diff options
Diffstat (limited to 'spartan/core/Spartan.thy')
| -rw-r--r-- | spartan/core/Spartan.thy | 147 |
1 files changed, 64 insertions, 83 deletions
diff --git a/spartan/core/Spartan.thy b/spartan/core/Spartan.thy index 1b9093b..a4ad300 100644 --- a/spartan/core/Spartan.thy +++ b/spartan/core/Spartan.thy @@ -79,16 +79,16 @@ axiomatization lt_trans: "i < j \<Longrightarrow> j < k \<Longrightarrow> i < k" axiomatization U :: \<open>lvl \<Rightarrow> o\<close> where - U_hierarchy: "i < j \<Longrightarrow> U i: U j" and - U_cumulative: "A: U i \<Longrightarrow> i < j \<Longrightarrow> A: U j" + Ui_in_Uj: "i < j \<Longrightarrow> U i: U j" and + in_Uj_if_in_Ui: "A: U i \<Longrightarrow> i < j \<Longrightarrow> A: U j" -lemma U_in_U: +lemma Ui_in_USi: "U i: U (S i)" - by (rule U_hierarchy, rule lt_S) + by (rule Ui_in_Uj, rule lt_S) -lemma lift_U: +lemma in_USi_if_in_Ui: "A: U i \<Longrightarrow> A: U (S i)" - by (erule U_cumulative, rule lt_S) + by (erule in_Uj_if_in_Ui, rule lt_S) subsection \<open>\<Prod>-type\<close> @@ -199,70 +199,61 @@ consts "rhs" :: \<open>'a\<close> ("..") ML_file \<open>congruence.ML\<close> -subsection \<open>Theorem attributes, type-checking and proof methods\<close> +subsection \<open>Proof methods and type-checking/inference\<close> -named_theorems intros and comps +named_theorems form and intro and intros and comp +\<comment> \<open>`intros` stores the introduction rule variants used by the + `intro` and `intros` methods.\<close> ML_file \<open>elimination.ML\<close> \<comment> \<open>elimination rules\<close> ML_file \<open>cases.ML\<close> \<comment> \<open>case reasoning rules\<close> lemmas - [intros] = anno PiF PiI SigF SigI and - [elims "?f"] = PiE and - [elims "?p"] = SigE and - [comps] = beta Sig_comp and + [form] = PiF SigF and + [intro] = PiI SigI and + [intros] = PiI[rotated] SigI and + [elim "?f"] = PiE and + [elim "?p"] = SigE and + [comp] = beta Sig_comp and [cong] = Pi_cong lam_cong Sig_cong ML_file \<open>typechecking.ML\<close> -ML_file \<open>tactics2.ML\<close> ML_file \<open>tactics.ML\<close> -method_setup assumptions = - \<open>Scan.succeed (fn ctxt => SIMPLE_METHOD ( - CHANGED (TRYALL (assumptions_tac ctxt))))\<close> +method_setup typechk = + \<open>Scan.succeed (K (CONTEXT_METHOD ( + CHEADGOAL o Types.check_infer)))\<close> method_setup known = - \<open>Scan.succeed (fn ctxt => SIMPLE_METHOD ( - CHANGED (TRYALL (known_tac ctxt))))\<close> + \<open>Scan.succeed (K (CONTEXT_METHOD ( + CHEADGOAL o Types.known_ctac)))\<close> + +method_setup rule = + \<open>Attrib.thms >> (fn ths => K (CONTEXT_METHOD ( + CHEADGOAL o SIDE_CONDS (rule_ctac ths))))\<close> + +method_setup dest = + \<open>Scan.lift (Scan.option (Args.parens Parse.int)) + -- Attrib.thms >> (fn (n_opt, ths) => K (CONTEXT_METHOD ( + CHEADGOAL o SIDE_CONDS (dest_ctac n_opt ths))))\<close> method_setup intro = - \<open>Scan.succeed (fn ctxt => SIMPLE_METHOD (HEADGOAL (intro_tac ctxt)))\<close> + \<open>Scan.succeed (K (CONTEXT_METHOD ( + CHEADGOAL o SIDE_CONDS (intro_ctac))))\<close> method_setup intros = - \<open>Scan.succeed (fn ctxt => SIMPLE_METHOD (HEADGOAL (intros_tac ctxt)))\<close> + \<open>Scan.succeed (K (CONTEXT_METHOD ( + CHEADGOAL o SIDE_CONDS (CREPEAT o intro_ctac))))\<close> method_setup elim = - \<open>Scan.repeat Args.term >> (fn tms => fn ctxt => - CONTEXT_METHOD (K (elim_context_tac tms ctxt 1)))\<close> + \<open>Scan.repeat