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# given an amount and coin denominations, | |
# compute the number of ways to make amount with coins of the given denoms | |
# 4, [1,2,3] -> 4 | |
def ways_to_make(amount, denoms): | |
# ways to make 4 | |
# ~ ways(4 - 3) + ways(4 - 2) + ways(4 - 1) ~ | |
# ways(1, largest=1) + ways(2, largest=1) | |
# dim 1: amount |
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dtrace: system integrity protection is on, some features will not be available | |
PID/THRD ELAPSD CPU SYSCALL(args) = return | |
27547/0x5b150b: 4 0 ulock_wake(0x1000002, 0x102F5A000, 0x0) = 0 0 | |
27547/0x5b13b5: 4 0 ulock_wake(0x1000002, 0x102F5A000, 0x0) = 0 0 | |
27547/0x5b1513: 4 1 ulock_wait(0x1010002, 0x102F5A000, 0x1102) = 1 0 | |
27547/0x5b1513: 2 0 ulock_wake(0x1000002, 0x102F5A000, 0x0) = 0 0 | |
27547/0x5b13b5: 2 0 ulock_wait(0x1010002, 0x102F5A000, 0x7C02) = 1 0 | |
27547/0x5b150b: 2 0 ulock_wake(0x1000002, 0x102F5A000, 0x0) = 0 0 | |
27547/0x5b150b: 1 0 ulock_wake(0x1000002, 0x102F5A000, 0x0) = 0 0 | |
27547/0x5b13b5: 2 0 ulock_wait(0x1010002, 0x102F5A000, 0x7C02) = 1 0 |
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{-# LANGUAGE DefaultSignatures #-} | |
{-# LANGUAGE DeriveAnyClass #-} | |
{-# LANGUAGE DeriveGeneric #-} | |
{-# LANGUAGE FlexibleContexts #-} | |
{-# LANGUAGE LambdaCase #-} | |
{-# LANGUAGE PolyKinds #-} | |
{-# LANGUAGE ScopedTypeVariables #-} | |
{-# LANGUAGE TypeApplications #-} | |
{-# LANGUAGE TypeOperators #-} |
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λ> :r | |
*** Chasing dependencies: | |
Chasing modules from: *Pact.Compile,*Pact.Eval,*Pact.Gas,*Pact.Native,*Pact.Native.Db,*Pact.Native.Internal,*Pact.Native.Time,*Pact.Native.Ops,*Pact.Native.Keysets,*Pact.Parse,*Pact.PersistPactDb,*Pact.Persist,*Pact.Persist.Pure,*Pact.Repl,*Pact.Repl.Lib,*Pact.Repl.Types,*Pact.Types.Exp,*Pact.Types.ExpParser,*Pact.Types.Gas,*Pact.Types.Hash,*Pact.Types.Info,*Pact.Types.Lang,*Pact.Types.Logger,*Pact.Types.Native,*Pact.Types.Parser,*Pact.Types.Persistence,*Pact.Types.Runtime,*Pact.Types.Orphans,*Pact.Types.Term,*Pact.Types.Type,*Pact.Types.Util,*Pact.Types.Version,*Crypto.Hash.Blake2Native,*Pact.Types.Typecheck,*Pact.Typechecker,*Pact.Analyze.Alloc,*Pact.Analyze.Eval,*Pact.Analyze.Eval.Invariant,*Pact.Analyze.Eval.Numerical,*Pact.Analyze.Eval.Prop,*Pact.Analyze.Eval.Core,*Pact.Analyze.Eval.Term,*Pact.Analyze.Check,*Pact.Analyze.Errors,*Pact.Analyze.Feature,*Pact.Analyze.LegacySFunArray,*Pact.Analyze.Model,*Pact.Analyze.Model.Dot,*Pact.Analyze.Model.Graph,*Pact.Analyze.Model.Tags, |
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(set-logic ALL) | |
; define List | |
(declare-datatypes (T) | |
((List | |
(nil) | |
(cons (head T) (tail List))))) | |
; define len | |
(declare-fun len ((List Int)) Int) |
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(declare-fun len ((List Int)) Int) | |
(declare-fun append ((List Int) (List Int)) (List Int)) | |
(declare-const xs (List Int)) | |
(declare-const ys (List Int)) | |
; len defining equations | |
(assert (forall ((xs (List Int))) | |
(= (len xs) | |
(ite (= xs nil) 0 (+ 1 (len (tail xs))))))) |
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(set-option :global-declarations true) | |
(set-option :smtlib2_compliant true) | |
(set-option :diagnostic-output-channel "stdout") | |
(set-option :produce-models true) | |
(set-logic ALL) | |
; --- literal constants --- | |
(define-fun two-digits () Real 100.0) | |
; --- skolem constants --- |
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** Calling: z3 -nw -in -smt2 | |
[GOOD] ; Automatically generated by SBV. Do not edit. | |
[GOOD] (set-option :print-success true) | |
[GOOD] (set-option :global-declarations true) | |
[GOOD] (set-option :smtlib2_compliant true) | |
[GOOD] (set-option :diagnostic-output-channel "stdout") | |
[GOOD] (set-option :produce-models true) | |
[GOOD] (set-logic ALL) | |
[GOOD] ; --- uninterpreted sorts --- | |
[GOOD] ; --- literal constants --- |
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(set-option :global-declarations true) | |
(set-option :smtlib2_compliant true) | |
(set-option :diagnostic-output-channel "stdout") | |
(set-option :produce-models true) | |
(set-logic ALL) | |
; --- literal constants --- | |
(define-fun two-digits () Real 100.0) | |
; --- skolem constants --- |
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(set-option :global-declarations true) | |
(set-option :smtlib2_compliant true) | |
(set-option :diagnostic-output-channel "stdout") | |
(set-option :produce-models true) | |
(set-logic ALL) | |
; --- uninterpreted sorts --- | |
; --- literal constants --- | |
(define-fun s3 () Real (/ 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.0 1.0)) | |
(define-fun s57 () Real 0.0) | |
(define-fun s82 () Real (/ 1.0 2.0)) |