 470 ---------------------------- spartan/core/elaboration.ML | 91 ------ spartan/core/elimination.ML | 48 --- spartan/core/eqsubst.ML | 442 --------------------------- spartan/core/equality.ML | 90 ------ spartan/core/focus.ML | 158 ---------- spartan/core/goals.ML | 213 ------------- spartan/core/implicits.ML | 87 ------ spartan/core/lib.ML | 193 ------------ spartan/core/tactics.ML | 180 ----------- spartan/core/types.ML | 113 ------- spartan/lib/List.thy | 191 ------------ spartan/lib/Maybe.thy | 75 ----- spartan/lib/Prelude.thy | 151 --------- 20 files changed, 4027 deletions(-) delete mode 100644 spartan/core/Spartan.thy delete mode 100644 spartan/core/calc.ML delete mode 100644 spartan/core/cases.ML delete mode 100644 spartan/core/comp.ML delete mode 100644 spartan/core/context_facts.ML delete mode 100644 spartan/core/context_tactical.ML delete mode 100644 spartan/core/elaborated_statement.ML delete mode 100644 spartan/core/elaboration.ML delete mode 100644 spartan/core/elimination.ML delete mode 100644 spartan/core/eqsubst.ML delete mode 100644 spartan/core/equality.ML delete mode 100644 spartan/core/focus.ML delete mode 100644 spartan/core/goals.ML delete mode 100644 spartan/core/implicits.ML delete mode 100644 spartan/core/lib.ML delete mode 100644 spartan/core/tactics.ML delete mode 100644 spartan/core/types.ML delete mode 100644 spartan/lib/List.thy delete mode 100644 spartan/lib/Maybe.thy delete mode 100644 spartan/lib/Prelude.thy (limited to 'spartan') diff --git a/spartan/core/Spartan.thy b/spartan/core/Spartan.thy deleted file mode 100644 index 5046b6a..0000000 --- a/spartan/core/Spartan.thy +++ /dev/null @@ -1,571 +0,0 @@ -text \Spartan type theory\ - -theory Spartan -imports - Pure - "HOL-Eisbach.Eisbach" - "HOL-Eisbach.Eisbach_Tools" -keywords - "Theorem" "Lemma" "Corollary" "Proposition" "Definition" :: thy_goal_stmt and - "assuming" :: prf_asm % "proof" and - "focus" "\<^item>" "\<^enum>" "\" "\" "~" :: prf_script_goal % "proof" and - "calc" "print_coercions" :: thy_decl and - "rhs" "def" "vars" :: quasi_command - -begin - -section \Notation\ - -declare [[eta_contract=false]] - -text \ -Rebind notation for meta-lambdas since we want to use \\\ for the object -lambdas. Metafunctions now use the binder \fn\. -\ -setup \ -let - val typ = Simple_Syntax.read_typ - fun mixfix (sy, ps, p) = Mixfix (Input.string sy, ps, p, Position.no_range) -in - Sign.del_syntax (Print_Mode.ASCII, true) - [("_lambda", typ "pttrns \ 'a \ logic", mixfix ("(3%_./ _)", [0, 3], 3))] - #> Sign.del_syntax Syntax.mode_default - [("_lambda", typ "pttrns \ 'a \ logic", mixfix ("(3\_./ _)", [0, 3], 3))] - #> Sign.add_syntax Syntax.mode_default - [("_lambda", typ "pttrns \ 'a \ logic", mixfix ("(3fn _./ _)", [0, 3], 3))] -end -\ - -syntax "_app" :: \logic \ logic \ logic\ (infixr "$" 3) -translations "a $ b" \ "a (b)" - -abbreviation (input) K where "K x \ fn _. x" - - -section \Metalogic\ - -text \ -HOAS embedding of dependent type theory: metatype of expressions, and typing -judgment. -\ - -typedecl o - -consts has_type :: \o \ o \ prop\ ("(2_:/ _)" 999) - - -section \Axioms\ - -subsection \Universes\ - -text \\-many cumulative Russell universes.\ - -typedecl lvl - -axiomatization - O :: \lvl\ and - S :: \lvl \ lvl\ and - lt :: \lvl \ lvl \ prop\ (infix "<" 900) - where - O_min: "O < S i" and - lt_S: "i < S i" and - lt_trans: "i < j \ j < k \ i < k" - -axiomatization U :: \lvl \ o\ where - Ui_in_Uj: "i < j \ U i: U j" and - U_cumul: "A: U i \ i < j \ A: U j" - -lemma Ui_in_USi: - "U i: U (S i)" - by (rule Ui_in_Uj, rule lt_S) - -lemma U_lift: - "A: U i \ A: U (S i)" - by (erule U_cumul, rule lt_S) - -subsection \\-type\ - -axiomatization - Pi :: \o \ (o \ o) \ o\ and - lam :: \o \ (o \ o) \ o\ and - app :: \o \ o \ o\ ("(1_ `_)" [120, 121] 120) - -syntax - "_Pi" :: \idts \ o \ o \ o\ ("(2\_: _./ _)" 30) - "_Pi2" :: \idts \ o \ o \ o\ - "_lam" :: \idts \ o \ o \ o\ ("(2\_: _./ _)" 30) - "_lam2" :: \idts \ o \ o \ o\ -translations - "\x xs: A. B" \ "CONST Pi A (fn x. _Pi2 xs A B)" - "_Pi2 x A B" \ "\x: A. B" - "\x: A. B" \ "CONST Pi A (fn x. B)" - "\x xs: A. b" \ "CONST lam A (fn x. _lam2 xs A b)" - "_lam2 x A b" \ "\x: A. b" - "\x: A. b" \ "CONST lam A (fn x. b)" - -abbreviation Fn (infixr "\" 40) where "A \ B \ \_: A. B" - -axiomatization where - PiF: "\A: U i; \x. x: A \ B x: U i\ \ \x: A. B x: U i" and - - PiI: "\A: U i; \x. x: A \ b x: B x\ \ \x: A. b x: \x: A. B x" and - - PiE: "\f: \x: A. B x; a: A\ \ f `a: B a" and - - beta: "\a: A; \x. x: A \ b x: B x\ \ (\x: A. b x) `a \ b a" and - - eta: "f: \x: A. B x \ \x: A. f `x \ f" and - - Pi_cong: "\ - \x. x: A \ B x \ B' x; - A: U i; - \x. x: A \ B x: U j; - \x. x: A \ B' x: U j - \ \ \x: A. B x \ \x: A. B' x" and - - lam_cong: "\\x. x: A \ b x \ c x; A: U i\ \ \x: A. b x \ \x: A. c x" - -subsection \\-type\ - -axiomatization - Sig :: \o \ (o \ o) \ o\ and - pair :: \o \ o \ o\ ("(2<_,/ _>)") and - SigInd :: \o \ (o \ o) \ (o \ o) \ (o \ o \ o) \ o \ o\ - -syntax "_Sum" :: \idt \ o \ o \ o\ ("(2\_: _./ _)" 20) - -translations "\x: A. B" \ "CONST Sig A (fn x. B)" - -abbreviation Prod (infixl "\" 60) - where "A \ B \ \_: A. B" - -abbreviation "and" (infixl "\" 60) - where "A \ B \ A \ B" - -axiomatization where - SigF: "\A: U i; \x. x: A \ B x: U i\ \ \x: A. B x: U i" and - - SigI: "\\x. x: A \ B x: U i; a: A; b: B a\ \ : \x: A. B x" and - - SigE: "\ - p: \x: A. B x; - A: U i; - \x. x : A \ B x: U j; - \p. p: \x: A. B x \ C p: U k; - \x y. \x: A; y: B x\ \ f x y: C - \ \ SigInd A (fn x. B x) (fn p. C p) f p: C p" and - - Sig_comp: "\ - a: A; - b: B a; - \x. x: A \ B x: U i; - \p. p: \x: A. B x \ C p: U i; - \x y. \x: A; y: B x\ \ f x y: C - \ \ SigInd A (fn x. B x) (fn p. C p) f \ f a b" and - - Sig_cong: "\ - \x. x: A \ B x \ B' x; - A: U i; - \x. x : A \ B x: U j; - \x. x : A \ B' x: U j - \ \ \x: A. B x \ \x: A. B' x" - - -section \Type checking & inference\ - -ML_file \lib.ML\ -ML_file \context_facts.ML\ -ML_file \context_tactical.ML\ - -\ \Rule attributes for the typechecker\ -named_theorems form and intr and comp - -\ \Elimination/induction automation and the `elim` attribute\ -ML_file \elimination.ML\ - -lemmas - [form] = PiF SigF and - [intr] = PiI SigI and - [elim ?f] = PiE and - [elim ?p] = SigE and - [comp] = beta Sig_comp and - [cong] = Pi_cong lam_cong Sig_cong - -\ \Subsumption rule\ -lemma sub: - assumes "a: A" "A \ A'" - shows "a: A'" - using assms by simp - -\ \Basic rewriting of computational equality\ -ML_file \~~/src/Tools/misc_legacy.ML\ -ML_file \~~/src/Tools/IsaPlanner/isand.ML\ -ML_file \~~/src/Tools/IsaPlanner/rw_inst.ML\ -ML_file \~~/src/Tools/IsaPlanner/zipper.ML\ -ML_file \~~/src/Tools/eqsubst.ML\ - -\ \Term normalization, type checking & inference\ -ML_file \types.ML\ - -method_setup typechk = - \Scan.succeed (K (CONTEXT_METHOD ( - CHEADGOAL o Types.check_infer)))\ - -method_setup known = - \Scan.succeed (K (CONTEXT_METHOD ( - CHEADGOAL o Types.known_ctac)))\ - -setup \ -let val typechk = fn ctxt => - NO_CONTEXT_TACTIC ctxt o Types.check_infer - (Simplifier.prems_of ctxt @ Context_Facts.known ctxt) -in - map_theory_simpset (fn ctxt => ctxt - addSolver (mk_solver "" typechk)) -end -\ - - -section \Statements and goals\ - -ML_file \focus.ML\ -ML_file \elaboration.ML\ -ML_file \elaborated_statement.ML\ -ML_file \goals.ML\ - - -section \Proof methods\ - -named_theorems intro \ \Logical introduction rules\ - -lemmas [intro] = PiI[rotated] SigI - -\ \Case reasoning rules\ -ML_file \cases.ML\ - -ML_file \tactics.ML\ - -method_setup rule = - \Attrib.thms >> (fn ths => K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 (rule_ctac ths))))\ - -method_setup dest = - \Scan.lift (Scan.option (Args.parens Parse.nat)) - -- Attrib.thms >> (fn (n_opt, ths) => K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 (dest_ctac n_opt ths))))\ - -method_setup intro = - \Scan.succeed (K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 intro_ctac)))\ - -method_setup intros = - \Scan.lift (Scan.option Parse.nat) >> (fn n_opt => - K (CONTEXT_METHOD (fn facts => - case n_opt of - SOME n => CREPEAT_N n (CHEADGOAL (SIDE_CONDS 0 intro_ctac facts)) - | NONE => CCHANGED (CREPEAT (CCHANGED ( - CHEADGOAL (SIDE_CONDS 0 intro_ctac facts)))))))\ - -method_setup elim = - \Scan.repeat Args.term >> (fn tms => K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 (elim_ctac tms))))\ - -method_setup cases = - \Args.term >> (fn tm => K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 (cases_ctac tm))))\ - -method elims = elim+ -method facts = fact+ - - -subsection \Reflexivity\ - -named_theorems refl -method refl = (rule refl) - - -subsection \Trivial proofs (modulo automatic discharge of side conditions)\ - -method_setup this = - \Scan.succeed (K (CONTEXT_METHOD (fn facts => - CHEADGOAL (SIDE_CONDS 0 - (CONTEXT_TACTIC' (fn ctxt => resolve_tac ctxt facts)) - facts))))\ - - -subsection \Rewriting\ - -consts compute_hole :: "'a::{}" ("\") - -lemma eta_expand: - fixes f :: "'a::{} \ 'b::{}" - shows "f \ fn x. f x" . - -lemma rewr_imp: - assumes "PROP A \ PROP B" - shows "(PROP A \ PROP C) \ (PROP B \ PROP C)" - apply (Pure.rule Pure.equal_intr_rule) - apply (drule equal_elim_rule2[OF assms]; assumption) - apply (drule equal_elim_rule1[OF assms]; assumption) - done - -lemma imp_cong_eq: - "(PROP A \ (PROP B \ PROP C) \ (PROP B' \ PROP C')) \ - ((PROP B \ PROP A \ PROP C) \ (PROP B' \ PROP A \ PROP C'))" - apply (Pure.intro Pure.equal_intr_rule) - apply (drule (1) cut_rl; drule Pure.equal_elim_rule1 Pure.equal_elim_rule2; - assumption)+ - apply (drule Pure.equal_elim_rule1 Pure.equal_elim_rule2; assumption)+ - done - -ML_file \~~/src/HOL/Library/cconv.ML\ -ML_file \comp.ML\ - -\ \\compute\ simplifies terms via computational equalities\ -method compute uses add = - changed \repeat_new \(simp add: comp add | subst comp); typechk?\\ - - -subsection \Calculational reasoning\ - -consts "rhs" :: \'a\ ("..") - -ML_file \calc.ML\ - - -section \Implicits\ - -text \ - \{}\ is used to mark implicit arguments in definitions, while \?\ is expanded - immediately for elaboration in statements. -\ - -consts - iarg :: \'a\ ("{}") - hole :: \'b\ ("?") - -ML_file \implicits.ML\ - -attribute_setup implicit = \Scan.succeed Implicits.implicit_defs_attr\ - -ML \val _ = Context.>> (Syntax_Phases.term_check 1 "" Implicits.make_holes)\ - -text \Automatically insert inhabitation judgments where needed:\ - -syntax inhabited :: \o \ prop\ ("(_)") -translations "inhabited A" \ "CONST has_type ? A" - - -subsection \Implicit lambdas\ - -definition lam_i where [implicit]: "lam_i f \ lam {} f" - -syntax - "_lam_i" :: \idts \ o \ o\ ("(2\_./ _)" 30) - "_lam_i2" :: \idts \ o \ o\ -translations - "\x xs. b" \ "CONST lam_i (fn x. _lam_i2 xs b)" - "_lam_i2 x b" \ "\x. b" - "\x. b" \ "CONST lam_i (fn x. b)" - -translations "\x. b" \ "\x: A. b" - - -section \Lambda coercion\ - -\ \Coerce object lambdas to meta-lambdas\ -abbreviation (input) lambda :: \o \ o \ o\ - where "lambda f \ fn x. f `x" - -ML_file \~~/src/Tools/subtyping.ML\ -declare [[coercion_enabled, coercion lambda]] - -translations "f x" \ "f `x" - - -section \Functions\ - -Lemma eta_exp: - assumes "f: \x: A. B x" - shows "f \ \x: A. f x" - by (rule eta[symmetric]) - -Lemma refine_codomain: - assumes - "A: U i" - "f: \x: A. B x" - "\x. x: A \ f `x: C x" - shows "f: \x: A. C x" - by (comp eta_exp) - -Lemma lift_universe_codomain: - assumes "A: U i" "f: A \ U j" - shows "f: A \ U (S j)" - using U_lift - by (rule refine_codomain) - -subsection \Function composition\ - -definition "funcomp A g f \ \x: A. g `(f `x)" - -syntax - "_funcomp" :: \o \ o \ o \ o\ ("(2_ \\<^bsub>_\<^esub>/ _)" [111, 0, 110] 110) -translations - "g \\<^bsub>A\<^esub> f" \ "CONST funcomp A g f" - -Lemma funcompI [type]: - assumes - "A: U i" - "B: U i" - "\x. x: B \ C x: U i" - "f: A \ B" - "g: \x: B. C x" - shows - "g \\<^bsub>A\<^esub> f: \x: A. C (f x)" - unfolding funcomp_def by typechk - -Lemma funcomp_assoc [comp]: - assumes - "A: U i" - "f: A \ B" - "g: B \ C" - "h: \x: C. D x" - shows - "(h \\<^bsub>B\<^esub> g) \\<^bsub>A\<^esub> f \ h \\<^bsub>A\<^esub> g \\<^bsub>A\<^esub> f" - unfolding funcomp_def by compute - -Lemma funcomp_lambda_comp [comp]: - assumes - "A: U i" - "\x. x: A \ b x: B" - "\x. x: B \ c x: C x" - shows - "(\x: B. c x) \\<^bsub>A\<^esub> (\x: A. b x) \ \x: A. c (b x)" - unfolding funcomp_def by compute - -Lemma funcomp_apply_comp [comp]: - assumes - "A: U i" "B: U i" "\x y. x: B \ C x: U i" - "f: A \ B" "g: \x: B. C x" - "x: A" - shows "(g \\<^bsub>A\<^esub> f) x \ g (f x)" - unfolding funcomp_def by compute - -subsection \Notation\ - -definition funcomp_i (infixr "\" 120) - where [implicit]: "funcomp_i g f \ g \\<^bsub>{}\<^esub> f" - -translations "g \ f" \ "g \\<^bsub>A\<^esub> f" - -subsection \Identity function\ - -abbreviation id where "id A \ \x: A. x" - -lemma - id_type [type]: "A: U i \ id A: A \ A" and - id_comp [comp]: "x: A \ (id A) x \ x" \ \for the occasional manual rewrite\ - by compute+ - -Lemma id_left [comp]: - assumes "A: U i" "B: U i" "f: A \ B" - shows "(id B) \\<^bsub>A\<^esub> f \ f" - by (comp eta_exp[of f]) (compute, rule eta) - -Lemma id_right [comp]: - assumes "A: U i" "B: U i" "f: A \ B" - shows "f \\<^bsub>A\<^esub> (id A) \ f" - by (comp eta_exp[of f]) (compute, rule eta) - -lemma id_U [type]: - "id (U i): U i \ U i" - using Ui_in_USi by typechk - - -section \Pairs\ - -definition "fst A B \ \p: \x: A. B x. SigInd A B (fn _. A) (fn x y. x) p" -definition "snd A B \ \p: \x: A. B x. SigInd A B (fn p. B (fst A B p)) (fn x y. y) p" - -Lemma fst_type [type]: - assumes "A: U i" "\x. x: A \ B x: U i" - shows "fst A B: (\x: A. B x) \ A" - unfolding fst_def by typechk - -Lemma fst_comp [comp]: - assumes - "A: U i" "\x. x: A \ B x: U i" "a: A" "b: B a" - shows "fst A B \ a" - unfolding fst_def by compute - -Lemma snd_type [type]: - assumes "A: U i" "\x. x: A \ B x: U i" - shows "snd A B: \p: \x: A. B x. B (fst A B p)" - unfolding snd_def by typechk - -Lemma snd_comp [comp]: - assumes "A: U i" "\x. x: A \ B x: U i" "a: A" "b: B a" - shows "snd A B \ b" - unfolding snd_def by compute - -subsection \Notation\ - -definition fst_i ("fst") - where [implicit]: "fst \ Spartan.fst {} {}" - -definition snd_i ("snd") - where [implicit]: "snd \ Spartan.snd {} {}" - -translations - "fst" \ "CONST Spartan.fst A B" - "snd" \ "CONST Spartan.snd A B" - -subsection \Projections\ - -Lemma fst [type]: - assumes - "A: U i" "\x. x: A \ B x: U i" - "p: \x: A. B x" - shows "fst p: A" - by typechk - -Lemma snd [type]: - assumes - "A: U i" "\x. x: A \ B x: U i" - "p: \x: A. B x" - shows "snd p: B (fst p)" - by typechk - -method fst for p::o = rule fst[where ?p=p] -method snd for p::o = rule snd[where ?p=p] - -text \Double projections:\ - -definition [implicit]: "p\<^sub>1\<^sub>1 p \ Spartan.fst {} {} (Spartan.fst {} {} p)" -definition [implicit]: "p\<^sub>1\<^sub>2 p \ Spartan.snd {} {} (Spartan.fst {} {} p)" -definition [implicit]: "p\<^sub>2\<^sub>1 p \ Spartan.fst {} {} (Spartan.snd {} {} p)" -definition [implicit]: "p\<^sub>2\<^sub>2 p \ Spartan.snd {} {} (Spartan.snd {} {} p)" - -translations - "CONST p\<^sub>1\<^sub>1 p" \ "fst (fst p)" - "CONST p\<^sub>1\<^sub>2 p" \ "snd (fst p)" - "CONST p\<^sub>2\<^sub>1 p" \ "fst (snd p)" - "CONST p\<^sub>2\<^sub>2 p" \ "snd (snd p)" - -Lemma (def) distribute_Sig: - assumes - "A: U i" - "\x. x: A \ B x: U i" - "\x. x: A \ C x: U i" - "p: \x: A. B x \ C x" - shows "(\x: A. B x) \ (\x: A. C x)" - proof intro - have "fst p: A" and "snd p: B (fst p) \ C (fst p)" - by typechk+ - thus ": \x: A. B x" - and ": \x: A. C x" - by typechk+ - qed - - -end diff --git a/spartan/core/calc.ML b/spartan/core/calc.ML deleted file mode 100644 index 67dc7fc..0000000 --- a/spartan/core/calc.ML +++ /dev/null @@ -1,87 +0,0 @@ -structure Calc = struct - -(* Calculational type context data - -A "calculational" type is a type expressing some congruence relation. In -particular, it has a notion of composition of terms that is often used to derive -proofs equationally. -*) - -structure RHS = Generic_Data ( - type T = (term * indexname) Termtab.table - val empty = Termtab.empty - val extend = I - val merge = Termtab.merge (Term.aconv o apply2 #1) -) - -fun register_rhs t var = - let - val key = Term.head_of t - val idxname = #1 (dest_Var var) - in - RHS.map (Termtab.update (key, (t, idxname))) - end - -fun lookup_calc ctxt t = - Termtab.lookup (RHS.get (Context.Proof ctxt)) (Term.head_of t) - - -(* Declaration *) - -local val Frees_to_Vars = - map_aterms (fn tm => - case tm of - Free (name, T) => Var (("*!"