Args.term >> (fn tms => K (CONTEXT_METHOD ( + CHEADGOAL o SIDE_CONDS (elim_ctac tms))))\<close> method elims = elim+ method_setup cases = - \<open>Args.term >> (fn tm => fn ctxt => SIMPLE_METHOD' (cases_tac tm ctxt))\<close> - -(*This could possibly use additional simplification hints via a simp: modifier*) -method_setup typechk' = - \<open>Scan.succeed (fn ctxt => SIMPLE_METHOD' ( - SIDE_CONDS (typechk_tac ctxt) ctxt)) - (* CHANGED (ALLGOALS (TRY o typechk_tac ctxt)))) *)\<close> - -method_setup rule' = - \<open>Attrib.thms >> (fn ths => fn ctxt => - SIMPLE_METHOD (HEADGOAL (SIDE_CONDS (rule_tac ths ctxt) ctxt)))\<close> - -method_setup dest = - \<open>Scan.lift (Scan.option (Args.parens Parse.int)) -- Attrib.thms - >> (fn (opt_n, ths) => fn ctxt => - SIMPLE_METHOD (HEADGOAL (SIDE_CONDS (dest_tac opt_n ths ctxt) ctxt)))\<close> - -(*NEW*) -method_setup typechk = - \<open>Scan.succeed (K (CONTEXT_METHOD ( - CHEADGOAL o Types.check_infer)))\<close> - -method_setup rule = - \<open>Attrib.thms >> (fn ths => K (CONTEXT_METHOD ( - CHEADGOAL o Tactics2.SIDE_CONDS (Tactics2.rule_tac ths))))\<close> + \<open>Args.term >> (fn tm => K (CONTEXT_METHOD ( + CHEADGOAL o SIDE_CONDS (cases_ctac tm))))\<close> subsection \<open>Reflexivity\<close> @@ -270,14 +261,13 @@ subsection \<open>Reflexivity\<close> named_theorems refl method refl = (rule refl) -subsection \<open>Trivial proofs modulo typechecking\<close> +subsection \<open>Trivial proofs (modulo automatic discharge of side conditions)\<close> method_setup this = - \<open>Scan.succeed (fn ctxt => METHOD ( - EVERY o map (HEADGOAL o - (fn ths => SIDE_CONDS (resolve_tac ctxt ths) ctxt) o - single) - ))\<close> + \<open>Scan.succeed (K (CONTEXT_METHOD (fn facts => + CHEADGOAL (SIDE_CONDS + (CONTEXT_TACTIC' (fn ctxt => resolve_tac ctxt facts)) + facts))))\<close> subsection \<open>Rewriting\<close> @@ -298,7 +288,7 @@ lemma eta_expand: lemma rewr_imp: assumes "PROP A \<equiv> PROP B" shows "(PROP A \<Longrightarrow> PROP C) \<equiv> (PROP B \<Longrightarrow> PROP C)" - apply (rule Pure.equal_intr_rule) + apply (Pure.rule Pure.equal_intr_rule) apply (drule equal_elim_rule2[OF assms]; assumption) apply (drule equal_elim_rule1[OF assms]; assumption) done @@ -316,9 +306,11 @@ ML_file \<open>~~/src/HOL/Library/cconv.ML\<close> ML_file \<open>rewrite.ML\<close> \<comment> \<open>\<open>reduce\<close> computes terms via judgmental equalities\<close> -setup \<open>map_theory_simpset (fn ctxt => ctxt addSolver (mk_solver "" typechk_tac))\<close> +setup \<open>map_theory_simpset (fn ctxt => + ctxt addSolver (mk_solver "" (fn ctxt' => + NO_CONTEXT_TACTIC ctxt' o Types.check_infer (Simplifier.prems_of ctxt'))))\<close> -method reduce uses add = (simp add: comps add | subst comps)+ +method reduce uses add = changed \<open>((simp add: comp add | sub comp); typechk?)+\<close> subsection \<open>Implicits\<close> @@ -387,11 +379,8 @@ lemma refine_codomain: lemma lift_universe_codomain: assumes "A: U i" "f: A \<rightarrow> U j" shows "f: A \<rightarrow> U (S j)" - (*FIXME: Temporary; should be fixed once all methods are rewritten to use - the new typechk*) - apply (Pure.rule refine_codomain, typechk, typechk) - apply (Pure.rule lift_U, typechk) - done + using in_USi_if_in_Ui[of "f {}"] + by (rule refine_codomain) subsection \<open>Function composition\<close> @@ -413,7 +402,7 @@ lemma funcompI [typechk]: "g \<circ>\<^bsub>A\<^esub> f: \<Prod>x: A. C (f x)" unfolding funcomp_def by typechk -lemma funcomp_assoc [comps]: +lemma funcomp_assoc [comp]: assumes "f: A \<rightarrow> B" "g: B \<rightarrow> C" @@ -423,7 +412,7 @@ lemma funcomp_assoc [comps]: "(h \<circ>\<^bsub>B\<^esub> g) \<circ>\<^bsub>A\<^esub> f \<equiv> h \<circ>\<^bsub>A\<^esub> g \<circ>\<^bsub>A\<^esub> f" unfolding funcomp_def by reduce -lemma funcomp_lambda_comp [comps]: +lemma funcomp_lambda_comp [comp]: assumes "A: U i" "\<And>x. x: A \<Longrightarrow> b x: B" @@ -432,7 +421,7 @@ lemma funcomp_lambda_comp [comps]: "(\<lambda>x: B. c x) \<circ>\<^bsub>A\<^esub> (\<lambda>x: A. b x) \<equiv> \<lambda>x: A. c (b x)" unfolding funcomp_def by reduce -lemma funcomp_apply_comp [comps]: +lemma funcomp_apply_comp [comp]: assumes "f: A \<rightarrow> B" "g: \<Prod>x: B. C x" "x: A" @@ -454,22 +443,22 @@ abbreviation id where "id A \<equiv> \<lambda>x: A. x" lemma id_type[typechk]: "A: U i \<Longrightarrow> id A: A \<rightarrow> A" and - id_comp [comps]: "x: A \<Longrightarrow> (id A) x \<equiv> x" \<comment> \<open>for the occasional manual rewrite\<close> - by reduce + id_comp [comp]: "x: A \<Longrightarrow> (id A) x \<equiv> x" \<comment> \<open>for the occasional manual rewrite\<close> + by reduce+ -lemma id_left [comps]: +lemma id_left [comp]: assumes "f: A \<rightarrow> B" "A: U i" "B: U i" shows "(id B) \<circ>\<^bsub>A\<^esub> f \<equiv> f" by (subst eta_exp[of f]) (reduce, rule eta) -lemma id_right [comps]: +lemma id_right [comp]: assumes "f: A \<rightarrow> B" "A: U i" "B: U i" shows "f \<circ>\<^bsub>A\<^esub> (id A) \<equiv> f" by (subst eta_exp[of f]) (reduce, rule eta) lemma id_U [typechk]: "id (U i): U i \<rightarrow> U i" - by typechk (fact U_in_U) + by typechk (rule Ui_in_USi) (*FIXME: Add annotation rule to typechecker*) section \<open>Pairs\<close> @@ -482,7 +471,7 @@ lemma fst_type [typechk]: shows "fst A B: (\<Sum>x: A. B x) \<rightarrow> A" unfolding fst_def by typechk -lemma fst_comp [comps]: +lemma fst_comp [comp]: assumes "a: A" "b: B a" @@ -496,10 +485,10 @@ lemma snd_type [typechk]: shows "snd A B: \<Prod>p: \<Sum>x: A. B x. B (fst A B p)" unfolding snd_def by typechk reduce -lemma snd_comp [comps]: +lemma snd_comp [comp]: assumes "a: A" "b: B a" "A: U i" "\<And>x. x: A \<Longrightarrow> B x: U i" shows "snd A B <a, b> \<equiv> b" - unfolding snd_def by reduce + unfolding snd_def by reduce+ subsection \<open>Notation\<close> @@ -509,7 +498,7 @@ definition fst_i ("fst") definition snd_i ("snd") where [implicit]: "snd \<equiv> Spartan.snd ? ?" -no_translations +translations "fst" \<leftharpoondown> "CONST Spartan.fst A B" "snd" \<leftharpoondown> "CONST Spartan.snd A B" @@ -520,22 +509,14 @@ Lemma fst [typechk]: "p: \<Sum>x: A. B x" "A: U i" "\<And>x. x: A \<Longrightarrow> B x: U i" shows "fst p: A" - \<comment> \<open>This can't be solved by a single application of `typechk`; it needs - multiple (two) passes. Something to do with constraint/subgoal reordering.\<close> - apply (Pure.rule elims) - apply (Pure.rule typechk) - apply known [1] - defer \<comment> \<open>The deferred subgoal is an inhabitation problem.\<close> - apply known [1] - by known - + by typechk Lemma snd [typechk]: assumes "p: \<Sum>x: A. B x" "A: U i" "\<And>x. x: A \<Longrightarrow> B x: U i" shows "snd p: B (fst p)" - by typechk+ + by typechk method fst for p::o = rule fst[of p] method snd for p::o = rule snd[of p] |