^name, 0), T) (*FIXME: Hacky naming!*) - | _ => tm) -in - -(*Declare the "right-hand side" of calculational types. Does not handle bound - variables, so no dependent RHS in declarations!*) -val _ = Outer_Syntax.local_theory \<^command_keyword>\calc\ - "declare right hand side of calculational type" - (Parse.term -- (\<^keyword>\rhs\ |-- Parse.term) >> - (fn (t_str, rhs_str) => fn lthy => - let - val (t, rhs) = apply2 (Frees_to_Vars o Syntax.read_term lthy) - (t_str, rhs_str) - in lthy |> - Local_Theory.background_theory ( - Context.theory_map (register_rhs t rhs)) - end)) - -end - - -(* Ditto "''" setup *) - -fun last_rhs ctxt = map_aterms (fn t => - case t of - Const (\<^const_name>\rhs\, _) => - let - val this_name = Name_Space.full_name (Proof_Context.naming_of ctxt) - (Binding.name Auto_Bind.thisN) - val this = #thms (the (Proof_Context.lookup_fact ctxt this_name)) - handle Option => [] - val rhs = - (case map Thm.prop_of this of - [prop] => - (let - val typ = Lib.type_of_typing (Logic.strip_assums_concl prop) - val (cong_pttrn, varname) = the (lookup_calc ctxt typ) - val unif_res = Pattern.unify (Context.Proof ctxt) - (cong_pttrn, typ) Envir.init - val rhs = #2 (the - (Vartab.lookup (Envir.term_env unif_res) varname)) - in - rhs - end handle Option => - error (".. can't match right-hand side of calculational type")) - | _ => Term.dummy) - in rhs end - | _ => t) - -val _ = Context.>> - (Syntax_Phases.term_check 5 "" (fn ctxt => map (last_rhs ctxt))) - - -end diff --git a/spartan/core/cases.ML b/spartan/core/cases.ML deleted file mode 100644 index 560a9f1..0000000 --- a/spartan/core/cases.ML +++ /dev/null @@ -1,42 +0,0 @@ -(* Title: cases.ML - Author: Joshua Chen - -Case reasoning. -*) - -structure Case: sig - -val rules: Proof.context -> thm list -val lookup_rule: Proof.context -> Termtab.key -> thm option -val register_rule: thm -> Context.generic -> Context.generic - -end = struct - -(* Context data *) - -(*Stores elimination rules together with a list of the indexnames of the - variables each rule eliminates. Keyed by head of the type being eliminated.*) -structure Rules = Generic_Data ( - type T = thm Termtab.table - val empty = Termtab.empty - val extend = I - val merge = Termtab.merge Thm.eq_thm_prop -) - -val rules = map #2 o Termtab.dest o Rules.get o Context.Proof -fun lookup_rule ctxt = Termtab.lookup (Rules.get (Context.Proof ctxt)) -fun register_rule rl = - let val hd = Term.head_of (Lib.type_of_typing (Thm.major_prem_of rl)) - in Rules.map (Termtab.update (hd, rl)) end - - -(* [cases] attribute *) -val _ = Theory.setup ( - Attrib.setup \<^binding>\cases\ - (Scan.succeed (Thm.declaration_attribute register_rule)) - "" - #> Global_Theory.add_thms_dynamic (\<^binding>\cases\, rules o Context.proof_of) -) - - -end diff --git a/spartan/core/comp.ML b/spartan/core/comp.ML deleted file mode 100644 index 2e50753..0000000 --- a/spartan/core/comp.ML +++ /dev/null @@ -1,468 +0,0 @@ -(* Title: compute.ML - Author: Christoph Traut, Lars Noschinski, TU Muenchen - Modified: Joshua Chen, University of Innsbruck - -This is a method for rewriting computational equalities that supports subterm -selection based on patterns. - -This code has been slightly modified from the original at HOL/Library/compute.ML -to incorporate automatic discharge of type-theoretic side conditions. - -Comment from the original code follows: - -The patterns accepted by compute are of the following form: - ::= | "concl" | "asm" | "for" "(" ")" - ::= (in | at ) [] - ::= [] ("to" ) - -This syntax was clearly inspired by Gonthier's and Tassi's language of -patterns but has diverged significantly during its development. - -We also allow introduction of identifiers for bound variables, -which can then be used to match arbitrary subterms inside abstractions. -*) - -infix 1 then_pconv; -infix 0 else_pconv; - -signature COMPUTE = -sig - type patconv = Proof.context -> Type.tyenv * (string * term) list -> cconv - val then_pconv: patconv * patconv -> patconv - val else_pconv: patconv * patconv -> patconv - val abs_pconv: patconv -> string option * typ -> patconv (*XXX*) - val fun_pconv: patconv -> patconv - val arg_pconv: patconv -> patconv - val imp_pconv: patconv -> patconv - val params_pconv: patconv -> patconv - val forall_pconv: patconv -> string option * typ option -> patconv - val all_pconv: patconv - val for_pconv: patconv -> (string option * typ option) list -> patconv - val concl_pconv: patconv -> patconv - val asm_pconv: patconv -> patconv - val asms_pconv: patconv -> patconv - val judgment_pconv: patconv -> patconv - val in_pconv: patconv -> patconv - val match_pconv: patconv -> term * (string option * typ) list -> patconv - val comps_pconv: term option -> thm list -> patconv - - datatype ('a, 'b) pattern = At | In | Term of 'a | Concl | Asm | For of 'b list - - val mk_hole: int -> typ -> term - - val compute_conv: Proof.context - -> (term * (string * typ) list, string * typ option) pattern list * term option - -> thm list - -> conv -end - -structure Compute : COMPUTE = -struct - -datatype ('a, 'b) pattern = At | In | Term of 'a | Concl | Asm | For of 'b list - -exception NO_TO_MATCH - -val holeN = Name.internal "_hole" - -fun prep_meta_eq ctxt = Simplifier.mksimps ctxt #> map Drule.zero_var_indexes - - -(* holes *) - -fun mk_hole i T = Var ((holeN, i), T) - -fun is_hole (Var ((name, _), _)) = (name = holeN) - | is_hole _ = false - -fun is_hole_const (Const (\<^const_name>\compute_hole\, _)) = true - | is_hole_const _ = false - -val hole_syntax = - let - (* Modified variant of Term.replace_hole *) - fun replace_hole Ts (Const (\<^const_name>\compute_hole\, T)) i = - (list_comb (mk_hole i (Ts ---> T), map_range Bound (length Ts)), i + 1) - | replace_hole Ts (Abs (x, T, t)) i = - let val (t', i') = replace_hole (T :: Ts) t i - in (Abs (x, T, t'), i') end - | replace_hole Ts (t $ u) i = - let - val (t', i') = replace_hole Ts t i - val (u', i'') = replace_hole Ts u i' - in (t' $ u', i'') end - | replace_hole _ a i = (a, i) - fun prep_holes ts = #1 (fold_map (replace_hole []) ts 1) - in - Context.proof_map (Syntax_Phases.term_check 101 "hole_expansion" (K prep_holes)) - #> Proof_Context.set_mode Proof_Context.mode_pattern - end - - -(* pattern conversions *) - -type patconv = Proof.context -> Type.tyenv * (string * term) list -> cterm -> thm - -fun (cv1 then_pconv cv2) ctxt tytenv ct = (cv1 ctxt tytenv then_conv cv2 ctxt tytenv) ct - -fun (cv1 else_pconv cv2) ctxt tytenv ct = (cv1 ctxt tytenv else_conv cv2 ctxt tytenv) ct - -fun raw_abs_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - Abs _ => CConv.abs_cconv (fn (x, ctxt') => cv x ctxt' tytenv) ctxt ct - | t => raise TERM ("raw_abs_pconv", [t]) - -fun raw_fun_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - _ $ _ => CConv.fun_cconv (cv ctxt tytenv) ct - | t => raise TERM ("raw_fun_pconv", [t]) - -fun raw_arg_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - _ $ _ => CConv.arg_cconv (cv ctxt tytenv) ct - | t => raise TERM ("raw_arg_pconv", [t]) - -fun abs_pconv cv (s,T) ctxt (tyenv, ts) ct = - let val u = Thm.term_of ct - in - case try (fastype_of #> dest_funT) u of - NONE => raise TERM ("abs_pconv: no function type", [u]) - | SOME (U, _) => - let - val tyenv' = - if T = dummyT then tyenv - else Sign.typ_match (Proof_Context.theory_of ctxt) (T, U) tyenv - val eta_expand_cconv = - case u of - Abs _=> Thm.reflexive - | _ => CConv.rewr_cconv @{thm eta_expand} - fun add_ident NONE _ l = l - | add_ident (SOME name) ct l = (name, Thm.term_of ct) :: l - val abs_cv = CConv.abs_cconv (fn (ct, ctxt) => cv ctxt (tyenv', add_ident s ct ts)) ctxt - in (eta_expand_cconv then_conv abs_cv) ct end - handle Pattern.MATCH => raise TYPE ("abs_pconv: types don't match", [T,U], [u]) - end - -fun fun_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - _ $ _ => CConv.fun_cconv (cv ctxt tytenv) ct - | Abs (_, T, _ $ Bound 0) => abs_pconv (fun_pconv cv) (NONE, T) ctxt tytenv ct - | t => raise TERM ("fun_pconv", [t]) - -local - -fun arg_pconv_gen cv0 cv ctxt tytenv ct = - case Thm.term_of ct of - _ $ _ => cv0 (cv ctxt tytenv) ct - | Abs (_, T, _ $ Bound 0) => abs_pconv (arg_pconv_gen cv0 cv) (NONE, T) ctxt tytenv ct - | t => raise TERM ("arg_pconv_gen", [t]) - -in - -fun arg_pconv ctxt = arg_pconv_gen CConv.arg_cconv ctxt -fun imp_pconv ctxt = arg_pconv_gen (CConv.concl_cconv 1) ctxt - -end - -(* Move to B in !!x_1 ... x_n. B. Do not eta-expand *) -fun params_pconv cv ctxt tytenv ct = - let val pconv = - case Thm.term_of ct of - Const (\<^const_name>\Pure.all\, _) $ Abs _ => (raw_arg_pconv o raw_abs_pconv) (fn _ => params_pconv cv) - | Const (\<^const_name>\Pure.all\, _) => raw_arg_pconv (params_pconv cv) - | _ => cv - in pconv ctxt tytenv ct end - -fun forall_pconv cv ident ctxt tytenv ct = - case Thm.term_of ct of - Const (\<^const_name>\Pure.all\, T) $ _ => - let - val def_U = T |> dest_funT |> fst |> dest_funT |> fst - val ident' = apsnd (the_default (def_U)) ident - in arg_pconv (abs_pconv cv ident') ctxt tytenv ct end - | t => raise TERM ("forall_pconv", [t]) - -fun all_pconv _ _ = Thm.reflexive - -fun for_pconv cv idents ctxt tytenv ct = - let - fun f rev_idents (Const (\<^const_name>\Pure.all\, _) $ t) = - let val (rev_idents', cv') = f rev_idents (case t of Abs (_,_,u) => u | _ => t) - in - case rev_idents' of - [] => ([], forall_pconv cv' (NONE, NONE)) - | (x :: xs) => (xs, forall_pconv cv' x) - end - | f rev_idents _ = (rev_idents, cv) - in - case f (rev idents) (Thm.term_of ct) of - ([], cv') => cv' ctxt tytenv ct - | _ => raise CTERM ("for_pconv", [ct]) - end - -fun concl_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - (Const (\<^const_name>\Pure.imp\, _) $ _) $ _ => imp_pconv (concl_pconv cv) ctxt tytenv ct - | _ => cv ctxt tytenv ct - -fun asm_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - (Const (\<^const_name>\Pure.imp\, _) $ _) $ _ => CConv.with_prems_cconv ~1 (cv ctxt tytenv) ct - | t => raise TERM ("asm_pconv", [t]) - -fun asms_pconv cv ctxt tytenv ct = - case Thm.term_of ct of - (Const (\<^const_name>\Pure.imp\, _) $ _) $ _ => - ((CConv.with_prems_cconv ~1 oo cv) else_pconv imp_pconv (asms_pconv cv)) ctxt tytenv ct - | t => raise TERM ("asms_pconv", [t]) - -fun judgment_pconv cv ctxt tytenv ct = - if Object_Logic.is_judgment ctxt (Thm.term_of ct) - then arg_pconv cv ctxt tytenv ct - else cv ctxt tytenv ct - -fun in_pconv cv ctxt tytenv ct = - (cv else_pconv - raw_fun_pconv (in_pconv cv) else_pconv - raw_arg_pconv (in_pconv cv) else_pconv - raw_abs_pconv (fn _ => in_pconv cv)) - ctxt tytenv ct - -fun replace_idents idents t = - let - fun subst ((n1, s)::ss) (t as Free (n2, _)) = if n1 = n2 then s else subst ss t - | subst _ t = t - in Term.map_aterms (subst idents) t end - -fun match_pconv cv (t,fixes) ctxt (tyenv, env_ts) ct = - let - val t' = replace_idents env_ts t - val thy = Proof_Context.theory_of ctxt - val u = Thm.term_of ct - - fun descend_hole fixes (Abs (_, _, t)) = - (case descend_hole fixes t of - NONE => NONE - | SOME (fix :: fixes', pos) => SOME (fixes', abs_pconv pos fix) - | SOME ([], _) => raise Match (* less fixes than abstractions on path to hole *)) - | descend_hole fixes (t as l $ r) = - let val (f, _) = strip_comb t - in - if is_hole f - then SOME (fixes, cv) - else - (case descend_hole fixes l of - SOME (fixes', pos) => SOME (fixes', fun_pconv pos) - | NONE => - (case descend_hole fixes r of - SOME (fixes', pos) => SOME (fixes', arg_pconv pos) - | NONE => NONE)) - end - | descend_hole fixes t = - if is_hole t then SOME (fixes, cv) else NONE - - val to_hole = descend_hole (rev fixes) #> the_default ([], cv) #> snd - in - case try (Pattern.match thy (apply2 Logic.mk_term (t',u))) (tyenv, Vartab.empty) of - NONE => raise TERM ("match_pconv: Does not match pattern", [t, t',u]) - | SOME (tyenv', _) => to_hole t ctxt (tyenv', env_ts) ct - end - -fun comps_pconv to thms ctxt (tyenv, env_ts) = - let - fun instantiate_normalize_env ctxt env thm = - let - val prop = Thm.prop_of thm - val norm_type = Envir.norm_type o Envir.type_env - val insts = Term.add_vars prop [] - |> map (fn x as (s, T) => - ((s, norm_type env T), Thm.cterm_of ctxt (Envir.norm_term env (Var x)))) - val tyinsts = Term.add_tvars prop [] - |> map (fn x => (x, Thm.ctyp_of ctxt (norm_type env (TVar x)))) - in Drule.instantiate_normalize (tyinsts, insts) thm end - - fun unify_with_rhs context to env thm = - let - val (_, rhs) = thm |> Thm.concl_of |> Logic.dest_equals - val env' = Pattern.unify context (Logic.mk_term to, Logic.mk_term rhs) env - handle Pattern.Unif => raise NO_TO_MATCH - in env' end - - fun inst_thm_to _ (NONE, _) thm = thm - | inst_thm_to (ctxt : Proof.context) (SOME to, env) thm = - instantiate_normalize_env ctxt (unify_with_rhs (Context.Proof ctxt) to env thm) thm - - fun inst_thm ctxt idents (to, tyenv) thm = - let - (* Replace any identifiers with their corresponding bound variables. *) - val maxidx = Term.maxidx_typs (map (snd o snd) (Vartab.dest tyenv)) 0 - val env = Envir.Envir {maxidx = maxidx, tenv = Vartab.empty, tyenv = tyenv} - val maxidx = Envir.maxidx_of env |> fold Term.maxidx_term (the_list to) - val thm' = Thm.incr_indexes (maxidx + 1) thm - in SOME (inst_thm_to ctxt (Option.map (replace_idents idents) to, env) thm') end - handle NO_TO_MATCH => NONE - - in CConv.rewrs_cconv (map_filter (inst_thm ctxt env_ts (to, tyenv)) thms) end - -fun compute_conv ctxt (pattern, to) thms ct = - let - fun apply_pat At = judgment_pconv - | apply_pat In = in_pconv - | apply_pat Asm = params_pconv o asms_pconv - | apply_pat Concl = params_pconv o concl_pconv - | apply_pat (For idents) = (fn cv => for_pconv cv (map (apfst SOME) idents)) - | apply_pat (Term x) = (fn cv => match_pconv cv (apsnd (map (apfst SOME)) x)) - - val cv = fold_rev apply_pat pattern - - fun distinct_prems th = - case Seq.pull (distinct_subgoals_tac th) of - NONE => th - | SOME (th', _) => th' - - val compute = comps_pconv to (maps (prep_meta_eq ctxt) thms) - in cv compute ctxt (Vartab.empty, []) ct |> distinct_prems end - -fun compute_export_tac ctxt (pat, pat_ctxt) thms = - let - val export = case pat_ctxt of - NONE => I - | SOME inner => singleton (Proof_Context.export inner ctxt) - in CCONVERSION (export o compute_conv ctxt pat thms) end - -val _ = - Theory.setup - let - fun mk_fix s = (Binding.name s, NONE, NoSyn) - - val raw_pattern : (string, binding * string option * mixfix) pattern list parser = - let - val sep = (Args.$$$ "at" >> K At) || (Args.$$$ "in" >> K In) - val atom = (Args.$$$ "asm" >> K Asm) || - (Args.$$$ "concl" >> K Concl) || - (Args.$$$ "for" |-- Args.parens (Scan.optional Parse.vars []) >> For) || - (Parse.term >> Term) - val sep_atom = sep -- atom >> (fn (s,a) => [s,a]) - - fun append_default [] = [Concl, In] - | append_default (ps as Term _ :: _) = Concl :: In :: ps - | append_default [For x, In] = [For x, Concl, In] - | append_default (For x :: (ps as In :: Term _:: _)) = For x :: Concl :: ps - | append_default ps = ps - - in Scan.repeats sep_atom >> (rev #> append_default) end - - fun context_lift (scan : 'a parser) f = fn (context : Context.generic, toks) => - let - val (r, toks') = scan toks - val (r', context') = Context.map_proof_result (fn ctxt => f ctxt r) context - in (r', (context', toks' : Token.T list)) end - - fun read_fixes fixes ctxt = - let fun read_typ (b, rawT, mx) = (b, Option.map (Syntax.read_typ ctxt) rawT, mx) - in Proof_Context.add_fixes (map read_typ fixes) ctxt end - - fun prep_pats ctxt (ps : (string, binding * string option * mixfix) pattern list) = - let - fun add_constrs ctxt n (Abs (x, T, t)) = - let - val (x', ctxt') = yield_singleton Proof_Context.add_fixes (mk_fix x) ctxt - in - (case add_constrs ctxt' (n+1) t of - NONE => NONE - | SOME ((ctxt'', n', xs), t') => - let - val U = Type_Infer.mk_param n [] - val u = Type.constraint (U --> dummyT) (Abs (x, T, t')) - in SOME ((ctxt'', n', (x', U) :: xs), u) end) - end - | add_constrs ctxt n (l $ r) = - (case add_constrs ctxt n l of - SOME (c, l') => SOME (c, l' $ r) - | NONE => - (case add_constrs ctxt n r of - SOME (c, r') => SOME (c, l $ r') - | NONE => NONE)) - | add_constrs ctxt n t = - if is_hole_const t then SOME ((ctxt, n, []), t) else NONE - - fun prep (Term s) (n, ctxt) = - let - val t = Syntax.parse_term ctxt s - val ((ctxt', n', bs), t') = - the_default ((ctxt, n, []), t) (add_constrs ctxt (n+1) t) - in (Term (t', bs), (n', ctxt')) end - | prep (For ss) (n, ctxt) = - let val (ns, ctxt') = read_fixes ss ctxt - in (For ns, (n, ctxt')) end - | prep At (n,ctxt) = (At, (n, ctxt)) - | prep In (n,ctxt) = (In, (n, ctxt)) - | prep Concl (n,ctxt) = (Concl, (n, ctxt)) - | prep Asm (n,ctxt) = (Asm, (n, ctxt)) - - val (xs, (_, ctxt')) = fold_map prep ps (0, ctxt) - - in (xs, ctxt') end - - fun prep_args ctxt (((raw_pats, raw_to), raw_ths)) = - let - - fun check_terms ctxt ps to = - let - fun safe_chop (0: int) xs = ([], xs) - | safe_chop n (x :: xs) = chop (n - 1) xs |>> cons x - | safe_chop _ _ = raise Match - - fun reinsert_pat _ (Term (_, cs)) (t :: ts) = - let val (cs', ts') = safe_chop (length cs) ts - in (Term (t, map dest_Free cs'), ts') end - | reinsert_pat _ (Term _) [] = raise Match - | reinsert_pat ctxt (For ss) ts = - let val fixes = map (fn s => (s, Variable.default_type ctxt s)) ss - in (For fixes, ts) end - | reinsert_pat _ At ts = (At, ts) - | reinsert_pat _ In ts = (In, ts) - | reinsert_pat _ Concl ts = (Concl, ts) - | reinsert_pat _ Asm ts = (Asm, ts) - - fun free_constr (s,T) = Type.constraint T (Free (s, dummyT)) - fun mk_free_constrs (Term (t, cs)) = t :: map free_constr cs - | mk_free_constrs _ = [] - - val ts = maps mk_free_constrs ps @ the_list to - |> Syntax.check_terms (hole_syntax ctxt) - val ctxt' = fold Variable.declare_term ts ctxt - val (ps', (to', ts')) = fold_map (reinsert_pat ctxt') ps ts - ||> (fn xs => case to of NONE => (NONE, xs) | SOME _ => (SOME (hd xs), tl xs)) - val _ = case ts' of (_ :: _) => raise Match | [] => () - in ((ps', to'), ctxt') end - - val (pats, ctxt') = prep_pats ctxt raw_pats - - val ths = Attrib.eval_thms ctxt' raw_ths - val to = Option.map (Syntax.parse_term ctxt') raw_to - - val ((pats', to'), ctxt'') = check_terms ctxt' pats to - - in ((pats', ths, (to', ctxt)), ctxt'') end - - val to_parser = Scan.option ((Args.$$$ "to") |-- Parse.term) - - val subst_parser = - let val scan = raw_pattern -- to_parser -- Parse.thms1 - in context_lift scan prep_args end - - fun compute_export_ctac inputs inthms = - CONTEXT_TACTIC' (fn ctxt => compute_export_tac ctxt inputs inthms) - in - Method.setup \<^binding>\cmp\ (subst_parser >> - (fn (pattern, inthms, (to, pat_ctxt)) => fn orig_ctxt => SIMPLE_METHOD' - (compute_export_tac orig_ctxt ((pattern, to), SOME pat_ctxt) inthms))) - "single-step rewriting, allowing subterm selection via patterns" #> - Method.setup \<^binding>\comp\ (subst_parser >> - (fn (pattern, inthms, (to, pat_ctxt)) => K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 - (compute_export_ctac ((pattern, to), SOME pat_ctxt) inthms))))) - "single-step rewriting with auto-typechecking" - end -end diff --git a/spartan/core/context_facts.ML b/spartan/core/context_facts.ML deleted file mode 100644 index 5aa7c70..0000000 --- a/spartan/core/context_facts.ML +++ /dev/null @@ -1,101 +0,0 @@ -structure Context_Facts: sig - -val Known: Proof.context -> thm Item_Net.T -val known: Proof.context -> thm list -val known_of: Proof.context -> term -> thm list -val register_known: thm -> Context.generic -> Context.generic -val register_knowns: thm list -> Context.generic -> Context.generic - -val Cond: Proof.context -> thm Item_Net.T -val cond: Proof.context -> thm list -val cond_of: Proof.context -> term -> thm list -val register_cond: thm -> Context.generic -> Context.generic -val register_conds: thm list -> Context.generic -> Context.generic - -val Eq: Proof.context -> thm Item_Net.T -val eq: Proof.context -> thm list -val eq_of: Proof.context -> term -> thm list -val register_eq: thm -> Context.generic -> Context.generic -val register_eqs: thm list -> Context.generic -> Context.generic - -val register_facts: thm list -> Proof.context -> Proof.context - -end = struct - -(* Known types *) - -structure Known = Generic_Data ( - type T = thm Item_Net.T - val empty = Item_Net.init Thm.eq_thm - (single o Lib.term_of_typing o Thm.prop_of) - val extend = I - val merge = Item_Net.merge -) - -val Known = Known.get o Context.Proof -val known = Item_Net.content o Known -fun known_of ctxt tm = Item_Net.retrieve (Known ctxt) tm - -fun register_known typing = - if Lib.is_typing (Thm.prop_of typing) then Known.map (Item_Net.update typing) - else error "Not a type judgment" - -fun register_knowns typings = foldr1 (op o) (map register_known typings) - - -(* Conditional type rules *) - -(*Two important cases: 1. general type inference rules and 2. type family - judgments*) - -structure Cond = Generic_Data ( - type T = thm Item_Net.T - val empty = Item_Net.init Thm.eq_thm - (single o Lib.term_of_typing o Thm.concl_of) - val extend = I - val merge = Item_Net.merge -) - -val Cond = Cond.get o Context.Proof -val cond = Item_Net.content o Cond -fun cond_of ctxt tm = Item_Net.retrieve (Cond ctxt) tm - -fun register_cond rule = - if Lib.is_typing (Thm.concl_of rule) then Cond.map (Item_Net.update rule) - else error "Not a conditional type judgment" - -fun register_conds rules = foldr1 (op o) (map register_cond rules) - - -(* Equality statements *) - -structure Eq = Generic_Data ( - type T = thm Item_Net.T - val empty = Item_Net.init Thm.eq_thm - (single o (#1 o Lib.dest_eq) o Thm.concl_of) - val extend = I - val merge = Item_Net.merge -) - -val Eq = Eq.get o Context.Proof -val eq = Item_Net.content o Eq -fun eq_of ctxt tm = Item_Net.retrieve (Eq ctxt) tm - -fun register_eq rule = - if Lib.is_eq (Thm.concl_of rule) then Eq.map (Item_Net.update rule) - else error "Not a definitional equality judgment" - -fun register_eqs rules = foldr1 (op o) (map register_eq rules) - - -(* Context assumptions *) - -fun register_facts ths = - let - val (facts, conds, eqs) = Lib.partition_judgments ths - val f = register_knowns facts handle Empty => I - val c = register_conds conds handle Empty => I - val e = register_eqs eqs handle Empty => I - in Context.proof_map (e o c o f) end - -end diff --git a/spartan/core/context_tactical.ML b/spartan/core/context_tactical.ML deleted file mode 100644 index d0fed61..0000000 --- a/spartan/core/context_tactical.ML +++ /dev/null @@ -1,256 +0,0 @@ -(* Title: context_tactical.ML - Author: Joshua Chen - -More context tactics, and context tactic combinators. - -Contains code modified from - ~~/Pure/search.ML - ~~/Pure/tactical.ML -*) - -infix 1 CTHEN CTHEN' CTHEN_ALL_NEW CTHEN_ALL_NEW_FWD -infix 0 CORELSE CAPPEND CORELSE' CAPPEND' - -structure Context_Tactical: -sig - -type context_tactic' = int -> context_tactic -val CONTEXT_TACTIC': (Proof.context -> int -> tactic) -> context_tactic' -val all_ctac: context_tactic -val no_ctac: context_tactic -val print_ctac: (Proof.context -> string) -> context_tactic -val CTHEN: context_tactic * context_tactic -> context_tactic -val CORELSE: context_tactic * context_tactic -> context_tactic -val CAPPEND: context_tactic * context_tactic -> context_tactic -val CTHEN': context_tactic' * context_tactic' -> context_tactic' -val CORELSE': context_tactic' * context_tactic' -> context_tactic' -val CAPPEND': context_tactic' * context_tactic' -> context_tactic' -val CTRY: context_tactic -> context_tactic -val CREPEAT: context_tactic -> context_tactic -val CREPEAT1: context_tactic -> context_tactic -val CREPEAT_N: int -> context_tactic -> context_tactic -val CFILTER: (context_state -> bool) -> context_tactic -> context_tactic -val CCHANGED: context_tactic -> context_tactic -val CTHEN_ALL_NEW: context_tactic' * context_tactic' -> context_tactic' -val CREPEAT_IN_RANGE: int -> int -> context_tactic' -> context_tactic -val CREPEAT_ALL_NEW: context_tactic' -> context_tactic' -val CTHEN_ALL_NEW_FWD: context_tactic' * context_tactic' -> context_tactic' -val CREPEAT_ALL_NEW_FWD: context_tactic' -> context_tactic' -val CHEADGOAL: context_tactic' -> context_tactic -val CALLGOALS: context_tactic' -> context_tactic -val CSOMEGOAL: context_tactic' -> context_tactic -val CRANGE: context_tactic' list -> context_tactic' -val CFIRST: context_tactic list -> context_tactic -val CFIRST': context_tactic' list -> context_tactic' -val CTHEN_BEST_FIRST: context_tactic -> (context_state -> bool) -> - (context_state -> int) -> context_tactic -> context_tactic -val CBEST_FIRST: (context_state -> bool) -> (context_state -> int) -> - context_tactic -> context_tactic -val CTHEN_ASTAR: context_tactic -> (context_state -> bool) -> - (int -> context_state -> int) -> context_tactic -> context_tactic -val CASTAR: (context_state -> bool) -> (int -> context_state -> int) -> - context_tactic -> context_tactic - -end = struct - -type context_tactic' = int -> context_tactic - -fun CONTEXT_TACTIC' tac i (ctxt, st) = TACTIC_CONTEXT ctxt ((tac ctxt i) st) - -val all_ctac = Seq.make_results o Seq.single -val no_ctac = K Seq.empty -fun print_ctac f (ctxt, st) = CONTEXT_TACTIC (print_tac ctxt (f ctxt)) (ctxt, st) - -fun (ctac1 CTHEN ctac2) cst = Seq.maps_results ctac2 (ctac1 cst) - -fun (ctac1 CORELSE ctac2) cst = - (case Seq.pull (ctac1 cst) of - NONE => ctac2 cst - | some => Seq.make (fn () => some)) - -fun (ctac1 CAPPEND ctac2) cst = - Seq.append (ctac1 cst) (Seq.make (fn () => Seq.pull (ctac2 cst))) - -fun (ctac1 CTHEN' ctac2) x = ctac1 x CTHEN ctac2 x -fun (ctac1 CORELSE' ctac2) x = ctac1 x CORELSE ctac2 x -fun (ctac1 CAPPEND' ctac2) x = ctac1 x CAPPEND ctac2 x - -fun CTRY ctac = ctac CORELSE all_ctac - -fun CREPEAT ctac = - let - fun rep qs cst = - (case Seq.pull (Seq.filter_results (ctac cst)) of - NONE => SOME (cst, Seq.make (fn () => repq qs)) - | SOME (cst', q) => rep (q :: qs) cst') - and repq [] = NONE - | repq (q :: qs) = - (case Seq.pull q of - NONE => repq qs - | SOME (cst, q) => rep (q :: qs) cst); - in fn cst => Seq.make_results (Seq.make (fn () => rep [] cst)) end - -fun CREPEAT1 ctac = ctac CTHEN CREPEAT ctac - -fun CREPEAT_N 0 _ = no_ctac - | CREPEAT_N n ctac = ctac CTHEN CREPEAT_N (n - 1) ctac - -fun CFILTER pred ctac cst = - ctac cst - |> Seq.filter_results - |> Seq.filter pred - |> Seq.make_results - -(*Only accept next states where the subgoals have changed*) -fun CCHANGED ctac (cst as (_, st)) = - CFILTER (fn (_, st') => not (Thm.eq_thm (st, st'))) ctac cst - -local - fun op THEN (f, g) x = Seq.maps_results g (f x) - - fun INTERVAL f i j x = - if i > j then Seq.make_results (Seq.single x) - else op THEN (f j, INTERVAL f i (j - 1)) x - - (*By Peter Lammich: apply tactic to subgoals in interval in a forward manner, - skipping over emerging subgoals*) - fun INTERVAL_FWD ctac l u (cst as (_, st)) = cst |> - (if l > u then all_ctac - else (ctac l CTHEN (fn cst' as (_, st') => - let val ofs = Thm.nprems_of st' - Thm.nprems_of st in - if ofs < ~1 - then raise THM ( - "INTERVAL_FWD: tactic solved more than one goal", ~1, [st, st']) - else INTERVAL_FWD ctac (l + 1 + ofs) (u + ofs) cst' - end))) -in - -fun (ctac1 CTHEN_ALL_NEW ctac2) i (cst as (_, st)) = - cst |> (ctac1 i CTHEN (fn cst' as (_, st') => - INTERVAL ctac2 i (i + Thm.nprems_of st' - Thm.nprems_of st) cst')) - -(*By Peter Lammich: apply ctac2 to all subgoals emerging from ctac1, in forward - manner*) -fun (ctac1 CTHEN_ALL_NEW_FWD ctac2) i (cst as (_, st)) = - cst |> (ctac1 i CTHEN (fn cst' as (_, st') => - INTERVAL_FWD ctac2 i (i + Thm.nprems_of st' - Thm.nprems_of st) cst')) - -(*Repeatedly apply ctac to the i-th until the k-th-from-last subgoals - (i.e. leave the last k subgoals alone), until no more changes appear in the - goal state.*) -fun CREPEAT_IN_RANGE i k ctac = - let fun interval_ctac (cst as (_, st)) = - INTERVAL_FWD ctac i (Thm.nprems_of st - k) cst - in CREPEAT (CCHANGED interval_ctac) end - -end - -fun CREPEAT_ALL_NEW ctac = - ctac CTHEN_ALL_NEW (CTRY o (fn i => CREPEAT_ALL_NEW ctac i)) - -fun CREPEAT_ALL_NEW_FWD ctac = - ctac CTHEN_ALL_NEW_FWD (CTRY o (fn i => CREPEAT_ALL_NEW_FWD ctac i)) - -fun CHEADGOAL ctac = ctac 1 - -fun CALLGOALS ctac (cst as (_, st)) = - let - fun doall 0 = all_ctac - | doall n = ctac n CTHEN doall (n - 1); - in doall (Thm.nprems_of st) cst end - -fun CSOMEGOAL ctac (cst as (_, st)) = - let - fun find 0 = no_ctac - | find n = ctac n CORELSE find (n - 1); - in find (Thm.nprems_of st) cst end - -fun CRANGE [] _ = all_ctac - | CRANGE (ctac :: ctacs) i = CRANGE ctacs (i + 1) CTHEN ctac i - -fun CFIRST ctacs = fold_rev (curry op CORELSE) ctacs no_ctac - -(*FIRST' [tac1,...,tacn] i equals tac1 i ORELSE ... ORELSE tacn i*) -fun CFIRST' ctacs = fold_rev (curry op CORELSE') ctacs (K no_ctac) - - -(** Search tacticals **) - -(* Best-first search *) - -structure Thm_Heap = Heap ( - type elem = int * thm; - val ord = prod_ord int_ord (Term_Ord.term_ord o apply2 Thm.prop_of) -) - -structure Context_State_Heap = Heap ( - type elem = int * context_state; - val ord = prod_ord int_ord (Term_Ord.term_ord o apply2 (Thm.prop_of o #2)) -) - -fun some_of_list [] = NONE - | some_of_list (x :: l) = SOME (x, Seq.make (fn () => some_of_list l)) - -(*Check for and delete duplicate proof states*) -fun delete_all_min (cst as (_, st)) heap = - if Context_State_Heap.is_empty heap then heap - else if Thm.eq_thm (st, #2 (#2 (Context_State_Heap.min heap))) - then delete_all_min cst (Context_State_Heap.delete_min heap) - else heap - -(*Best-first search for a state that satisfies satp (incl initial state) - Function sizef estimates size of problem remaining (smaller means better). - tactic tac0 sets up the initial priority queue, while tac1 searches it. *) -fun CTHEN_BEST_FIRST ctac0 satp sizef ctac = - let - fun pairsize cst = (sizef cst, cst); - fun bfs (news, nst_heap) = - (case List.partition satp news of - ([], nonsats) => next (fold_rev Context_State_Heap.insert (map pairsize nonsats) nst_heap) - | (sats, _) => some_of_list sats) - and next nst_heap = - if Context_State_Heap.is_empty nst_heap then NONE - else - let - val (n, cst) = Context_State_Heap.min nst_heap; - in - bfs (Seq.list_of (Seq.filter_results (ctac cst)), delete_all_min cst (Context_State_Heap.delete_min nst_heap)) - end; - fun btac cst = bfs (Seq.list_of (Seq.filter_results (ctac0 cst)), Context_State_Heap.empty) - in fn cst => Seq.make_results (Seq.make (fn () => btac cst)) end - -(*Ordinary best-first search, with no initial tactic*) -val CBEST_FIRST = CTHEN_BEST_FIRST all_ctac - - -(* A*-like search *) - -(*Insertion into priority queue of states, marked with level*) -fun insert_with_level (lnth: int * int * context_state) [] = [lnth] - | insert_with_level (l, m, cst) ((l', n, cst') :: csts) = - if n < m then (l', n, cst') :: insert_with_level (l, m, cst) csts - else if n = m andalso Thm.eq_thm (#2 cst, #2 cst') then (l', n, cst') :: csts - else (l, m, cst) :: (l', n, cst') :: csts; - -fun CTHEN_ASTAR ctac0 satp costf ctac = - let - fun bfs (news, nst, level) = - let fun cost cst = (level, costf level cst, cst) in - (case List.partition satp news of - ([], nonsats) => next (fold_rev (insert_with_level o cost) nonsats nst) - | (sats, _) => some_of_list sats) - end - and next [] = NONE - | next ((level, n, cst) :: nst) = - bfs (Seq.list_of (Seq.filter_results (ctac cst)), nst, level + 1) - in fn cst => Seq.make_results - (Seq.make (fn () => bfs (Seq.list_of (Seq.filter_results (ctac0 cst)), [], 0))) - end - -(*Ordinary ASTAR, with no initial tactic*) -val CASTAR = CTHEN_ASTAR all_ctac; - - -end - -open Context_Tactical diff --git a/spartan/core/elaborated_statement.ML b/spartan/core/elaborated_statement.ML deleted file mode 100644 index 33f88cf..0000000 --- a/spartan/core/elaborated_statement.ML +++ /dev/null @@ -1,470 +0,0 @@ -(* Title: elaborated_statement.ML - Author: Joshua Chen - -Term elaboration for goal statements and proof commands. - -Contains code from parts of - ~~/Pure/Isar/element.ML and - ~~/Pure/Isar/expression.ML -in both verbatim and modified forms. -*) - -structure Elaborated_Statement: sig - -val read_goal_statement: - (string, string, Facts.ref) Element.ctxt list -> - (string, string) Element.stmt -> - Proof.context -> - (Attrib.binding * (term * term list) list) list * Proof.context - -end = struct - - -(* Elaborated goal statements *) - -local - -fun mk_type T = (Logic.mk_type T, []) -fun mk_term t = (t, []) -fun mk_propp (p, pats) = (Type.constraint propT p, pats) - -fun dest_type (T, []) = Logic.dest_type T -fun dest_term (t, []) = t -fun dest_propp (p, pats) = (p, pats) - -fun extract_inst (_, (_, ts)) = map mk_term ts -fun restore_inst ((l, (p, _)), cs) = (l, (p, map dest_term cs)) - -fun extract_eqns es = map (mk_term o snd) es -fun restore_eqns (es, cs) = map2 (fn (b, _) => fn c => (b, dest_term c)) es cs - -fun extract_elem (Element.Fixes fixes) = map (#2 #> the_list #> map mk_type) fixes - | extract_elem (Element.Constrains csts) = map (#2 #> single #> map mk_type) csts - | extract_elem (Element.Assumes asms) = map (#2 #> map mk_propp) asms - | extract_elem (Element.Defines defs) = map (fn (_, (t, ps)) => [mk_propp (t, ps)]) defs - | extract_elem (Element.Notes _) = [] - | extract_elem (Element.Lazy_Notes _) = [] - -fun restore_elem (Element.Fixes fixes, css) = - (fixes ~~ css) |> map (fn ((x, _, mx), cs) => - (x, cs |> map dest_type |> try hd, mx)) |> Element.Fixes - | restore_elem (Element.Constrains csts, css) = - (csts ~~ css) |> map (fn ((x, _), cs) => - (x, cs |> map dest_type |> hd)) |> Element.Constrains - | restore_elem (Element.Assumes asms, css) = - (asms ~~ css) |> map (fn ((b, _), cs) => (b, map dest_propp cs)) |> Element.Assumes - | restore_elem (Element.Defines defs, css) = - (defs ~~ css) |> map (fn ((b, _), [c]) => (b, dest_propp c)) |> Element.Defines - | restore_elem (elem as Element.Notes _, _) = elem - | restore_elem (elem as Element.Lazy_Notes _, _) = elem - -fun prep (_, pats) (ctxt, t :: ts) = - let val ctxt' = Proof_Context.augment t ctxt - in - ((t, Syntax.check_props - (Proof_Context.set_mode Proof_Context.mode_pattern ctxt') pats), - (ctxt', ts)) - end - -fun check cs ctxt = - let - val (cs', (ctxt', _)) = fold_map prep cs - (ctxt, Syntax.check_terms - (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) (map fst cs)) - in (cs', ctxt') end - -fun inst_morphism params ((prfx, mandatory), insts') ctxt = - let - (*parameters*) - val parm_types = map #2 params; - val type_parms = fold Term.add_tfreesT parm_types []; - - (*type inference*) - val parm_types' = map (Type_Infer.paramify_vars o Logic.varifyT_global) parm_types; - val type_parms' = fold Term.add_tvarsT parm_types' []; - val checked = - (map (Logic.mk_type o TVar) type_parms' @ map2 Type.constraint parm_types' insts') - |> Syntax.check_terms (Config.put Type_Infer.object_logic false ctxt) - val (type_parms'', insts'') = chop (length type_parms') checked; - - (*context*) - val ctxt' = fold Proof_Context.augment checked ctxt; - val certT = Thm.trim_context_ctyp o Thm.ctyp_of ctxt'; - val cert = Thm.trim_context_cterm o Thm.cterm_of ctxt'; - - (*instantiation*) - val instT = - (type_parms ~~ map Logic.dest_type type_parms'') - |> map_filter (fn (v, T) => if TFree v = T then NONE else SOME (v, T)); - val cert_inst = - ((map #1 params ~~ map (Term_Subst.instantiateT_frees instT) parm_types) ~~ insts'') - |> map_filter (fn (v, t) => if Free v = t then NONE else SOME (v, cert t)); - in - (Element.instantiate_normalize_morphism (map (apsnd certT) instT, cert_inst) $> - Morphism.binding_morphism "Expression.inst" (Binding.prefix mandatory prfx), ctxt') - end; - -fun abs_def ctxt = - Thm.cterm_of ctxt #> Assumption.assume ctxt #> Local_Defs.abs_def_rule ctxt #> Thm.prop_of; - -fun declare_elem prep_var (Element.Fixes fixes) ctxt = - let val (vars, _) = fold_map prep_var fixes ctxt - in ctxt |> Proof_Context.add_fixes vars |> snd end - | declare_elem prep_var (Element.Constrains csts) ctxt = - ctxt |> fold_map (fn (x, T) => prep_var (Binding.name x, SOME T, NoSyn)) csts |> snd - | declare_elem _ (Element.Assumes _) ctxt = ctxt - | declare_elem _ (Element.Defines _) ctxt = ctxt - | declare_elem _ (Element.Notes _) ctxt = ctxt - | declare_elem _ (Element.Lazy_Notes _) ctxt = ctxt; - -fun parameters_of thy strict (expr, fixed) = - let - val ctxt = Proof_Context.init_global thy; - - fun reject_dups message xs = - (case duplicates (op =) xs of - [] => () - | dups => error (message ^ commas dups)); - - fun parm_eq ((p1, mx1), (p2, mx2)) = - p1 = p2 andalso - (Mixfix.equal (mx1, mx2) orelse - error ("Conflicting syntax for parameter " ^ quote p1 ^ " in expression" ^ - Position.here_list [Mixfix.pos_of mx1, Mixfix.pos_of mx2])); - - fun params_loc loc = Locale.params_of thy loc |> map (apfst #1); - fun params_inst (loc, (prfx, (Expression.Positional insts, eqns))) = - let - val ps = params_loc loc; - val d = length ps - length insts; - val insts' = - if d < 0 then - error ("More arguments than parameters in instantiation of locale " ^ - quote (Locale.markup_name ctxt loc)) - else insts @ replicate d NONE; - val ps' = (ps ~~ insts') |> - map_filter (fn (p, NONE) => SOME p | (_, SOME _) => NONE); - in (ps', (loc, (prfx, (Expression.Positional insts', eqns)))) end - | params_inst (loc, (prfx, (Expression.Named insts, eqns))) = - let - val _ = - reject_dups "Duplicate instantiation of the following parameter(s): " - (map fst insts); - val ps' = (insts, params_loc loc) |-> fold (fn (p, _) => fn ps => - if AList.defined (op =) ps p then AList.delete (op =) p ps - else error (quote p ^ " not a parameter of instantiated expression")); - in (ps', (loc, (prfx, (Expression.Named insts, eqns)))) end; - fun params_expr is = - let - val (is', ps') = fold_map (fn i => fn ps => - let - val (ps', i') = params_inst i; - val ps'' = distinct parm_eq (ps @ ps'); - in (i', ps'') end) is [] - in (ps', is') end; - - val (implicit, expr') = params_expr expr; - - val implicit' = map #1 implicit; - val fixed' = map (Variable.check_name o #1) fixed; - val _ = reject_dups "Duplicate fixed parameter(s): " fixed'; - val implicit'' = - if strict then [] - else - let - val _ = - reject_dups - "Parameter(s) declared simultaneously in expression and for clause: " - (implicit' @ fixed'); - in map (fn (x, mx) => (Binding.name x, NONE, mx)) implicit end; - in (expr', implicit'' @ fixed) end; - -fun parse_elem prep_typ prep_term ctxt = - Element.map_ctxt - {binding = I, - typ = prep_typ ctxt, - term = prep_term (Proof_Context.set_mode Proof_Context.mode_schematic ctxt), - pattern = prep_term (Proof_Context.set_mode Proof_Context.mode_pattern ctxt), - fact = I, - attrib = I}; - -fun prepare_stmt prep_prop prep_obtains ctxt stmt = - (case stmt of - Element.Shows raw_shows => - raw_shows |> (map o apsnd o map) (fn (t, ps) => - (prep_prop (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) t, - map (prep_prop (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)) ps)) - | Element.Obtains raw_obtains => - let - val ((_, thesis), thesis_ctxt) = Obtain.obtain_thesis ctxt; - val obtains = prep_obtains thesis_ctxt thesis raw_obtains; - in map (fn (b, t) => ((b, []), [(t, [])])) obtains end); - -fun finish_fixes (parms: (string * typ) list) = map (fn (binding, _, mx) => - let val x = Binding.name_of binding - in (binding, AList.lookup (op =) parms x, mx) end) - -fun finish_inst ctxt (loc, (prfx, inst)) = - let - val thy = Proof_Context.theory_of ctxt; - val (morph, _) = inst_morphism (map #1 (Locale.params_of thy loc)) (prfx, inst) ctxt; - in (loc, morph) end - -fun closeup _ _ false elem = elem - | closeup (outer_ctxt, ctxt) parms true elem = - let - (*FIXME consider closing in syntactic phase -- before type checking*) - fun close_frees t = - let - val rev_frees = - Term.fold_aterms (fn Free (x, T) => - if Variable.is_fixed outer_ctxt x orelse AList.defined (op =) parms x then I - else insert (op =) (x, T) | _ => I) t []; - in fold (Logic.all o Free) rev_frees t end; - - fun no_binds [] = [] - | no_binds _ = error "Illegal term bindings in context element"; - in - (case elem of - Element.Assumes asms => Element.Assumes (asms |> map (fn (a, propps) => - (a, map (fn (t, ps) => (close_frees t, no_binds ps)) propps))) - | Element.Defines defs => Element.Defines (defs |> map (fn ((name, atts), (t, ps)) => - let val ((c, _), t') = Local_Defs.cert_def ctxt (K []) (close_frees t) - in ((Thm.def_binding_optional (Binding.name c) name, atts), (t', no_binds ps)) end)) - | e => e) - end - -fun finish_elem _ parms _ (Element.Fixes fixes) = Element.Fixes (finish_fixes parms fixes) - | finish_elem _ _ _ (Element.Constrains _) = Element.Constrains [] - | finish_elem ctxts parms do_close (Element.Assumes asms) = closeup ctxts parms do_close (Element.Assumes asms) - | finish_elem ctxts parms do_close (Element.Defines defs) = closeup ctxts parms do_close (Element.Defines defs) - | finish_elem _ _ _ (elem as Element.Notes _) = elem - | finish_elem _ _ _ (elem as Element.Lazy_Notes _) = elem - -fun check_autofix insts eqnss elems concl ctxt = - let - val inst_cs = map extract_inst insts; - val eqns_cs = map extract_eqns eqnss; - val elem_css = map extract_elem elems; - val concl_cs = (map o map) mk_propp (map snd concl); - (*Type inference*) - val (inst_cs' :: eqns_cs' :: css', ctxt') = - (fold_burrow o fold_burrow) check (inst_cs :: eqns_cs :: elem_css @ [concl_cs]) ctxt; - val (elem_css', [concl_cs']) = chop (length elem_css) css'; - in - ((map restore_inst (insts ~~ inst_cs'), - map restore_eqns (eqnss ~~ eqns_cs'), - map restore_elem (elems ~~ elem_css'), - map fst concl ~~ concl_cs'), ctxt') - end - -fun prep_full_context_statement - parse_typ parse_prop - prep_obtains prep_var_elem prep_inst prep_eqns prep_attr prep_var_inst prep_expr - {strict, do_close, fixed_frees} raw_import init_body raw_elems raw_stmt - ctxt1 - = - let - val thy = Proof_Context.theory_of ctxt1 - val (raw_insts, fixed) = parameters_of thy strict (apfst (prep_expr thy) raw_import) - fun prep_insts_cumulative (loc, (prfx, (inst, eqns))) (i, insts, eqnss, ctxt) = - let - val params = map #1 (Locale.params_of thy loc) - val inst' = prep_inst ctxt (map #1 params) inst - val parm_types' = - params |> map (#2 #> Logic.varifyT_global #> - Term.map_type_tvar (fn ((x, _), S) => TVar ((x, i), S)) #> - Type_Infer.paramify_vars) - val inst'' = map2 Type.constraint parm_types' inst' - val insts' = insts @ [(loc, (prfx, inst''))] - val ((insts'', _, _, _), ctxt2) = check_autofix insts' [] [] [] ctxt - val inst''' = insts'' |> List.last |> snd |> snd - val (inst_morph, _) = inst_morphism params (prfx, inst''') ctxt - val ctxt' = Locale.activate_declarations (loc, inst_morph) ctxt2 - handle ERROR msg => if null eqns then error msg else - (Locale.tracing ctxt1 - (msg ^ "\nFalling back to reading rewrites clause before activation."); - ctxt2) - val attrss = map (apsnd (map (prep_attr ctxt)) o fst) eqns - val eqns' = (prep_eqns ctxt' o map snd) eqns - val eqnss' = [attrss ~~ eqns'] - val ((_, [eqns''], _, _), _) = check_autofix insts'' eqnss' [] [] ctxt' - val rewrite_morph = eqns' - |> map (abs_def ctxt') - |> Variable.export_terms ctxt' ctxt - |> Element.eq_term_morphism (Proof_Context.theory_of ctxt) - |> the_default Morphism.identity - val ctxt'' = Locale.activate_declarations (loc, inst_morph $> rewrite_morph) ctxt - val eqnss' = eqnss @ [attrss ~~ Variable.export_terms ctxt' ctxt eqns'] - in (i + 1, insts', eqnss', ctxt'') end - - fun prep_elem raw_elem ctxt = - let - val ctxt' = ctxt - |> Context_Position.set_visible false - |> declare_elem prep_var_elem raw_elem - |> Context_Position.restore_visible ctxt - val elems' = parse_elem parse_typ parse_prop ctxt' raw_elem - in (elems', ctxt') end - - val fors = fold_map prep_var_inst fixed ctxt1 |> fst - val ctxt2 = ctxt1 |> Proof_Context.add_fixes fors |> snd - val (_, insts', eqnss', ctxt3) = fold prep_insts_cumulative raw_insts (0, [], [], ctxt2) - - fun prep_stmt elems ctxt = - check_autofix insts' [] elems (prepare_stmt parse_prop prep_obtains ctxt raw_stmt) ctxt - - val _ = - if fixed_frees then () - else - (case fold (fold (Variable.add_frees ctxt3) o snd o snd) insts' [] of - [] => () - | frees => error ("Illegal free variables in expression: " ^ - commas_quote (map (Syntax.string_of_term ctxt3 o Free) (rev frees)))) - - val ((insts, _, elems', concl), ctxt4) = ctxt3 - |> init_body - |> fold_map prep_elem raw_elems - |-> prep_stmt - - (*parameters from expression and elements*) - val xs = maps (fn Element.Fixes fixes => map (Variable.check_name o #1) fixes | _ => []) - (Element.Fixes fors :: elems') - val (parms, ctxt5) = fold_map Proof_Context.inferred_param xs ctxt4 - val fors' = finish_fixes parms fors - val fixed = map (fn (b, SOME T, mx) => ((Binding.name_of b, T), mx)) fors' - val deps = map (finish_inst ctxt5) insts - val elems'' = map (finish_elem (ctxt1, ctxt5) parms do_close) elems' - in ((fixed, deps, eqnss', elems'', concl), (parms, ctxt5)) end - -fun prep_inst prep_term ctxt parms (Expression.Positional insts) = - (insts ~~ parms) |> map - (fn (NONE, p) => Free (p, dummyT) - | (SOME t, _) => prep_term ctxt t) - | prep_inst prep_term ctxt parms (Expression.Named insts) = - parms |> map (fn p => - (case AList.lookup (op =) insts p of - SOME t => prep_term ctxt t | - NONE => Free (p, dummyT))) -fun parse_inst x = prep_inst Syntax.parse_term x -fun check_expr thy instances = map (apfst (Locale.check thy)) instances - -val read_full_context_statement = prep_full_context_statement - Syntax.parse_typ Syntax.parse_prop Obtain.parse_obtains - Proof_Context.read_var parse_inst Syntax.read_props Attrib.check_src - Proof_Context.read_var check_expr - -fun filter_assumes ((x as Element.Assumes _) :: xs) = x :: filter_assumes xs - | filter_assumes (_ :: xs) = filter_assumes xs - | filter_assumes [] = [] - -fun prep_statement prep activate raw_elems raw_stmt ctxt = - let - val ((_, _, _, elems, concl), _) = - prep {strict = true, do_close = false, fixed_frees = true} - ([], []) I raw_elems raw_stmt ctxt - - val (elems', ctxt') = ctxt - |> Proof_Context.set_stmt true - |> fold_map activate elems - |> apsnd (Proof_Context.restore_stmt ctxt) - - val assumes = filter_assumes elems' - val assms = flat (flat (map - (fn (Element.Assumes asms) => - map (fn (_, facts) => map (Thm.cterm_of ctxt' o #1) facts) asms) - assumes)) - val concl' = Elab.elaborate ctxt' assms concl handle error => concl - in (concl', ctxt') end - -fun activate_i elem ctxt = - let - val elem' = - (case (Element.map_ctxt_attrib o map) Token.init_assignable elem of - Element.Defines defs => - Element.Defines (defs |> map (fn ((a, atts), (t, ps)) => - ((Thm.def_binding_optional - (Binding.name (#1 (#1 (Local_Defs.cert_def ctxt (K []) t)))) a, atts), - (t, ps)))) - | Element.Assumes assms => Element.Assumes (Elab.elaborate ctxt [] assms) - | e => e); - val ctxt' = Context.proof_map (Element.init elem') ctxt; - in ((Element.map_ctxt_attrib o map) Token.closure elem', ctxt') end - -fun activate raw_elem ctxt = - let val elem = raw_elem |> Element.map_ctxt - {binding = I, - typ = I, - term = I, - pattern = I, - fact = Proof_Context.get_fact ctxt, - attrib = Attrib.check_src ctxt} - in activate_i elem ctxt end - -in - -val read_goal_statement = prep_statement read_full_context_statement activate - -end - - -(* Proof assumption command *) - -local - -val structured_statement = - Parse_Spec.statement -- Parse_Spec.if_statement' -- Parse.for_fixes - >> (fn ((shows, assumes), fixes) => (fixes, assumes, shows)) - -fun these_factss more_facts (named_factss, state) = - (named_factss, state |> Proof.set_facts (maps snd named_factss @ more_facts)) - -fun gen_assume prep_statement prep_att export raw_fixes raw_prems raw_concls state = - let - val ctxt = Proof.context_of state; - - val bindings = map (apsnd (map (prep_att ctxt)) o fst) raw_concls; - val {fixes = params, assumes = prems_propss, shows = concl_propss, result_binds, text, ...} = - #1 (prep_statement raw_fixes raw_prems (map snd raw_concls) ctxt); - val propss = (map o map) (Logic.close_prop params (flat prems_propss)) concl_propss; - in - state - |> Proof.assert_forward - |> Proof.map_context_result (fn ctxt => - ctxt - |> Proof_Context.augment text - |> fold Variable.maybe_bind_term result_binds - |> fold_burrow (Assumption.add_assms export o map (Thm.cterm_of ctxt)) propss - |-> (fn premss => fn ctxt => - (premss, Context_Facts.register_facts (flat premss) ctxt)) - |-> (fn premss => - Proof_Context.note_thmss "" (bindings ~~ (map o map) (fn th => ([th], [])) premss))) - |> these_factss [] |> #2 - end - -val assume = - gen_assume Proof_Context.cert_statement (K I) Assumption.assume_export - -in - -val _ = Outer_Syntax.command \<^command_keyword>\assuming\ "elaborated assumption" - (structured_statement >> (fn (a, b, c) => Toplevel.proof (fn state => - let - val ctxt = Proof.context_of state - - fun read_option_typ NONE = NONE - | read_option_typ (SOME s) = SOME (Syntax.read_typ ctxt s) - fun read_terms (s, ss) = - let val f = Syntax.read_term ctxt in (f s, map f ss) end - - val a' = map (fn (b, s, m) => (b, read_option_typ s, m)) a - val b' = map (map read_terms) b - val c' = c |> map (fn ((b, atts), ss) => - ((b, map (Attrib.attribute_cmd ctxt) atts), map read_terms ss)) - val c'' = Elab.elaborate ctxt [] c' - in assume a' b' c'' state end))) - -end - - -end \ No newline at end of file diff --git a/spartan/core/elaboration.ML b/spartan/core/elaboration.ML deleted file mode 100644 index 9e5e0bd..0000000 --- a/spartan/core/elaboration.ML +++ /dev/null @@ -1,91 +0,0 @@ -(* Title: elaboration.ML - Author: Joshua Chen - -Basic term elaboration. -*) - -structure Elab: sig - -val elab: Proof.context -> cterm list -> term -> Envir.env -val elab_stmt: Proof.context -> cterm list -> term -> Envir.env * term -val elaborate: Proof.context -> cterm list -> ('a * (term * term list) list) list -> ('a * (term * term list) list) list - -end = struct - -(*Elaborate `tm` by solving the inference problem `tm: {}`, knowing `assums`, - which are fully elaborated, in `ctxt`. Return a substitution.*) -fun elab ctxt assums tm = - if Lib.no_vars tm - then Envir.init - else - let - val inf = Goal.init (Thm.cterm_of ctxt (Lib.typing_of_term tm)) - val res = Types.check_infer (map Thm.assume assums) 1 (ctxt, inf) - val tm' = - Thm.prop_of (#2 (Seq.hd (Seq.filter_results res))) - |> Lib.dest_prop |> Lib.term_of_typing - handle TERM ("dest_typing", [t]) => - let val typ = Logic.unprotect (Logic.strip_assums_concl t) - |> Lib.term_of_typing - in - error ("Elaboration of " ^ Syntax.string_of_term ctxt typ ^ " failed") - end - in - Seq.hd (Unify.matchers (Context.Proof ctxt) [(tm, tm')]) - end - handle Option => error - ("Elaboration of " ^ Syntax.string_of_term ctxt tm ^ " failed") - -(*Recursively elaborate a statement \x ... y. \...\ \ P x ... y by elaborating - only the types of typing judgments (in particular, does not look at judgmental - equality statements). Could also elaborate the terms of typing judgments, but - for now we assume that these are always free variables in all the cases we're - interested in.*) -fun elab_stmt ctxt assums stmt = - let - val stmt = Lib.dest_prop stmt - fun subst_term env = Envir.subst_term (Envir.type_env env, Envir.term_env env) - in - if Lib.no_vars stmt orelse Lib.is_eq stmt then - (Envir.init, stmt) - else if Lib.is_typing stmt then - let - val typ = Lib.type_of_typing stmt - val subst = elab ctxt assums typ - in (subst, subst_term subst stmt) end - else - let - fun elab' assums (x :: xs) = - let - val (env, x') = elab_stmt ctxt assums x - val assums' = - if Lib.no_vars x' then Thm.cterm_of ctxt x' :: assums else assums - in env :: elab' assums' xs end - | elab' _ [] = [] - val (prems, concl) = Lib.decompose_goal ctxt stmt - val subst = fold (curry Envir.merge) (elab' assums prems) Envir.init - val prems' = map (Thm.cterm_of ctxt o subst_term subst) prems - val subst' = - if Lib.is_typing concl then - let val typ = Lib.type_of_typing concl - in Envir.merge (subst, elab ctxt (assums @ prems') typ) end - else subst - in (subst', subst_term subst' stmt) end - end - -(*Apply elaboration to the list format that assumptions and goal statements are - given in*) -fun elaborate ctxt known assms = - let - fun subst_term env = Envir.subst_term (Envir.type_env env, Envir.term_env env) - fun elab_fact (fact, xs) assums = - let val (subst, fact') = elab_stmt ctxt assums fact in - ((fact', map (subst_term subst) xs), Thm.cterm_of ctxt fact' :: assums) - end - fun elab (b, facts) assums = - let val (facts', assums') = fold_map elab_fact facts assums - in ((b, facts'), assums') end - in #1 (fold_map elab assms known) end - - -end diff --git a/spartan/core/elimination.ML b/spartan/core/elimination.ML deleted file mode 100644 index cf9d21e..0000000 --- a/spartan/core/elimination.ML +++ /dev/null @@ -1,48 +0,0 @@ -(* Title: elimination.ML - Author: Joshua Chen - -Type elimination setup. -*) - -structure Elim: sig - -val Rules: Proof.context -> (thm * indexname list) Termtab.table -val rules: Proof.context -> (thm * indexname list) list -val lookup_rule: Proof.context -> Termtab.key -> (thm * indexname list) option -val register_rule: term list -> thm -> Context.generic -> Context.generic - -end = struct - -(** Context data **) - -(* Elimination rule data *) - -(*Stores elimination rules together with a list of the indexnames of the - variables each rule eliminates. Keyed by head of the type being eliminated.*) -structure Rules = Generic_Data ( - type T = (thm * indexname list) Termtab.table - val empty = Termtab.empty - val extend = I - val merge = Termtab.merge (eq_fst Thm.eq_thm_prop) -) - -val Rules = Rules.get o Context.Proof -fun rules ctxt = map (op #2) (Termtab.dest (Rules ctxt)) -fun lookup_rule ctxt = Termtab.lookup (Rules ctxt) -fun register_rule tms rl = - let val hd = Term.head_of (Lib.type_of_typing (Thm.major_prem_of rl)) - in Rules.map (Termtab.update (hd, (rl, map (#1 o dest_Var) tms))) end - - -(* [elim] attribute *) -val _ = Theory.setup ( - Attrib.setup \<^binding>\elim\ - (Scan.repeat Args.term_pattern >> - (Thm.declaration_attribute o register_rule)) - "" - #> Global_Theory.add_thms_dynamic (\<^binding>\elim\, - fn context => map #1 (rules (Context.proof_of context))) -) - - -end diff --git a/spartan/core/eqsubst.ML b/spartan/core/eqsubst.ML deleted file mode 100644 index 5ae8c73..0000000 --- a/spartan/core/eqsubst.ML +++ /dev/null @@ -1,442 +0,0 @@ -(* Title: eqsubst.ML - Author: Lucas Dixon, University of Edinburgh - Modified: Joshua Chen, University of Innsbruck - -Perform a substitution using an equation. - -This code is slightly modified from the original at Tools/eqsubst..ML, -to incorporate auto-typechecking for type theory. -*) - -signature EQSUBST = -sig - type match = - ((indexname * (sort * typ)) list (* type instantiations *) - * (indexname * (typ * term)) list) (* term instantiations *) - * (string * typ) list (* fake named type abs env *) - * (string * typ) list (* type abs env *) - * term (* outer term *) - - type searchinfo = - Proof.context - * int (* maxidx *) - * Zipper.T (* focusterm to search under *) - - datatype 'a skipseq = SkipMore of int | SkipSeq of 'a Seq.seq Seq.seq - - val skip_first_asm_occs_search: ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> int -> 'b -> 'c skipseq - val skip_first_occs_search: int -> ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> 'b -> 'c Seq.seq - val skipto_skipseq: int -> 'a Seq.seq Seq.seq -> 'a skipseq - - (* tactics *) - val eqsubst_asm_tac: Proof.context -> int list -> thm list -> int -> tactic - val eqsubst_asm_tac': Proof.context -> - (searchinfo -> int -> term -> match skipseq) -> int -> thm -> int -> tactic - val eqsubst_tac: Proof.context -> - int list -> (* list of occurrences to rewrite, use [0] for any *) - thm list -> int -> tactic - val eqsubst_tac': Proof.context -> - (searchinfo -> term -> match Seq.seq) (* search function *) - -> thm (* equation theorem to rewrite with *) - -> int (* subgoal number in goal theorem *) - -> thm (* goal theorem *) - -> thm Seq.seq (* rewritten goal theorem *) - - (* search for substitutions *) - val valid_match_start: Zipper.T -> bool - val search_lr_all: Zipper.T -> Zipper.T Seq.seq - val search_lr_valid: (Zipper.T -> bool) -> Zipper.T -> Zipper.T Seq.seq - val searchf_lr_unify_all: searchinfo -> term -> match Seq.seq Seq.seq - val searchf_lr_unify_valid: searchinfo -> term -> match Seq.seq Seq.seq - val searchf_bt_unify_valid: searchinfo -> term -> match Seq.seq Seq.seq -end; - -structure EqSubst: EQSUBST = -struct - -(* changes object "=" to meta "==" which prepares a given rewrite rule *) -fun prep_meta_eq ctxt = - Simplifier.mksimps ctxt #> map Drule.zero_var_indexes; - -(* make free vars into schematic vars with index zero *) -fun unfix_frees frees = - fold (K (Thm.forall_elim_var 0)) frees o Drule.forall_intr_list frees; - - -type match = - ((indexname * (sort * typ)) list (* type instantiations *) - * (indexname * (typ * term)) list) (* term instantiations *) - * (string * typ) list (* fake named type abs env *) - * (string * typ) list (* type abs env *) - * term; (* outer term *) - -type searchinfo = - Proof.context - * int (* maxidx *) - * Zipper.T; (* focusterm to search under *) - - -(* skipping non-empty sub-sequences but when we reach the end - of the seq, remembering how much we have left to skip. *) -datatype 'a skipseq = - SkipMore of int | - SkipSeq of 'a Seq.seq Seq.seq; - -(* given a seqseq, skip the first m non-empty seq's, note deficit *) -fun skipto_skipseq m s = - let - fun skip_occs n sq = - (case Seq.pull sq of - NONE => SkipMore n - | SOME (h, t) => - (case Seq.pull h of - NONE => skip_occs n t - | SOME _ => if n <= 1 then SkipSeq (Seq.cons h t) else skip_occs (n - 1) t)) - in skip_occs m s end; - -(* note: outerterm is the taget with the match replaced by a bound - variable : ie: "P lhs" beocmes "%x. P x" - insts is the types of instantiations of vars in lhs - and typinsts is the type instantiations of types in the lhs - Note: Final rule is the rule lifted into the ontext of the - taget thm. *) -fun mk_foo_match mkuptermfunc Ts t = - let - val ty = Term.type_of t - val bigtype = rev (map snd Ts) ---> ty - fun mk_foo 0 t = t - | mk_foo i t = mk_foo (i - 1) (t $ (Bound (i - 1))) - val num_of_bnds = length Ts - (* foo_term = "fooabs y0 ... yn" where y's are local bounds *) - val foo_term = mk_foo num_of_bnds (Bound num_of_bnds) - in Abs ("fooabs", bigtype, mkuptermfunc foo_term) end; - -(* T is outer bound vars, n is number of locally bound vars *) -(* THINK: is order of Ts correct...? or reversed? *) -fun mk_fake_bound_name n = ":b_" ^ n; -fun fakefree_badbounds Ts t = - let val (FakeTs, Ts, newnames) = - fold_rev (fn (n, ty) => fn (FakeTs, Ts, usednames) => - let - val newname = singleton (Name.variant_list usednames) n - in - ((mk_fake_bound_name newname, ty) :: FakeTs, - (newname, ty) :: Ts, - newname :: usednames) - end) Ts ([], [], []) - in (FakeTs, Ts, Term.subst_bounds (map Free FakeTs, t)) end; - -(* before matching we need to fake the bound vars that are missing an - abstraction. In this function we additionally construct the - abstraction environment, and an outer context term (with the focus - abstracted out) for use in rewriting with RW_Inst.rw *) -fun prep_zipper_match z = - let - val t = Zipper.trm z - val c = Zipper.ctxt z - val Ts = Zipper.C.nty_ctxt c - val (FakeTs', Ts', t') = fakefree_badbounds Ts t - val absterm = mk_foo_match (Zipper.C.apply c) Ts' t' - in - (t', (FakeTs', Ts', absterm)) - end; - -(* Unification with exception handled *) -(* given context, max var index, pat, tgt; returns Seq of instantiations *) -fun clean_unify ctxt ix (a as (pat, tgt)) = - let - (* type info will be re-derived, maybe this can be cached - for efficiency? *) - val pat_ty = Term.type_of pat; - val tgt_ty = Term.type_of tgt; - (* FIXME is it OK to ignore the type instantiation info? - or should I be using it? *) - val typs_unify = - SOME (Sign.typ_unify (Proof_Context.theory_of ctxt) (pat_ty, tgt_ty) (Vartab.empty, ix)) - handle Type.TUNIFY => NONE; - in - (case typs_unify of - SOME (typinsttab, ix2) => - let - (* FIXME is it right to throw away the flexes? - or should I be using them somehow? *) - fun mk_insts env = - (Vartab.dest (Envir.type_env env), - Vartab.dest (Envir.term_env env)); - val initenv = - Envir.Envir {maxidx = ix2, tenv = Vartab.empty, tyenv = typinsttab}; - val useq = Unify.smash_unifiers (Context.Proof ctxt) [a] initenv - handle ListPair.UnequalLengths => Seq.empty - | Term.TERM _ => Seq.empty; - fun clean_unify' useq () = - (case (Seq.pull useq) of - NONE => NONE - | SOME (h, t) => SOME (mk_insts h, Seq.make (clean_unify' t))) - handle ListPair.UnequalLengths => NONE - | Term.TERM _ => NONE; - in - (Seq.make (clean_unify' useq)) - end - | NONE => Seq.empty) - end; - -(* Unification for zippers *) -(* Note: Ts is a modified version of the original names of the outer - bound variables. New names have been introduced to make sure they are - unique w.r.t all names in the term and each other. usednames' is - oldnames + new names. *) -fun clean_unify_z ctxt maxidx pat z = - let val (t, (FakeTs, Ts, absterm)) = prep_zipper_match z in - Seq.map (fn insts => (insts, FakeTs, Ts, absterm)) - (clean_unify ctxt maxidx (t, pat)) - end; - - -fun bot_left_leaf_of (l $ _) = bot_left_leaf_of l - | bot_left_leaf_of (Abs (_, _, t)) = bot_left_leaf_of t - | bot_left_leaf_of x = x; - -(* Avoid considering replacing terms which have a var at the head as - they always succeed trivially, and uninterestingly. *) -fun valid_match_start z = - (case bot_left_leaf_of (Zipper.trm z) of - Var _ => false - | _ => true); - -(* search from top, left to right, then down *) -val search_lr_all = ZipperSearch.all_bl_ur; - -(* search from top, left to right, then down *) -fun search_lr_valid validf = - let - fun sf_valid_td_lr z = - let val here = if validf z then [Zipper.Here z] else [] in - (case Zipper.trm z of - _ $ _ => - [Zipper.LookIn (Zipper.move_down_left z)] @ here @ - [Zipper.LookIn (Zipper.move_down_right z)] - | Abs _ => here @ [Zipper.LookIn (Zipper.move_down_abs z)] - | _ => here) - end; - in Zipper.lzy_search sf_valid_td_lr end; - -(* search from bottom to top, left to right *) -fun search_bt_valid validf = - let - fun sf_valid_td_lr z = - let val here = if validf z then [Zipper.Here z] else [] in - (case Zipper.trm z of - _ $ _ => - [Zipper.LookIn (Zipper.move_down_left z), - Zipper.LookIn (Zipper.move_down_right z)] @ here - | Abs _ => [Zipper.LookIn (Zipper.move_down_abs z)] @ here - | _ => here) - end; - in Zipper.lzy_search sf_valid_td_lr end; - -fun searchf_unify_gen f (ctxt, maxidx, z) lhs = - Seq.map (clean_unify_z ctxt maxidx lhs) (Zipper.limit_apply f z); - -(* search all unifications *) -val searchf_lr_unify_all = searchf_unify_gen search_lr_all; - -(* search only for 'valid' unifiers (non abs subterms and non vars) *) -val searchf_lr_unify_valid = searchf_unify_gen (search_lr_valid valid_match_start); - -val searchf_bt_unify_valid = searchf_unify_gen (search_bt_valid valid_match_start); - -(* apply a substitution in the conclusion of the theorem *) -(* cfvs are certified free var placeholders for goal params *) -(* conclthm is a theorem of for just the conclusion *) -(* m is instantiation/match information *) -(* rule is the equation for substitution *) -fun apply_subst_in_concl ctxt i st (cfvs, conclthm) rule m = - RW_Inst.rw ctxt m rule conclthm - |> unfix_frees cfvs - |> Conv.fconv_rule Drule.beta_eta_conversion - |> (fn r => resolve_tac ctxt [r] i st); - -(* substitute within the conclusion of goal i of gth, using a meta -equation rule. Note that we assume rule has var indicies zero'd *) -fun prep_concl_subst ctxt i gth = - let - val th = Thm.incr_indexes 1 gth; - val tgt_term = Thm.prop_of th; - - val (fixedbody, fvs) = IsaND.fix_alls_term ctxt i tgt_term; - val cfvs = rev (map (Thm.cterm_of ctxt) fvs); - - val conclterm = Logic.strip_imp_concl fixedbody; - val conclthm = Thm.trivial (Thm.cterm_of ctxt conclterm); - val maxidx = Thm.maxidx_of th; - val ft = - (Zipper.move_down_right (* ==> *) - o Zipper.move_down_left (* Trueprop *) - o Zipper.mktop - o Thm.prop_of) conclthm - in - ((cfvs, conclthm), (ctxt, maxidx, ft)) - end; - -(* substitute using an object or meta level equality *) -fun eqsubst_tac' ctxt searchf instepthm i st = - let - val (cvfsconclthm, searchinfo) = prep_concl_subst ctxt i st; - val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm); - fun rewrite_with_thm r = - let val (lhs,_) = Logic.dest_equals (Thm.concl_of r) in - searchf searchinfo lhs - |> Seq.maps (apply_subst_in_concl ctxt i st cvfsconclthm r) - end; - in stepthms |> Seq.maps rewrite_with_thm end; - - -(* General substitution of multiple occurrences using one of - the given theorems *) - -fun skip_first_occs_search occ srchf sinfo lhs = - (case skipto_skipseq occ (srchf sinfo lhs) of - SkipMore _ => Seq.empty - | SkipSeq ss => Seq.flat ss); - -(* The "occs" argument is a list of integers indicating which occurrence -w.r.t. the search order, to rewrite. Backtracking will also find later -occurrences, but all earlier ones are skipped. Thus you can use [0] to -just find all rewrites. *) - -fun eqsubst_tac ctxt occs thms i st = - let val nprems = Thm.nprems_of st in - if nprems < i then Seq.empty else - let - val thmseq = Seq.of_list thms; - fun apply_occ occ st = - thmseq |> Seq.maps (fn r => - eqsubst_tac' ctxt - (skip_first_occs_search occ searchf_lr_unify_valid) r - (i + (Thm.nprems_of st - nprems)) st); - val sorted_occs = Library.sort (rev_order o int_ord) occs; - in - Seq.maps distinct_subgoals_tac (Seq.EVERY (map apply_occ sorted_occs) st) - end - end; - - -(* apply a substitution inside assumption j, keeps asm in the same place *) -fun apply_subst_in_asm ctxt i st rule ((cfvs, j, _, pth),m) = - let - val st2 = Thm.rotate_rule (j - 1) i st; (* put premice first *) - val preelimrule = - RW_Inst.rw ctxt m rule pth - |> (Seq.hd o prune_params_tac ctxt) - |> Thm.permute_prems 0 ~1 (* put old asm first *) - |> unfix_frees cfvs (* unfix any global params *) - |> Conv.fconv_rule Drule.beta_eta_conversion; (* normal form *) - in - (* ~j because new asm starts at back, thus we subtract 1 *) - Seq.map (Thm.rotate_rule (~ j) (Thm.nprems_of rule + i)) - (dresolve_tac ctxt [preelimrule] i st2) - end; - - -(* prepare to substitute within the j'th premise of subgoal i of gth, -using a meta-level equation. Note that we assume rule has var indicies -zero'd. Note that we also assume that premt is the j'th premice of -subgoal i of gth. Note the repetition of work done for each -assumption, i.e. this can be made more efficient for search over -multiple assumptions. *) -fun prep_subst_in_asm ctxt i gth j = - let - val th = Thm.incr_indexes 1 gth; - val tgt_term = Thm.prop_of th; - - val (fixedbody, fvs) = IsaND.fix_alls_term ctxt i tgt_term; - val cfvs = rev (map (Thm.cterm_of ctxt) fvs); - - val asmt = nth (Logic.strip_imp_prems fixedbody) (j - 1); - val asm_nprems = length (Logic.strip_imp_prems asmt); - - val pth = Thm.trivial ((Thm.cterm_of ctxt) asmt); - val maxidx = Thm.maxidx_of th; - - val ft = - (Zipper.move_down_right (* trueprop *) - o Zipper.mktop - o Thm.prop_of) pth - in ((cfvs, j, asm_nprems, pth), (ctxt, maxidx, ft)) end; - -(* prepare subst in every possible assumption *) -fun prep_subst_in_asms ctxt i gth = - map (prep_subst_in_asm ctxt i gth) - ((fn l => Library.upto (1, length l)) - (Logic.prems_of_goal (Thm.prop_of gth) i)); - - -(* substitute in an assumption using an object or meta level equality *) -fun eqsubst_asm_tac' ctxt searchf skipocc instepthm i st = - let - val asmpreps = prep_subst_in_asms ctxt i st; - val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm); - fun rewrite_with_thm r = - let - val (lhs,_) = Logic.dest_equals (Thm.concl_of r); - fun occ_search occ [] = Seq.empty - | occ_search occ ((asminfo, searchinfo)::moreasms) = - (case searchf searchinfo occ lhs of - SkipMore i => occ_search i moreasms - | SkipSeq ss => - Seq.append (Seq.map (Library.pair asminfo) (Seq.flat ss)) - (occ_search 1 moreasms)) (* find later substs also *) - in - occ_search skipocc asmpreps |> Seq.maps (apply_subst_in_asm ctxt i st r) - end; - in stepthms |> Seq.maps rewrite_with_thm end; - - -fun skip_first_asm_occs_search searchf sinfo occ lhs = - skipto_skipseq occ (searchf sinfo lhs); - -fun eqsubst_asm_tac ctxt occs thms i st = - let val nprems = Thm.nprems_of st in - if nprems < i then Seq.empty - else - let - val thmseq = Seq.of_list thms; - fun apply_occ occ st = - thmseq |> Seq.maps (fn r => - eqsubst_asm_tac' ctxt - (skip_first_asm_occs_search searchf_lr_unify_valid) occ r - (i + (Thm.nprems_of st - nprems)) st); - val sorted_occs = Library.sort (rev_order o int_ord) occs; - in - Seq.maps distinct_subgoals_tac (Seq.EVERY (map apply_occ sorted_occs) st) - end - end; - -(* combination method that takes a flag (true indicates that subst - should be done to an assumption, false = apply to the conclusion of - the goal) as well as the theorems to use *) -val _ = - let - val parser = - Scan.lift (Args.mode "asm" - -- Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) - -- Attrib.thms - fun eqsubst_asm_ctac occs inthms = - CONTEXT_TACTIC' (fn ctxt => eqsubst_asm_tac ctxt occs inthms) - fun eqsubst_ctac occs inthms = - CONTEXT_TACTIC' (fn ctxt => eqsubst_tac ctxt occs inthms) - in - Theory.setup ( - Method.setup \<^binding>\sub\ - (parser >> (fn ((asm, occs), inthms) => fn ctxt => SIMPLE_METHOD' ( - (if asm then eqsubst_asm_tac else eqsubst_tac) ctxt occs inthms))) - "single-step substitution" (* #> - Method.setup \<^binding>\subst\ - (parser >> (fn ((asm, occs), inthms) => K (CONTEXT_METHOD ( - CHEADGOAL o SIDE_CONDS 0 - ((if asm then eqsubst_asm_ctac else eqsubst_ctac) occs inthms))))) - "single-step substitution with automatic discharge of side conditions" *) - ) - end - -end; diff --git a/spartan/core/equality.ML b/spartan/core/equality.ML deleted file mode 100644 index 023147b..0000000 --- a/spartan/core/equality.ML +++ /dev/null @@ -1,90 +0,0 @@ -(* Title: equality.ML - Author: Joshua Chen - -Equality reasoning with identity types. -*) - -structure Equality: -sig - -val dest_Id: term -> term * term * term - -val push_hyp_tac: term * term -> Proof.context -> int -> tactic -val induction_tac: term -> term -> term -> term -> Proof.context -> tactic -val equality_context_tac: Facts.ref -> Proof.context -> context_tactic - -end = struct - -fun dest_Id tm = case tm of - Const (\<^const_name>\Id\, _) $ A $ x $ y => (A, x, y) - | _ => error "dest_Id" - -(*Context assumptions that have already been pushed into the type family*) -structure Inserts = Proof_Data ( - type T = term Item_Net.T - val init = K (Item_Net.init Term.aconv_untyped single) -) - -fun push_hyp_tac (t, _) = - Subgoal.FOCUS_PARAMS (fn {context = ctxt, concl, ...} => - let - val (_, C) = Lib.dest_typing (Thm.term_of concl) - val B = Thm.cterm_of ctxt (Lib.lambda_var t C) - val a = Thm.cterm_of ctxt t - (*The resolvent is PiE[where ?B=B and ?a=a]*) - val resolvent = - Drule.infer_instantiate' ctxt [NONE, NONE, SOME B, SOME a] @{thm PiE} - in - HEADGOAL (resolve_tac ctxt [resolvent]) - THEN SOMEGOAL (known_tac ctxt) - end) - -fun induction_tac p A x y ctxt = - let - val [p, A, x, y] = map (Thm.cterm_of ctxt) [p, A, x, y] - in - HEADGOAL (resolve_tac ctxt - [Drule.infer_instantiate' ctxt [SOME p, SOME A, SOME x, SOME y] @{thm IdE}]) - end - -val side_conds_tac = TRY oo typechk_tac - -fun equality_context_tac fact ctxt = - let - val eq_th = Proof_Context.get_fact_single ctxt fact - val (p, (A, x, y)) = (Lib.dest_typing ##> dest_Id) (Thm.prop_of eq_th) - - val hyps = - Facts.props (Proof_Context.facts_of ctxt) - |> filter (fn (th, _) => Lib.is_typing (Thm.prop_of th)) - |> map (Lib.dest_typing o Thm.prop_of o fst) - |> filter_out (fn (t, _) => - Term.aconv (t, p) orelse Item_Net.member (Inserts.get ctxt) t) - |> map (fn (t, T) => ((t, T), Lib.subterm_count_distinct [p, x, y] T)) - |> filter (fn (_, i) => i > 0) - (*`t1: T1` comes before `t2: T2` if T1 contains t2 as subterm. - If they are incomparable, then order by decreasing - `subterm_count [p, x, y] T`*) - |> sort (fn (((t1, _), i), ((_, T2), j)) => - Lib.cond_order (Lib.subterm_order T2 t1) (int_ord (j, i))) - |> map #1 - - val record_inserts = - Inserts.map (fold (fn (t, _) => fn net => Item_Net.update t net) hyps) - - val tac = - fold (fn hyp => fn tac => tac THEN HEADGOAL (push_hyp_tac hyp ctxt)) - hyps all_tac - THEN ( - induction_tac p A x y ctxt - THEN RANGE (replicate 3 (typechk_tac ctxt) @ [side_conds_tac ctxt]) 1 - ) - THEN ( - REPEAT_DETERM_N (length hyps) (SOMEGOAL (resolve_tac ctxt @{thms PiI})) - THEN ALLGOALS (side_conds_tac ctxt) - ) - in - fn (ctxt, st) => Context_Tactic.TACTIC_CONTEXT (record_inserts ctxt) (tac st) - end - -end diff --git a/spartan/core/focus.ML b/spartan/core/focus.ML deleted file mode 100644 index b963cfe..0000000 --- a/spartan/core/focus.ML +++ /dev/null @@ -1,158 +0,0 @@ -(* Title: focus.ML - Author: Joshua Chen - -Focus on head subgoal, with optional variable renaming. - -Modified from code contained in ~~/Pure/Isar/subgoal.ML. -*) - -local - -fun reverse_prems imp = - let val (prems, concl) = (Drule.strip_imp_prems imp, Drule.strip_imp_concl imp) - in fold (curry mk_implies) prems concl end - -fun gen_focus ctxt i bindings raw_st = - let - val st = raw_st - |> Thm.solve_constraints - |> Thm.transfer' ctxt - |> Raw_Simplifier.norm_hhf_protect ctxt - - val ((schematic_types, [st']), ctxt1) = Variable.importT [st] ctxt - - val ((params, goal), ctxt2) = - Variable.focus_cterm bindings (Thm.cprem_of st' i) ctxt1 - - val (asms, concl) = - (Drule.strip_imp_prems goal, Drule.strip_imp_concl goal) - - fun intern_var_assms asm (asms, concl) = - if Lib.no_vars (Thm.term_of asm) - then (asm :: asms, concl) - else (asms, Drule.mk_implies (asm, concl)) - - val (asms', concl') = fold intern_var_assms asms ([], concl) - |> apfst rev |> apsnd reverse_prems - - val (inst, ctxt3) = Variable.import_inst true (map Thm.term_of (asms')) ctxt2 - val schematic_terms = map (apsnd (Thm.cterm_of ctxt3)) (#2 inst) - val schematics = (schematic_types, schematic_terms) - val asms' = map (Thm.instantiate_cterm schematics) asms' - val concl' = Thm.instantiate_cterm schematics concl' - val (prems, context) = Assumption.add_assumes asms' ctxt3 - in - ({context = context, params = params, prems = prems, - asms = asms', concl = concl', schematics = schematics}, Goal.init concl') - end - -fun param_bindings ctxt (param_suffix, raw_param_specs) st = - let - val _ = if Thm.no_prems st then error "No subgoals!" else () - val subgoal = #1 (Logic.dest_implies (Thm.prop_of st)) - val subgoal_params = - map (apfst (Name.internal o Name.clean)) (Term.strip_all_vars subgoal) - |> Term.variant_frees subgoal |> map #1 - - val n = length subgoal_params - val m = length raw_param_specs - val _ = - m <= n orelse - error ("Excessive subgoal parameter specification" ^ - Position.here_list (map snd (drop n raw_param_specs))) - - val param_specs = raw_param_specs - |> map - (fn (NONE, _) => NONE - | (SOME x, pos) => - let - val b = #1 (#1 (Proof_Context.cert_var (Binding.make (x, pos), NONE, NoSyn) ctxt)) - val _ = Variable.check_name b - in SOME b end) - |> param_suffix ? append (replicate (n - m) NONE) - - fun bindings (SOME x :: xs) (_ :: ys) = x :: bindings xs ys - | bindings (NONE :: xs) (y :: ys) = Binding.name y :: bindings xs ys - | bindings _ ys = map Binding.name ys - in bindings param_specs subgoal_params end - -fun gen_schematic_subgoal prep_atts raw_result_binding param_specs state = - let - val _ = Proof.assert_backward state - - val state1 = state - |> Proof.map_context (Proof_Context.set_mode Proof_Context.mode_schematic) - |> Proof.refine_insert [] - - val {context = ctxt, facts, goal = st} = Proof.raw_goal state1 - val result_binding = apsnd (map (prep_atts ctxt)) raw_result_binding - - val subgoal_focus = #1 - (gen_focus ctxt 1 (SOME (param_bindings ctxt param_specs st)) st) - - val prems = #prems subgoal_focus - - fun after_qed (ctxt'', [[result]]) = - Proof.end_block #> (fn state' => - let - val ctxt' = Proof.context_of state' - val results' = - Proof_Context.export ctxt'' ctxt' (Conjunction.elim_conjunctions result) - in - state' - |> Proof.refine_primitive (fn _ => fn _ => - Subgoal.retrofit ctxt'' ctxt' (#params subgoal_focus) (#asms subgoal_focus) 1 - (Goal.protect 0 result) st - |> Seq.hd) - |> Proof.map_context - (#2 o Proof_Context.note_thmss "" [(result_binding, [(results', [])])]) - end) - #> Proof.reset_facts - #> Proof.enter_backward - in - state1 - |> Proof.enter_forward - |> Proof.using_facts [] - |> Proof.begin_block - |> Proof.map_context (fn _ => - #context subgoal_focus - |> Proof_Context.note_thmss "" [((Binding.name "prems", []), [(prems, [])])] - |> snd - |> Context_Facts.register_facts prems) - |> Proof.internal_goal (K (K ())) (Proof_Context.get_mode ctxt) true "subgoal" - NONE after_qed [] [] [(Binding.empty_atts, [(Thm.term_of (#concl subgoal_focus), [])])] - |> #2 - |> Proof.using_facts (facts @ prems) - |> pair subgoal_focus - end - -val opt_fact_binding = - Scan.optional ((Parse.binding -- Parse.opt_attribs || Parse.attribs >> pair Binding.empty) --| Args.colon) - Binding.empty_atts - -val for_params = Scan.optional - (\<^keyword>\vars\ |-- - Parse.!!! ((Scan.option Parse.dots >> is_some) -- - (Scan.repeat1 (Parse.maybe_position Parse.name_position)))) - (false, []) - -val schematic_subgoal_cmd = gen_schematic_subgoal Attrib.attribute_cmd - -val parser = opt_fact_binding -- for_params >> (fn (fact, params) => - Toplevel.proofs (Seq.make_results o Seq.single o #2 o schematic_subgoal_cmd fact params)) - -in - -(** Outer syntax commands **) - -val _ = Outer_Syntax.command \<^command_keyword>\focus\ - "focus on first subgoal within backward refinement, without instantiating schematic vars" - parser - -val _ = Outer_Syntax.command \<^command_keyword>\\<^item>\ "focus bullet" parser -val _ = Outer_Syntax.command \<^command_keyword>\\<^enum>\ "focus bullet" parser -val _ = Outer_Syntax.command \<^command_keyword>\\\ "focus bullet" parser -val _ = Outer_Syntax.command \<^command_keyword>\\\ "focus bullet" parser -val _ = Outer_Syntax.command \<^command_keyword>\~\ "focus bullet" parser - -end diff --git a/spartan/core/goals.ML b/spartan/core/goals.ML deleted file mode 100644 index 7d52495..0000000 --- a/spartan/core/goals.ML +++ /dev/null @@ -1,213 +0,0 @@ -(* Title: goals.ML - Author: Joshua Chen - -Goal statements and proof term export. - -Modified from code contained in ~~/Pure/Isar/specification.ML. -*) - -local - -val long_keyword = - Parse_Spec.includes >> K "" || - Parse_Spec.long_statement_keyword - -val long_statement = - Scan.optional - (Parse_Spec.opt_thm_name ":" --| Scan.ahead long_keyword) - Binding.empty_atts - -- Scan.optional Parse_Spec.includes [] - -- Parse_Spec.long_statement >> - (fn ((binding, includes), (elems, concl)) => - (true, binding, includes, elems, concl)) - -val short_statement = - Parse_Spec.statement -- Parse_Spec.if_statement -- Parse.for_fixes >> - (fn ((shows, assumes), fixes) => - (false, Binding.empty_atts, [], - [Element.Fixes fixes, Element.Assumes assumes], Element.Shows shows) - ) - -fun prep_statement prep_att prep_stmt raw_elems raw_stmt ctxt = - let - val (stmt, elems_ctxt) = prep_stmt raw_elems raw_stmt ctxt - val prems = Assumption.local_prems_of elems_ctxt ctxt - val stmt_ctxt = - fold (fold (Proof_Context.augment o fst) o snd) stmt elems_ctxt - in case raw_stmt - of Element.Shows _ => - let val stmt' = Attrib.map_specs (map prep_att) stmt - in (([], prems, stmt', NONE), stmt_ctxt) end - | Element.Obtains raw_obtains => - let - val asms_ctxt = stmt_ctxt - |> fold (fn ((name, _), asm) => - snd o Proof_Context.add_assms Assumption.assume_export - [((name, [Context_Rules.intro_query NONE]), asm)]) stmt - val that = Assumption.local_prems_of asms_ctxt stmt_ctxt - val ([(_, that')], that_ctxt) = asms_ctxt - |> Proof_Context.set_stmt true - |> Proof_Context.note_thmss "" - [((Binding.name Auto_Bind.thatN, []), [(that, [])])] - ||> Proof_Context.restore_stmt asms_ctxt - val stmt' = - [(Binding.empty_atts, [(#2 (#1 (Obtain.obtain_thesis ctxt)), [])])] - in - ((Obtain.obtains_attribs raw_obtains, prems, stmt', SOME that'), - that_ctxt) - end - end - -fun define_proof_term name (local_name, [th]) lthy = - let - fun make_name_binding suffix local_name = - let val base_local_name = Long_Name.base_name local_name - in Binding.qualified_name - ((case base_local_name of "" => name | _ => base_local_name) ^ - (case suffix - of SOME "prf" => "_prf" - | SOME "def" => "_def" - | _ => "")) - end - - val (prems, concl) = - (Logic.strip_assums_hyp (Thm.prop_of th), - Logic.strip_assums_concl (Thm.prop_of th)) - in - if not (Lib.is_typing concl) then ([], lthy) - else let - val prems_vars = distinct Term.aconv (flat - (map (Lib.collect_subterms is_Var) prems)) - - val concl_vars = Lib.collect_subterms is_Var - (Lib.term_of_typing concl) - - val params = inter Term.aconv concl_vars prems_vars - - val prf_tm = fold_rev lambda params (Lib.term_of_typing concl) - - val ((_, (_, raw_def)), lthy') = Local_Theory.define - ((make_name_binding NONE local_name, Mixfix.NoSyn), - ((make_name_binding (SOME "prf") local_name, []), prf_tm)) lthy - - val def = fold - (fn th1 => fn th2 => Thm.combination th2 th1) - (map (Thm.reflexive o Thm.cterm_of lthy) params) - raw_def - - val ((_, def'), lthy'') = Local_Theory.note - ((make_name_binding (SOME "def") local_name, []), [def]) - lthy' - in - (def', lthy'') - end - end - | define_proof_term _ _ _ = error - ("Unimplemented: proof terms for multiple facts in one statement") - -fun gen_schematic_theorem - bundle_includes prep_att prep_stmt - gen_prf_tm long kind - before_qed after_qed - (name, raw_atts) raw_includes raw_elems raw_concl - do_print lthy - = - let - val _ = Local_Theory.assert lthy - val elems = raw_elems |> map (Element.map_ctxt_attrib (prep_att lthy)) - val ((more_atts, prems, stmt, facts), goal_ctxt) = lthy - |> bundle_includes raw_includes - |> prep_statement (prep_att lthy) prep_stmt elems raw_concl - val atts = more_atts @ map (prep_att lthy) raw_atts - val pos = Position.thread_data () - val prems_name = if long then Auto_Bind.assmsN else Auto_Bind.thatN - - fun gen_and_after_qed results goal_ctxt' = - let - val results' = burrow - (map (Goal.norm_result lthy) o Proof_Context.export goal_ctxt' lthy) - results - - val ((res, lthy'), substmts) = - if forall (Binding.is_empty_atts o fst) stmt - then ((map (pair "") results', lthy), false) - else - (Local_Theory.notes_kind kind - (map2 (fn (b, _) => fn ths => (b, [(ths, [])])) stmt results') - lthy, - true) - - val (res', lthy'') = - if gen_prf_tm - then - let - val (prf_tm_defs, new_lthy) = fold - (fn result => fn (defs, lthy) => - apfst (fn new_defs => defs @ new_defs) - (define_proof_term (Binding.name_of name) result lthy)) - res - ([], lthy') - val res_folded = - map (apsnd (map (Local_Defs.fold new_lthy prf_tm_defs))) res - in - Local_Theory.notes_kind kind - [((name, @{attributes [type]} @ atts), - [(maps #2 res_folded, [])])] - new_lthy - end - else - Local_Theory.notes_kind kind - [((name, atts), [(maps #2 res, [])])] - lthy' - - val _ = Proof_Display.print_results do_print pos lthy'' - ((kind, Binding.name_of name), map (fn (_, ths) => ("", ths)) res') - - val _ = - if substmts then map - (fn (name, ths) => Proof_Display.print_results do_print pos lthy'' - (("and", name), [("", ths)])) - res - else [] - in - after_qed results' lthy'' - end - in - goal_ctxt - |> not (null prems) ? - (Proof_Context.note_thmss "" [((Binding.name prems_name, []), [(prems, [])])] - #> snd #> Context_Facts.register_facts prems) - |> Proof.theorem before_qed gen_and_after_qed (map snd stmt) - |> (case facts of NONE => I | SOME ths => Proof.refine_insert ths) - end - -val schematic_theorem_cmd = - gen_schematic_theorem - Bundle.includes_cmd - Attrib.check_src - Elaborated_Statement.read_goal_statement - -fun theorem spec descr = - Outer_Syntax.local_theory_to_proof' spec ("state " ^ descr) - (Scan.option (Args.parens (Args.$$$ "def")) - -- (long_statement || short_statement) >> - (fn (opt_derive, (long, binding, includes, elems, concl)) => - schematic_theorem_cmd - (case opt_derive of SOME "def" => true | _ => false) - long descr NONE (K I) binding includes elems concl)) - -fun definition spec descr = - Outer_Syntax.local_theory_to_proof' spec "definition via proof" - ((long_statement || short_statement) >> - (fn (long, binding, includes, elems, concl) => schematic_theorem_cmd - true long descr NONE (K I) binding includes elems concl)) - -in - -val _ = theorem \<^command_keyword>\Theorem\ "Theorem" -val _ = theorem \<^command_keyword>\Lemma\ "Lemma" -val _ = theorem \<^command_keyword>\Corollary\ "Corollary" -val _ = theorem \<^command_keyword>\Proposition\ "Proposition" -val _ = definition \<^command_keyword>\Definition\ "Definition" - -end diff --git a/spartan/core/implicits.ML b/spartan/core/implicits.ML deleted file mode 100644 index 2b63f49..0000000 --- a/spartan/core/implicits.ML +++ /dev/null @@ -1,87 +0,0 @@ -(* Title: implicits.ML - Author: Joshua Chen - -Implicit arguments. -*) - -structure Implicits : -sig - -val implicit_defs: Proof.context -> (term * term) Symtab.table -val implicit_defs_attr: attribute -val make_holes: Proof.context -> term list -> term list - -end = struct - -structure Defs = Generic_Data ( - type T = (term * term) Symtab.table - val empty = Symtab.empty - val extend = I - val merge = Symtab.merge (Term.aconv o apply2 #1) -) - -val implicit_defs = Defs.get o Context.Proof - -val implicit_defs_attr = Thm.declaration_attribute (fn th => - let - val (t, def) = Lib.dest_eq (Thm.prop_of th) - val (head, args) = Term.strip_comb t - val def' = fold_rev lambda args def - in - Defs.map (Symtab.update (Term.term_name head, (head, def'))) - end) - -fun make_holes_single ctxt tm name_ctxt = - let - fun iarg_to_hole (Const (\<^const_name>\iarg\, T)) = - Const (\<^const_name>\hole\, T) - | iarg_to_hole t = t - - fun expand head args = - let fun betapplys (head', args') = - Term.betapplys (map_aterms iarg_to_hole head', args') - in - case head of - Abs (x, T, t) => - list_comb (Abs (x, T, Lib.traverse_term expand t), args) - | _ => - case Symtab.lookup (implicit_defs ctxt) (Term.term_name head) of - SOME (t, def) => betapplys - (Envir.expand_atom - (Term.fastype_of head) - (Term.fastype_of t, def), - args) - | NONE => list_comb (head, args) - end - - fun holes_to_vars t = - let - val count = Lib.subterm_count (Const (\<^const_name>\hole\, dummyT)) - - fun subst (Const (\<^const_name>\hole\, T)) (Var (idx, _)::_) Ts = - let - val bounds = map Bound (0 upto (length Ts - 1)) - val T' = foldr1 (op -->) (Ts @ [T]) - in - foldl1 (op $) (Var (idx, T')::bounds) - end - | subst (Abs (x, T, t)) vs Ts = Abs (x, T, subst t vs (T::Ts)) - | subst (t $ u) vs Ts = - let val n = count t - in subst t (take n vs) Ts $ subst u (drop n vs) Ts end - | subst t _ _ = t - - val names = Name.invent name_ctxt "*" (count t) - val vars = map (fn n => Var ((n, 0), dummyT)) names - in - (subst t vars [], fold Name.declare names name_ctxt) - end - in - holes_to_vars (Lib.traverse_term expand tm) - end - -fun make_holes ctxt tms = #1 - (fold_map (make_holes_single ctxt) tms (Variable.names_of ctxt)) - - -end diff --git a/spartan/core/lib.ML b/spartan/core/lib.ML deleted file mode 100644 index e43ad98..0000000 --- a/spartan/core/lib.ML +++ /dev/null @@ -1,193 +0,0 @@ -structure Lib : -sig - -(*Lists*) -val max: ('a * 'a -> bool) -> 'a list -> 'a -val maxint: int list -> int - -(*Terms*) -val no_vars: term -> bool -val is_rigid: term -> bool -val is_eq: term -> bool -val dest_prop: term -> term -val dest_eq: term -> term * term -val mk_Var: string -> int -> typ -> term -val lambda_var: term -> term -> term - -val is_typing: term -> bool -val mk_typing: term -> term -> term -val dest_typing: term -> term * term -val term_of_typing: term -> term -val type_of_typing: term -> term -val mk_Pi: term -> term -> term -> term - -val typing_of_term: term -> term - -(*Goals*) -val decompose_goal: Proof.context -> term -> term list * term -val rigid_typing_concl: term -> bool - -(*Theorems*) -val partition_judgments: thm list -> thm list * thm list * thm list - -(*Subterms*) -val has_subterm: term list -> term -> bool -val subterm_count: term -> term -> int -val subterm_count_distinct: term list -> term -> int -val traverse_term: (term -> term list -> term) -> term -> term -val collect_subterms: (term -> bool) -> term -> term list - -(*Orderings*) -val subterm_order: term -> term -> order -val cond_order: order -> order -> order - -end = struct - - -(** Lists **) - -fun max gt (x::xs) = fold (fn a => fn b => if gt (a, b) then a else b) xs x - | max _ [] = error "max of empty list" - -val maxint = max (op >) - - -(** Terms **) - -(* Meta *) - -val no_vars = not o exists_subterm is_Var - -val is_rigid = not o is_Var o head_of - -fun is_eq (Const (\<^const_name>\Pure.eq\, _) $ _ $ _) = true - | is_eq _ = false - -fun dest_prop (Const (\<^const_name>\Pure.prop\, _) $ P) = P - | dest_prop P = P - -fun dest_eq (Const (\<^const_name>\Pure.eq\, _) $ t $ def) = (t, def) - | dest_eq _ = error "dest_eq" - -fun mk_Var name idx T = Var ((name, idx), T) - -fun lambda_var x tm = - let - fun var_args (Var (idx, T)) = Var (idx, \<^typ>\o\ --> T) $ x - | var_args t = t - in - tm |> map_aterms var_args - |> lambda x - end - -(* Object *) - -fun is_typing (Const (\<^const_name>\has_type\, _) $ _ $ _) = true - | is_typing _ = false - -fun mk_typing t T = \<^const>\has_type\ $ t $ T - -fun dest_typing (Const (\<^const_name>\has_type\, _) $ t $ T) = (t, T) - | dest_typing t = raise TERM ("dest_typing", [t]) - -val term_of_typing = #1 o dest_typing -val type_of_typing = #2 o dest_typing - -fun mk_Pi v typ body = Const (\<^const_name>\Pi\, dummyT) $ typ $ lambda v body - -fun typing_of_term tm = \<^const>\has_type\ $ tm $ Var (("*?", 0), \<^typ>\o\) -(*The above is a bit hacky; basically we need to guarantee that the schematic - var is fresh. This works for now because no other code in the Isabelle system - or the current logic uses this identifier.*) - - -(** Goals **) - -(*Breaks a goal \x ... y. \P1; ... Pn\ \ Q into ([P1, ..., Pn], Q), fixing - \-quantified variables and keeping schematics.*) -fun decompose_goal ctxt goal = - let - val focus = - #1 (Subgoal.focus_prems ctxt 1 NONE (Thm.trivial (Thm.cterm_of ctxt goal))) - - val schematics = #2 (#schematics focus) - |> map (fn (v, ctm) => (Thm.term_of ctm, Var v)) - in - map Thm.prop_of (#prems focus) @ [Thm.term_of (#concl focus)] - |> map (subst_free schematics) - |> (fn xs => chop (length xs - 1) xs) |> apsnd the_single - end - handle List.Empty => error "Lib.decompose_goal" - -fun rigid_typing_concl goal = - let val concl = Logic.strip_assums_concl goal - in is_typing concl andalso is_rigid (term_of_typing concl) end - - -(** Theorems **) -fun partition_judgments ths = - let - fun part [] facts conds eqs = (facts, conds, eqs) - | part (th::ths) facts conds eqs = - if is_typing (Thm.prop_of th) then - part ths (th::facts) conds eqs - else if is_typing (Thm.concl_of th) then - part ths facts (th::conds) eqs - else part ths facts conds (th::eqs) - in part ths [] [] [] end - - -(** Subterms **) - -fun has_subterm tms = - Term.exists_subterm - (foldl1 (op orf) (map (fn t => fn s => Term.aconv_untyped (s, t)) tms)) - -fun subterm_count s t = - let - fun count (t1 $ t2) i = i + count t1 0 + count t2 0 - | count (Abs (_, _, t)) i = i + count t 0 - | count t i = if Term.aconv_untyped (s, t) then i + 1 else i - in - count t 0 - end - -(*Number of distinct subterms in `tms` that appear in `tm`*) -fun subterm_count_distinct tms tm = - length (filter I (map (fn t => has_subterm [t] tm) tms)) - -(* - "Folds" a function f over the term structure of t by traversing t from child - nodes upwards through parents. At each node n in the term syntax tree, f is - additionally passed a list of the results of f at all children of n. -*) -fun traverse_term f t = - let - fun map_aux (Abs (x, T, t)) = Abs (x, T, map_aux t) - | map_aux t = - let - val (head, args) = Term.strip_comb t - val args' = map map_aux args - in - f head args' - end - in - map_aux t - end - -fun collect_subterms f (t $ u) = collect_subterms f t @ collect_subterms f u - | collect_subterms f (Abs (_, _, t)) = collect_subterms f t - | collect_subterms f t = if f t then [t] else [] - - -(** Orderings **) - -fun subterm_order t1 t2 = - if has_subterm [t1] t2 then LESS - else if has_subterm [t2] t1 then GREATER - else EQUAL - -fun cond_order o1 o2 = case o1 of EQUAL => o2 | _ => o1 - - -end diff --git a/spartan/core/tactics.ML b/spartan/core/tactics.ML deleted file mode 100644 index 923a3a7..0000000 --- a/spartan/core/tactics.ML +++ /dev/null @@ -1,180 +0,0 @@ -(* Title: tactics.ML - Author: Joshua Chen - -General tactics for dependent type theory. -*) - -structure Tactics: -sig - -val solve_side_conds: int Config.T -val SIDE_CONDS: int -> context_tactic' -> thm list -> context_tactic' -val rule_ctac: thm list -> context_tactic' -val dest_ctac: int option -> thm list -> context_tactic' -val intro_ctac: context_tactic' -val elim_ctac: term list -> context_tactic' -val cases_ctac: term -> context_tactic' - -end = struct - - -(* Side conditions *) -val solve_side_conds = Attrib.setup_config_int \<^binding>\solve_side_conds\ (K 2) - -fun SIDE_CONDS j ctac facts i (cst as (ctxt, st)) = cst |> - (case Config.get ctxt solve_side_conds of - 1 => (ctac CTHEN_ALL_NEW (CTRY o Types.known_ctac facts)) i - | 2 => ctac i CTHEN CREPEAT_IN_RANGE (i + j) (Thm.nprems_of st - i) - (CTRY o CREPEAT_ALL_NEW_FWD (Types.check_infer facts)) - | _ => ctac i) - - -(* rule, dest, intro *) - -local - fun mk_rules _ ths [] = ths - | mk_rules n ths ths' = - let val ths'' = foldr1 (op @) - (map - (fn th => [rotate_prems n (th RS @{thm PiE})] handle THM _ => []) - ths') - in - mk_rules n (ths @ ths') ths'' - end -in - -(*Resolves with given rules*) -fun rule_ctac ths i (ctxt, st) = - TACTIC_CONTEXT ctxt (resolve_tac ctxt (mk_rules 0 [] ths) i st) - -(*Attempts destruct-resolution with the n-th premise of the given rules*) -fun dest_ctac opt_n ths i (ctxt, st) = - TACTIC_CONTEXT ctxt (dresolve_tac ctxt - (mk_rules (case opt_n of NONE => 0 | SOME 0 => 0 | SOME n => n-1) [] ths) - i st) - -end - -(*Applies an appropriate introduction rule*) -val intro_ctac = CONTEXT_TACTIC' (fn ctxt => SUBGOAL (fn (goal, i) => - let val concl = Logic.strip_assums_concl goal in - if Lib.is_typing concl andalso Lib.is_rigid (Lib.type_of_typing concl) - then resolve_tac ctxt (Named_Theorems.get ctxt \<^named_theorems>\intro\) i - else no_tac - end)) - - -(* Induction/elimination *) - -(*Pushes a known typing t:T into a \-type. - This tactic is well-behaved only when t is sufficiently well specified - (otherwise there might be multiple possible judgments t:T that unify, and - which is chosen is undefined).*) -fun internalize_fact_tac t = - Subgoal.FOCUS_PARAMS (fn {context = ctxt, concl = raw_concl, ...} => - let - val concl = Logic.strip_assums_concl (Thm.term_of raw_concl) - val C = Lib.type_of_typing concl - val B = Thm.cterm_of ctxt (Lib.lambda_var t C) - val a = Thm.cterm_of ctxt t - (*The resolvent is PiE[where ?B=B and ?a=a]*) - val resolvent = - Drule.infer_instantiate' ctxt [NONE, NONE, SOME B, SOME a] @{thm PiE} - in - HEADGOAL (resolve_tac ctxt [resolvent]) - (*Unify with the correct type T*) - THEN SOMEGOAL (NO_CONTEXT_TACTIC ctxt o Types.known_ctac []) - end) - -fun elim_core_tac tms types ctxt = - let - val rule_insts = map ((Elim.lookup_rule ctxt) o Term.head_of) types - val rules = flat (map - (fn rule_inst => case rule_inst of - NONE => [] - | SOME (rl, idxnames) => [Drule.infer_instantiate ctxt - (idxnames ~~ map (Thm.cterm_of ctxt) tms) rl]) - rule_insts) - in - resolve_tac ctxt rules - THEN' RANGE (replicate (length tms) (NO_CONTEXT_TACTIC ctxt o Types.check_infer [])) - end handle Option => K no_tac - -(*Premises that have already been pushed into the \-type*) -structure Inserts = Proof_Data ( - type T = term Item_Net.T - val init = K (Item_Net.init Term.aconv_untyped single) -) - -fun elim_ctac tms = - case tms of - [] => CONTEXT_TACTIC' (fn ctxt => eresolve_tac ctxt (map #1 (Elim.rules ctxt))) - | major :: _ => CONTEXT_SUBGOAL (fn (goal, _) => fn cst as (ctxt, st) => - let - val facts = map Thm.prop_of (Context_Facts.known ctxt) - val prems = Logic.strip_assums_hyp goal - val template = Lib.typing_of_term major - val types = filter (fn th => Term.could_unify (template, th)) (facts @ prems) - |> map Lib.type_of_typing - in case types of - [] => no_ctac cst - | _ => - let - val inserts = facts @ prems - |> filter Lib.is_typing - |> map Lib.dest_typing - |> filter_out (fn (t, _) => - Term.aconv (t, major) orelse Item_Net.member (Inserts.get ctxt) t) - |> map (fn (t, T) => ((t, T), Lib.subterm_count_distinct tms T)) - |> filter (fn (_, i) => i > 0) - (*`t1: T1` comes before `t2: T2` if T1 contains t2 as subterm. - If they are incomparable, then order by decreasing - `subterm_count [p, x, y] T`*) - |> sort (fn (((t1, _), i), ((_, T2), j)) => - Lib.cond_order (Lib.subterm_order T2 t1) (int_ord (j, i))) - |> map (#1 o #1) - val record_inserts = Inserts.map (fold Item_Net.update inserts) - val tac = - (*Push premises having a subterm in `tms` into a \*) - fold (fn t => fn tac => - tac THEN HEADGOAL (internalize_fact_tac t ctxt)) - inserts all_tac - (*Apply elimination rule*) - THEN HEADGOAL ( - elim_core_tac tms types ctxt - (*Pull pushed premises back out*) - THEN_ALL_NEW (SUBGOAL (fn (_, i) => - REPEAT_DETERM_N (length inserts) - (resolve_tac ctxt @{thms PiI[rotated]} i)))) - in - TACTIC_CONTEXT (record_inserts ctxt) (tac st) - end - end) - -fun cases_ctac tm = - let fun tac ctxt = - SUBGOAL (fn (goal, i) => - let - val facts = Proof_Context.facts_of ctxt - val prems = Logic.strip_assums_hyp goal - val template = Lib.typing_of_term tm - val types = - map (Thm.prop_of o #1) (Facts.could_unify facts template) - @ filter (fn prem => Term.could_unify (template, prem)) prems - |> map Lib.type_of_typing - val res = (case types of - [typ] => Drule.infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt tm)] - (the (Case.lookup_rule ctxt (Term.head_of typ))) - | [] => raise Option - | _ => raise error (Syntax.string_of_term ctxt tm ^ "not uniquely typed")) - handle Option => - error ("No case rule known for " ^ (Syntax.string_of_term ctxt tm)) - in - resolve_tac ctxt [res] i - end) - in CONTEXT_TACTIC' tac end - - -end - -open Tactics diff --git a/spartan/core/types.ML b/spartan/core/types.ML deleted file mode 100644 index 5e0d484..0000000 --- a/spartan/core/types.ML +++ /dev/null @@ -1,113 +0,0 @@ -(* Title: types.ML - Author: Joshua Chen - -Type-checking infrastructure. -*) - -structure Types: sig - -val debug_typechk: bool Config.T - -val known_ctac: thm list -> int -> context_tactic -val check_infer: thm list -> int -> context_tactic - -end = struct - -open Context_Facts - -(** [type] attribute **) - -val _ = Theory.setup ( - Attrib.setup \<^binding>\type\ - (Scan.succeed (Thm.declaration_attribute (fn th => - if Thm.no_prems th then register_known th else register_cond th))) - "" - #> Global_Theory.add_thms_dynamic (\<^binding>\type\, - fn context => let val ctxt = Context.proof_of context in - known ctxt @ cond ctxt end) -) - - -(** Context tactics for type-checking and elaboration **) - -val debug_typechk = Attrib.setup_config_bool \<^binding>\debug_typechk\ (K false) - -fun debug_tac ctxt s = - if Config.get ctxt debug_typechk then print_tac ctxt s else all_tac - -(*Solves goals without metavariables and type inference problems by assumption - from inline premises or resolution with facts*) -fun known_ctac facts = CONTEXT_SUBGOAL (fn (goal, i) => fn (ctxt, st) => - TACTIC_CONTEXT ctxt - let val concl = Logic.strip_assums_concl goal in - if Lib.no_vars concl orelse - (Lib.is_typing concl andalso Lib.no_vars (Lib.term_of_typing concl)) - then - let val ths = known ctxt @ facts - in st |> - (assume_tac ctxt ORELSE' resolve_tac ctxt ths THEN_ALL_NEW K no_tac) i - end - else Seq.empty - end) - -(*Simple bidirectional typing tactic with some backtracking search over input - facts.*) -fun check_infer_step facts i (ctxt, st) = - let - val refine_tac = SUBGOAL (fn (goal, i) => - if Lib.rigid_typing_concl goal - then - let - val net = Tactic.build_net ( - map (Simplifier.norm_hhf ctxt) facts - @(cond ctxt) - @(Named_Theorems.get ctxt \<^named_theorems>\form\) - @(Named_Theorems.get ctxt \<^named_theorems>\intr\) - @(map #1 (Elim.rules ctxt))) - in resolve_from_net_tac ctxt net i end - else no_tac) - - val sub_tac = SUBGOAL (fn (goal, i) => - let val concl = Logic.strip_assums_concl goal in - if Lib.is_typing concl - andalso Lib.is_rigid (Lib.term_of_typing concl) - andalso Lib.no_vars (Lib.type_of_typing concl) - then - (resolve_tac ctxt @{thms sub} - THEN' SUBGOAL (fn (_, i) => - NO_CONTEXT_TACTIC ctxt (check_infer facts i)) - THEN' compute_tac ctxt facts - THEN_ALL_NEW K no_tac) i - else no_tac end) - - val ctxt' = ctxt (*TODO: Use this to store already-derived typing judgments*) - in - TACTIC_CONTEXT ctxt' ( - (NO_CONTEXT_TACTIC ctxt' o known_ctac facts - ORELSE' refine_tac - ORELSE' sub_tac) i st) - end - -and check_infer facts i (cst as (_, st)) = - let - val ctac = check_infer_step facts - in - cst |> (ctac i CTHEN - CREPEAT_IN_RANGE i (Thm.nprems_of st - i) (CTRY o CREPEAT_ALL_NEW_FWD ctac)) - end - -and compute_tac ctxt facts = - let - val comps = Named_Theorems.get ctxt \<^named_theorems>\comp\ - val ss = simpset_of ctxt - val ss' = simpset_of (empty_simpset ctxt addsimps comps) - val ctxt' = put_simpset (merge_ss (ss, ss')) ctxt - in - SUBGOAL (fn (_, i) => - ((CHANGED o asm_simp_tac ctxt' ORELSE' EqSubst.eqsubst_tac ctxt [0] comps) - THEN_ALL_NEW SUBGOAL (fn (_, i) => - NO_CONTEXT_TACTIC ctxt (check_infer facts i))) i) - end - - -end diff --git a/spartan/lib/List.thy b/spartan/lib/List.thy deleted file mode 100644 index 4beb9b6..0000000 --- a/spartan/lib/List.thy +++ /dev/null @@ -1,191 +0,0 @@ -chapter \Lists\ - -theory List -imports Maybe - -begin - -(*TODO: Inductive type and recursive function definitions. The ad-hoc - axiomatization below should be subsumed once general inductive types are - properly implemented.*) - -axiomatization - List :: \o \ o\ and - nil :: \o \ o\ and - cons :: \o \ o \ o \ o\ and - ListInd :: \o \ (o \ o) \ o \ (o \ o \ o \ o) \ o \ o\ -where - ListF: "A: U i \ List A: U i" and - - List_nil: "A: U i \ nil A: List A" and - - List_cons: "\x: A; xs: List A\ \ cons A x xs: List A" and - - ListE: "\ - xs: List A; - c\<^sub>0: C (nil A); - \x xs rec. \x: A; xs: List A; rec: C xs\ \ f x xs rec: C (cons A x xs); - \xs. xs: List A \ C xs: U i - \ \ ListInd A (fn xs. C xs) c\<^sub>0 (fn x xs rec. f x xs rec) xs: C xs" and - - List_comp_nil: "\ - c\<^sub>0: C (nil A); - \x xs rec. \x: A; xs: List A; rec: C xs\ \ f x xs rec: C (cons A x xs); - \xs. xs: List A \ C xs: U i - \ \ ListInd A (fn xs. C xs) c\<^sub>0 (fn x xs rec. f x xs rec) (nil A) \ c\<^sub>0" and - - List_comp_cons: "\ - xs: List A; - c\<^sub>0: C (nil A); - \x xs rec. \x: A; xs: List A; rec: C xs\ \ f x xs rec: C (cons A x xs); - \xs. xs: List A \ C xs: U i - \ \ - ListInd A (fn xs. C xs) c\<^sub>0 (fn x xs rec. f x xs rec) (cons A x xs) \ - f x xs (ListInd A (fn xs. C xs) c\<^sub>0 (fn x xs rec. f x xs rec) xs)" - -lemmas - [form] = ListF and - [intr, intro] = List_nil List_cons and - [elim "?xs"] = ListE and - [comp] = List_comp_nil List_comp_cons - -abbreviation "ListRec A C \ ListInd A (fn _. C)" - -Lemma list_cases [cases]: - assumes - "xs: List A" and - nil_case: "c\<^sub>0: C (nil A)" and - cons_case: "\x xs. \x: A; xs: List A\ \ f x xs: C (cons A x xs)" and - "\xs. xs: List A \ C xs: U i" - shows "C xs" - by (elim xs) (fact nil_case, rule cons_case) - - -section \Notation\ - -definition nil_i ("[]") - where [implicit]: "[] \ nil {}" - -definition cons_i (infixr "#" 120) - where [implicit]: "x # xs \ cons {} x xs" - -translations - "[]" \ "CONST List.nil A" - "x # xs" \ "CONST List.cons A x xs" -syntax - "_list" :: \args \ o\ ("[_]") -translations - "[x, xs]" \ "x # [xs]" - "[x]" \ "x # []" - - -section \Standard functions\ - -subsection \Head and tail\ - -Definition head: - assumes "A: U i" "xs: List A" - shows "Maybe A" -proof (cases xs) - show "none: Maybe A" by intro - show "\x. x: A \ some x: Maybe A" by intro -qed - -Definition tail: - assumes "A: U i" "xs: List A" - shows "List A" -proof (cases xs) - show "[]: List A" by intro - show "\xs. xs: List A \ xs: List A" . -qed - -definition head_i ("head") where [implicit]: "head xs \ List.head {} xs" -definition tail_i ("tail") where [implicit]: "tail xs \ List.tail {} xs" - -translations - "head" \ "CONST List.head A" - "tail" \ "CONST List.tail A" - -Lemma head_type [type]: - assumes "A: U i" "xs: List A" - shows "head xs: Maybe A" - unfolding head_def by typechk - -Lemma head_of_cons [comp]: - assumes "A: U i" "x: A" "xs: List A" - shows "head (x # xs) \ some x" - unfolding head_def by compute - -Lemma tail_type [type]: - assumes "A: U i" "xs: List A" - shows "tail xs: List A" - unfolding tail_def by typechk - -Lemma tail_of_cons [comp]: - assumes "A: U i" "x: A" "xs: List A" - shows "tail (x # xs) \ xs" - unfolding tail_def by compute - -subsection \Append\ - -Definition app: - assumes "A: U i" "xs: List A" "ys: List A" - shows "List A" - apply (elim xs) - \<^item> by (fact \ys:_\) - \<^item> vars x _ rec - proof - show "x # rec: List A" by typechk qed - done - -definition app_i ("app") where [implicit]: "app xs ys \ List.app {} xs ys" - -translations "app" \ "CONST List.app A" - -subsection \Map\ - -Definition map: - assumes "A: U i" "B: U i" "f: A \ B" "xs: List A" - shows "List B" -proof (elim xs) - show "[]: List B" by intro - next fix x ys - assuming "x: A" "ys: List B" - show "f x # ys: List B" by typechk -qed - -definition map_i ("map") where [implicit]: "map \ List.map {} {}" - -translations "map" \ "CONST List.map A B" - -Lemma map_type [type]: - assumes "A: U i" "B: U i" "f: A \ B" "xs: List A" - shows "map f xs: List B" - unfolding map_def by typechk - - -subsection \Reverse\ - -Definition rev: - assumes "A: U i" "xs: List A" - shows "List A" - apply (elim xs) - \<^item> by (rule List_nil) - \<^item> vars x _ rec proof - show "app rec [x]: List A" by typechk qed - done - -definition rev_i ("rev") where [implicit]: "rev \ List.rev {}" - -translations "rev" \ "CONST List.rev A" - -Lemma rev_type [type]: - assumes "A: U i" "xs: List A" - shows "rev xs: List A" - unfolding rev_def by typechk - -Lemma rev_nil [comp]: - assumes "A: U i" - shows "rev (nil A) \ nil A" - unfolding rev_def by compute - - -end diff --git a/spartan/lib/Maybe.thy b/spartan/lib/Maybe.thy deleted file mode 100644 index 452acc2..0000000 --- a/spartan/lib/Maybe.thy +++ /dev/null @@ -1,75 +0,0 @@ -chapter \Maybe type\ - -theory Maybe -imports Prelude - -begin - -text \Defined as a sum.\ - -definition "Maybe A \ A \ \" -definition "none A \ inr A \ tt" -definition "some A a \ inl A \ a" - -lemma - MaybeF: "A: U i \ Maybe A: U i" and - Maybe_none: "A: U i \ none A: Maybe A" and - Maybe_some: "a: A \ some A a: Maybe A" - unfolding Maybe_def none_def some_def by typechk+ - -Definition MaybeInd: - assumes - "A: U i" - "\m. m: Maybe A \ C m: U i" - "c\<^sub>0: C (none A)" - "\a. a: A \ f a: C (some A a)" - "m: Maybe A" - shows "C m" - using assms[unfolded Maybe_def none_def some_def, type] - apply (elim m) - apply fact - apply (elim, fact) - done - -Lemma Maybe_comp_none: - assumes - "A: U i" - "c\<^sub>0: C (none A)" - "\a. a: A \ f a: C (some A a)" - "\m. m: Maybe A \ C m: U i" - shows "MaybeInd A C c\<^sub>0 f (none A) \ c\<^sub>0" - using assms - unfolding Maybe_def MaybeInd_def none_def some_def - by compute - -Lemma Maybe_comp_some: - assumes - "A: U i" - "a: A" - "c\<^sub>0: C (none A)" - "\a. a: A \ f a: C (some A a)" - "\m. m: Maybe A \ C m: U i" - shows "MaybeInd A C c\<^sub>0 f (some A a) \ f a" - using assms - unfolding Maybe_def MaybeInd_def none_def some_def - by compute - -lemmas - [form] = MaybeF and - [intr, intro] = Maybe_none Maybe_some and - [comp] = Maybe_comp_none Maybe_comp_some and - MaybeE [elim "?m"] = MaybeInd[rotated 4] -lemmas - Maybe_cases [cases] = MaybeE - -abbreviation "MaybeRec A C \ MaybeInd A (K C)" - -definition none_i ("none") where [implicit]: "none \ Maybe.none {}" -definition some_i ("some") where [implicit]: "some a \ Maybe.some {} a" - -translations - "none" \ "CONST Maybe.none A" - "some a" \ "CONST Maybe.some A a" - - -end diff --git a/spartan/lib/Prelude.thy b/spartan/lib/Prelude.thy deleted file mode 100644 index 56adbfc..0000000 --- a/spartan/lib/Prelude.thy +++ /dev/null @@ -1,151 +0,0 @@ -theory Prelude -imports Spartan - -begin - -section \Sum type\ - -axiomatization - Sum :: \o \ o \ o\ and - inl :: \o \ o \ o \ o\ and - inr :: \o \ o \ o \ o\ and - SumInd :: \o \ o \ (o \ o) \ (o \ o) \ (o \ o) \ o \ o\ - -notation Sum (infixl "\" 50) - -axiomatization where - SumF: "\A: U i; B: U i\ \ A \ B: U i" and - - Sum_inl: "\B: U i; a: A\ \ inl A B a: A \ B" and - - Sum_inr: "\A: U i; b: B\ \ inr A B b: A \ B" and - - SumE: "\ - s: A \ B; - \s. s: A \ B \ C s: U i; - \a. a: A \ c a: C (inl A B a); - \b. b: B \ d b: C (inr A B b) - \ \ SumInd A B (fn s. C s) (fn a. c a) (fn b. d b) s: C s" and - - Sum_comp_inl: "\ - a: A; - \s. s: A \ B \ C s: U i; - \a. a: A \ c a: C (inl A B a); - \b. b: B \ d b: C (inr A B b) - \ \ SumInd A B (fn s. C s) (fn a. c a) (fn b. d b) (inl A B a) \ c a" and - - Sum_comp_inr: "\ - b: B; - \s. s: A \ B \ C s: U i; - \a. a: A \ c a: C (inl A B a); - \b. b: B \ d b: C (inr A B b) - \ \ SumInd A B (fn s. C s) (fn a. c a) (fn b. d b) (inr A B b) \ d b" - -lemmas - [form] = SumF and - [intr] = Sum_inl Sum_inr and - [intro] = Sum_inl[rotated] Sum_inr[rotated] and - [elim ?s] = SumE and - [comp] = Sum_comp_inl Sum_comp_inr - -method left = rule Sum_inl -method right = rule Sum_inr - - -section \Empty and unit types\ - -axiomatization - Top :: \o\ and - tt :: \o\ and - TopInd :: \(o \ o) \ o \ o \ o\ -and - Bot :: \o\ and - BotInd :: \(o \ o) \ o \ o\ - -notation Top ("\") and Bot ("\") - -axiomatization where - TopF: "\: U i" and - - TopI: "tt: \" and - - TopE: "\a: \; \x. x: \ \ C x: U i; c: C tt\ \ TopInd (fn x. C x) c a: C a" and - - Top_comp: "\\x. x: \ \ C x: U i; c: C tt\ \ TopInd (fn x. C x) c tt \ c" -and - BotF: "\: U i" and - - BotE: "\x: \; \x. x: \ \ C x: U i\ \ BotInd (fn x. C x) x: C x" - -lemmas - [form] = TopF BotF and - [intr, intro] = TopI and - [elim ?a] = TopE and - [elim ?x] = BotE and - [comp] = Top_comp - - -section \Booleans\ - -definition "Bool \ \ \ \" -definition "true \ inl \ \ tt" -definition "false \ inr \ \ tt" - -Lemma - BoolF: "Bool: U i" and - Bool_true: "true: Bool" and - Bool_false: "false: Bool" - unfolding Bool_def true_def false_def by typechk+ - -\ \Definitions like these should be handled by a future function package\ -Definition ifelse [rotated 1]: - assumes *[unfolded Bool_def true_def false_def]: - "\x. x: Bool \ C x: U i" - "x: Bool" - "a: C true" - "b: C false" - shows "C x" - using assms[unfolded Bool_def true_def false_def, type] - by (elim x) (elim, fact)+ - -Lemma if_true: - assumes - "\x. x: Bool \ C x: U i" - "a: C true" - "b: C false" - shows "ifelse C true a b \ a" - unfolding ifelse_def true_def - using assms unfolding Bool_def true_def false_def - by compute - -Lemma if_false: - assumes - "\x. x: Bool \ C x: U i" - "a: C true" - "b: C false" - shows "ifelse C false a b \ b" - unfolding ifelse_def false_def - using assms unfolding Bool_def true_def false_def - by compute - -lemmas - [form] = BoolF and - [intr, intro] = Bool_true Bool_false and - [comp] = if_true if_false and - [elim ?x] = ifelse -lemmas - BoolE = ifelse - -subsection \Notation\ - -definition ifelse_i ("if _ then _ else _") - where [implicit]: "if x then a else b \ ifelse {} x a b" - -translations "if x then a else b" \ "CONST ifelse C x a b" - -subsection \Logical connectives\ - -definition not ("!_") where "!x \ ifelse (K Bool) x false true" - - -end -- cgit v1.2.3